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Sample records for adaptive linear quadratic

  1. Linear quadratic optimal control for symmetric systems

    NASA Technical Reports Server (NTRS)

    Lewis, J. H.; Martin, C. F.

    1983-01-01

    Special symmetries are present in many control problems. This paper addresses the problem of determining linear-quadratic optimal control problems whose solutions preserve the symmetry of the initial linear control system.

  2. Stochastic Linear Quadratic Optimal Control Problems

    SciTech Connect

    Chen, S.; Yong, J.

    2001-07-01

    This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.

  3. Communications circuit including a linear quadratic estimator

    DOEpatents

    Ferguson, Dennis D.

    2015-07-07

    A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.

  4. A Model for Quadratic Outliers in Linear Regression.

    ERIC Educational Resources Information Center

    Elashoff, Janet Dixon; Elashoff, Robert M.

    This paper introduces a model for describing outliers (observations which are extreme in some sense or violate the apparent pattern of other observations) in linear regression which can be viewed as a mixture of a quadratic and a linear regression. The maximum likelihood estimators of the parameters in the model are derived and their asymptotic…

  5. Design of Linear Quadratic Regulators and Kalman Filters

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.; Geyser, L.

    1986-01-01

    AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

  6. A decentralized linear quadratic control design method for flexible structures

    NASA Technical Reports Server (NTRS)

    Su, Tzu-Jeng; Craig, Roy R., Jr.

    1990-01-01

    A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass

  7. Reaction Wheel Control Design Using Linear Quadratic Controller

    NASA Astrophysics Data System (ADS)

    Nubli Muhamad, Nur; Susanto, Erwin; Syihabuddin, Budi; Prasetya Dwi Wibawa, Ig.

    2016-01-01

    This paper studies the design of active attitude control system of a nanosatellite in a single axis. In this paper, we consider dc motor based reaction wheel as an actuator, because of its pointing accuracy. However, the power consumption of the dc motor is often relatively large and needed to be optimized. Linear quadratic controller is supposed to have an ability to minimize power consumption and able to enhance the system performance. To show the advantage of this method, simulation result of attitude response, state trajectory, and trajectory of DC motor voltage are presented.

  8. Longitudinal force distribution using quadratically constrained linear programming

    NASA Astrophysics Data System (ADS)

    Klomp, M.

    2011-12-01

    In this paper, a new method is presented for the optimisation of force distribution for combined traction/braking and cornering. In order to provide a general, simple and flexible problem formulation, the optimisation is addressed as a quadratically constrained linear programming (QCLP) problem. Apart from fast numerical solutions, different driveline configurations can be included in the QCLP problem in a very straightforward fashion. The optimisation of the distribution of the individual wheel forces using the quasi-steady-state assumption is known to be useful for the study of the influence of particular driveline configurations on the combined lateral and longitudinal grip envelope of a particular vehicle-driveline configuration. The addition of the QCLP problem formulation makes another powerful tool available to the vehicle dynamics analyst to perform such studies.

  9. Repopulation Kinetics and the Linear-Quadratic Model

    NASA Astrophysics Data System (ADS)

    O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

    2009-08-01

    The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

  10. Integrability of Quadratic Non-autonomous Quantum Linear Systems

    NASA Astrophysics Data System (ADS)

    Lopez, Raquel

    The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is

  11. A linear quadratic regulator approach to the stabilization of uncertain linear systems

    NASA Technical Reports Server (NTRS)

    Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.

    1990-01-01

    This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.

  12. Linear versus quadratic portfolio optimization model with transaction cost

    NASA Astrophysics Data System (ADS)

    Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah

    2014-06-01

    Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.

  13. Linear quadratic optimal controller for cable-driven parallel robots

    NASA Astrophysics Data System (ADS)

    Abdolshah, Saeed; Shojaei Barjuei, Erfan

    2015-12-01

    In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work-space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional- integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.

  14. Singular linear quadratic control problem for systems with linear and constant delay

    NASA Astrophysics Data System (ADS)

    Sesekin, A. N.; Andreeva, I. Yu.; Shlyakhov, A. S.

    2016-12-01

    This article is devoted to the singular linear-quadratic optimization problem on the trajectories of the linear non-autonomous system of differential equations with linear and constant delay. It should be noted that such task does not solve the class of integrable controls, so to ensure the existence of a solution is needed to expand the class of controls to include the control impulse components. For the problem under consideration, we have built program control containing impulse components in the initial and final moments time. This is done under certain assumptions on the functional and the right side of the control system.

  15. Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Thompson, P. M.

    1979-01-01

    Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

  16. Singular linear-quadratic control problem for systems with linear delay

    SciTech Connect

    Sesekin, A. N.

    2013-12-18

    A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.

  17. Optimal Control Using Pontryagin's Maximum Principle in a Linear Quadratic Differential Game

    NASA Astrophysics Data System (ADS)

    Khakestari, Marzieh; Ibragimov, Gafurjan; Suleiman, Mohamed

    This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.

  18. Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

    NASA Technical Reports Server (NTRS)

    Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar

    1989-01-01

    A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

  19. Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft

    NASA Technical Reports Server (NTRS)

    Carpenter, J. Russell

    1999-01-01

    A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.

  20. Propagator for the time-dependent charged oscillator via linear and quadratic invariants

    SciTech Connect

    Abdalla, M. Sebawe Choi, Jeong-Ryeol

    2007-12-15

    The problem of a charged particle in the presence of a variable magnetic field is considered. Using the linear and the quadratic invariants as a tool, the wave functions in Fock state as well as in coherent state are obtained. The corresponding propagators which propagate the wave functions in the space-time are derived. Using numerical computations we have managed to draw some plots for the real, imaginary, and absolute values of the propagators. This has been used to analyze the properties of the propagators associated with both of the linear and the quadratic invariants. It has been shown that there is no essential difference between the behavior of the absolute value of the propagators in both of the linear and the quadratic invariants.

  1. Sequential design of linear quadratic state regulators via the optimal root-locus techniques

    NASA Technical Reports Server (NTRS)

    Shieh, L. S.; Dib, H. M.; Yates, R. E.

    1988-01-01

    The use of well-known root-locus techniques for sequentially finding the weighting matrices and the linear quadratic state regulators of multivariable control systems in the frequency domain is considered. This sequential design method permits the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system; it also allows some optimal closed-loop poles to be placed in a specific region of the complex plane. In addition, it provides a design procedure for determining the weighting matrices and linear quadratic state regulators for the optimal control of multivariable systems in the frequency domain.

  2. Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.

    PubMed

    McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T

    2013-12-13

    Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model.

  3. Design of linear quadratic regulators with eigenvalue placement in a specified region

    NASA Technical Reports Server (NTRS)

    Shieh, Leang-San; Zhen, Liu; Coleman, Norman P.

    1990-01-01

    Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.

  4. A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

    NASA Technical Reports Server (NTRS)

    Fleming, P.

    1985-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

  5. Time Domain Design of Robust Controllers for LQG (Linear Quadratic Gaussian); Application to Large Space Structures

    DTIC Science & Technology

    1985-12-01

    schemes involving more general perturbations. Also Desoer et al [8] have established conditions for stability robustness of linear multivarible...address regulators with quadratic performance indices. Desoer et al [8] have established conditions for stability robust- ness of linear...p. 45-46. 8. Desoer , C.A., Callier, F.M. and Chan, W.S., "Robustness of Stability Conditions for Linear Time Invariant Feedback Systems," IEEE

  6. Linear quadratic servo control of a reusable rocket engine

    NASA Technical Reports Server (NTRS)

    Musgrave, Jeffrey L.

    1991-01-01

    A design method for a servo compensator is developed in the frequency domain using singular values. The method is applied to a reusable rocket engine. An intelligent control system for reusable rocket engines was proposed which includes a diagnostic system, a control system, and an intelligent coordinator which determines engine control strategies based on the identified failure modes. The method provides a means of generating various linear multivariable controllers capable of meeting performance and robustness specifications and accommodating failure modes identified by the diagnostic system. Command following with set point control is necessary for engine operation. A Kalman filter reconstructs the state while loop transfer recovery recovers the required degree of robustness while maintaining satisfactory rejection of sensor noise from the command error. The approach is applied to the design of a controller for a rocket engine satisfying performance constraints in the frequency domain. Simulation results demonstrate the performance of the linear design on a nonlinear engine model over all power levels during mainstage operation.

  7. A tutorial on the LQG/LTR method. [Linear Quadratic Gaussian/Loop Transfer Recovery

    NASA Technical Reports Server (NTRS)

    Athans, M.

    1986-01-01

    In this paper the so-called Linear-Quadratic-Gaussian method with Loop-Transfer-Recovery is surveyed. The objective is to provide a pragmatic exposition, with special emphasis on the step-by-step characteristics for designing multivariable feedback control systems.

  8. Structural reliability and robustness properties of optimal linear-quadratic multivariable regulators

    NASA Technical Reports Server (NTRS)

    Wong, P.-K.; Stein, G.; Athans, M.

    1979-01-01

    Strong sufficient conditions are derived for the robustness of optimal linear-quadratic (LQ) regulators to large parameter perturbations. In particular, it is shown that under certain conditions LQ designs remain stable in the presence of actuator channel failures. The general results can be specialized to provide insight into the gain margin, gain reduction, and phase margin properties of optimal LQ regulators.

  9. Graphical Description of Johnson-Neyman Outcomes for Linear and Quadratic Regression Surfaces.

    ERIC Educational Resources Information Center

    Schafer, William D.; Wang, Yuh-Yin

    A modification of the usual graphical representation of heterogeneous regressions is described that can aid in interpreting significant regions for linear or quadratic surfaces. The standard Johnson-Neyman graph is a bivariate plot with the criterion variable on the ordinate and the predictor variable on the abscissa. Regression surfaces are drawn…

  10. A Method for Selecting between Linear and Quadratic Classification Models in Discriminant Analysis.

    ERIC Educational Resources Information Center

    Meshbane, Alice; Morris, John D.

    A method for comparing the cross validated classification accuracies of linear and quadratic classification rules is presented under varying data conditions for the k-group classification problem. With this method, separate-group as well as total-group proportions of correct classifications can be compared for the two rules. McNemar's test for…

  11. Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

    NASA Astrophysics Data System (ADS)

    Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

    2015-10-01

    In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

  12. Stability and monotone convergence of generalised policy iteration for discrete-time linear quadratic regulations

    NASA Astrophysics Data System (ADS)

    Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

    2016-03-01

    In this paper, we analyse the convergence and stability properties of generalised policy iteration (GPI) applied to discrete-time linear quadratic regulation problems. GPI is one kind of the generalised adaptive dynamic programming methods used for solving optimal control problems, and is composed of policy evaluation and policy improvement steps. To analyse the convergence and stability of GPI, the dynamic programming (DP) operator is defined. Then, GPI and its equivalent formulas are presented based on the notation of DP operator. The convergence of the approximate value function to the exact one in policy evaluation is proven based on the equivalent formulas. Furthermore, the positive semi-definiteness, stability, and the monotone convergence (PI-mode and VI-mode convergence) of GPI are presented under certain conditions on the initial value function. The online least square method is also presented for the implementation of GPI. Finally, some numerical simulations are carried out to verify the effectiveness of GPI as well as to further investigate the convergence and stability properties.

  13. A new one-layer neural network for linear and quadratic programming.

    PubMed

    Gao, Xingbao; Liao, Li-Zhi

    2010-06-01

    In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective function is convex on the set defined by equality constraints. Compared with existing one-layer neural networks for quadratic programming problems, the proposed neural network has the least neurons and requires weak stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.

  14. An application of nonlinear programming to the design of regulators of a linear-quadratic formulation

    NASA Technical Reports Server (NTRS)

    Fleming, P.

    1983-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

  15. Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis. Final Report

    NASA Technical Reports Server (NTRS)

    Thompson, P. M.

    1980-01-01

    Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.

  16. Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

    1989-01-01

    A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

  17. Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

  18. Robustness in linear quadratic feedback design with application to an aircraft control problem

    NASA Technical Reports Server (NTRS)

    Patel, R. V.; Sridhar, B.; Toda, M.

    1977-01-01

    Some new results concerning robustness and asymptotic properties of error bounds of a linear quadratic feedback design are applied to an aircraft control problem. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed based on Linear Quadratic (LQ) theory and the results developed in this paper. The variation of the error bounds to changes in the weighting matrices in the LQ design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable error bound for variations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.

  19. The quadratically damped oscillator: A case study of a non-linear equation of motion

    NASA Astrophysics Data System (ADS)

    Smith, B. R.

    2012-09-01

    The equation of motion for a quadratically damped oscillator, where the damping is proportional to the square of the velocity, is a non-linear second-order differential equation. Non-linear equations of motion such as this are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions. Like all second-order ordinary differential equations, it has a corresponding first-order partial differential equation, whose independent solutions constitute the constants of the motion. These constants readily provide an approximate solution correct to first order in the damping constant. They also reveal that the quadratically damped oscillator is never critically damped or overdamped, and that to first order in the damping constant the oscillation frequency is identical to the natural frequency. The technique described has close ties to standard tools such as integral curves in phase space and phase portraits.

  20. Linear-Quadratic Control of a MEMS Micromirror using Kalman Filtering

    DTIC Science & Technology

    2011-12-01

    fluid is also assumed; this is reasonable based on work [69] on gas flows over pure silicon, which demonstrated diffuse accommodation despite orders of...models for squeezed-film dampers with inertial and rarefied gas effects,” J. Micromech. Microeng., vol. 14, pp. 1109-1118, Jun. 2004. [60] P. S...given voltage input and capacitance measurements , which are then used by a Linear Quadratic controller to generate a closed- loop voltage control

  1. A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

    NASA Technical Reports Server (NTRS)

    Hanson, R. J.; Krogh, Fred T.

    1992-01-01

    A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

  2. A linear quadratic tracker for Control Moment Gyro based attitude control of the Space Station

    NASA Technical Reports Server (NTRS)

    Kaidy, J. T.

    1986-01-01

    The paper discusses a design for an attitude control system for the Space Station which produces fast response, with minimal overshoot and cross-coupling with the use of Control Moment Gyros (CMG). The rigid body equations of motion are linearized and discretized and a Linear Quadratic Regulator (LQR) design and analysis study is performed. The resulting design is then modified such that integral and differential terms are added to the state equations to enhance response characteristics. Methods for reduction of computation time through channelization are discussed as well as the reduction of initial torque requirements.

  3. Searchless tuning of linear controllers for the minimum of quadratic criterion

    NASA Astrophysics Data System (ADS)

    Pikina, G. A.; Burtseva, Yu. S.

    2014-03-01

    A searchless method of calculating the tunings of typical controllers is developed for linear plants with a time delay, the use of which makes it possible to minimize the quadratic criterion I 2 with respect to an internal disturbance. The basic idea of the method consists in obtaining the complex frequency response of a suboptimal linear controller, followed by approaching the characteristic of a typical controller to this frequency response in the essential frequency band using the least squares method. Recommendations on selecting the smoothing filter time constant and the suboptimal system's dynamic error are given for a system comprising a PID controller and a second-order plant with a time delay.

  4. A new gradient-based neural network for solving linear and quadratic programming problems.

    PubMed

    Leung, Y; Chen, K Z; Jiao, Y C; Gao, X B; Leung, K S

    2001-01-01

    A new gradient-based neural network is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory, and LaSalle invariance principle to solve linear and quadratic programming problems. In particular, a new function F(x, y) is introduced into the energy function E(x, y) such that the function E(x, y) is convex and differentiable, and the resulting network is more efficient. This network involves all the relevant necessary and sufficient optimality conditions for convex quadratic programming problems. For linear programming and quadratic programming (QP) problems with unique and infinite number of solutions, we have proven strictly that for any initial point, every trajectory of the neural network converges to an optimal solution of the QP and its dual problem. The proposed network is different from the existing networks which use the penalty method or Lagrange method, and the inequality constraints are properly handled. The simulation results show that the proposed neural network is feasible and efficient.

  5. Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory

    NASA Technical Reports Server (NTRS)

    Koppang, Paul; Leland, Robert

    1996-01-01

    Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.

  6. Quadratic Herman-Wallis factors in the fundamental bands of linear molecules

    NASA Astrophysics Data System (ADS)

    Watson, James K. G.

    1987-10-01

    General theoretical formulas are derived for the coefficients in the terms M˜12 and M˜13 of the effective molecular dipole moment operator, and applied to the parallel and perpendicular fundamentals of linear molecules. The Herman-Wallis factors for P- and R-branch lines are F PR = [1 + A 1m + A 2PRm 2] 2, m = δ J( J' + J″ + 1)/2 and for Q-branch lines F Q = [1 + A 2QJ ( J + 1)] 2 The quadratic coefficients A2PR and A2Q depend on up to cubic potential derivatives and quadratic dipole derivatives. Calculated A2PR and A2Q values for the fundamentals of CO 2 do not agree well with recent measurements of Johns, and possible reasons for the discrepancies are discussed.

  7. Mechanistic model of radiation-induced cancer after fractionated radiotherapy using the linear-quadratic formula

    SciTech Connect

    Schneider, Uwe

    2009-04-15

    A simple mechanistic model for predicting cancer induction after fractionated radiotherapy is developed. The model is based upon the linear-quadratic model. The inductions of carcinomas and sarcomas are modeled separately. The linear-quadratic model of cell kill is applied to normal tissues which are unintentionally irradiated during a cancer treatment with radiotherapy. Tumor induction is modeled such that each transformation process results in a tumor cell. The microscopic transformation parameter was chosen such that in the limit of low dose and acute exposure, the parameters of the linear-no-threshold model for tumor induction were approached. The differential equations describing carcinoma and sarcoma inductions can be solved analytically. Cancer induction in this model is a function of treatment dose, the cell kill parameters ({alpha},{beta}), the tumor induction variable ({mu}), and the repopulation parameter ({xi}). Carcinoma induction shows a bell shaped behavior as long as cell repopulation is small. Assuming large cell repopulation rates, a plateaulike function is approached. In contrast, sarcoma induction is negligible for low doses and increases with increasing dose up to a constant value. The proposed model describes carcinoma and sarcoma inductions after fractionated radiotherapy as an analytical function of four parameters. In the limit of low dose and for an instant irradiation it reproduces the results of the linear-no-threshold model. The obtained dose-response curves for cancer induction can be implemented with other models such as the organ-equivalent dose model to predict second cancers after radiotherapy.

  8. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

    NASA Astrophysics Data System (ADS)

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2002-02-01

    For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied.

  9. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

    SciTech Connect

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2002-02-28

    For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied.

  10. Comparing linear and quadratic models of the human auditory system using EEG.

    PubMed

    Power, Alan J; Reilly, Richard B; Lalor, Edmund C

    2011-01-01

    Recent studies have highlighted the importance of system identification as an approach for assessing sensory processing in humans using electroencephalography (EEG). These studies typically use linear impulse response estimates of visual and, more recently, auditory function. These methods, which are known as the VESPA and AESPA (Visual/Auditory Evoked Spread Spectrum Analysis) respectively, have been found to be useful for studying sensory processing in both healthy populations and clinical groups and for studying the effects of cognition on sensory processing. While a nonlinear extension of the VESPA has been previously described, no such extension has yet been examined for the AESPA. This paper investigates such an extension and quantifies the relative contribution of linear and quadratic processes to the EEG in response to novel auditory stimuli. While the ability to accurately predict novel EEG is poor, it is highly significant, with a slightly, but again significantly, greater ability to predict using a quadratic model (r=0.0418) over a linear model (r=0.0361).

  11. Quadratic Blind Linear Unmixing: A Graphical User Interface for Tissue Characterization

    PubMed Central

    Gutierrez-Navarro, O.; Campos-Delgado, D.U.; Arce-Santana, E. R.; Jo, Javier A.

    2016-01-01

    Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. PMID:26589467

  12. Quadratic blind linear unmixing: A graphical user interface for tissue characterization.

    PubMed

    Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A

    2016-02-01

    Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition.

  13. Sequential design of linear quadratic state regulators with prescribed eigenvalues and specified relative stability

    NASA Technical Reports Server (NTRS)

    Ganesan, Sekar; Shieh, Leang S.; Mehio, Mohamad M.

    1991-01-01

    This paper considers the problem of optimal regulator design of linear multivariable systems with prescribed pole locations and/or poles corresponding to specified relative stability. A sequential method based on the frequency-domain optimality condition is proposed for achieving the desired pole assignment and determination of the corresponding quadratic performance index. This design method enables the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

  14. Simultaneous structural and control optimization via linear quadratic regulator eigenstructure assignment

    NASA Technical Reports Server (NTRS)

    Becus, G. A.; Lui, C. Y.; Venkayya, V. B.; Tischler, V. A.

    1987-01-01

    A method for simultaneous structural and control design of large flexible space structures (LFSS) to reduce vibration generated by disturbances is presented. Desired natural frequencies and damping ratios for the closed loop system are achieved by using a combination of linear quadratic regulator (LQR) synthesis and numerical optimization techniques. The state and control weighing matrices (Q and R) are expressed in terms of structural parameters such as mass and stiffness. The design parameters are selected by numerical optimization so as to minimize the weight of the structure and to achieve the desired closed-loop eigenvalues. An illustrative example of the design of a two bar truss is presented.

  15. ORACLS: A system for linear-quadratic-Gaussian control law design

    NASA Technical Reports Server (NTRS)

    Armstrong, E. S.

    1978-01-01

    A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

  16. Modelling Ocean Dissipation in Icy Satellites: A Comparison of Linear and Quadratic Friction

    NASA Astrophysics Data System (ADS)

    Hay, H.; Matsuyama, I.

    2015-12-01

    Although subsurface oceans are confirmed in Europa, Ganymede, Callisto, and strongly suspected in Enceladus and Titan, the exact mechanism required to heat and maintain these liquid reservoirs over Solar System history remains a mystery. Radiogenic heating can supply enough energy for large satellites whereas tidal dissipation provides the best explanation for the presence of oceans in small icy satellites. The amount of thermal energy actually contributed to the interiors of these icy satellites through oceanic tidal dissipation is largely unquantified. Presented here is a numerical model that builds upon previous work for quantifying tidally dissipated energy in the subsurface oceans of the icy satellites. Recent semi-analytical models (Tyler, 2008 and Matsuyama, 2014) have solved the Laplace Tidal Equations to estimate the time averaged energy flux over an orbital period in icy satellite oceans, neglecting the presence of a solid icy shell. These models are only able to consider linear Rayleigh friction. The numerical model presented here is compared to one of these semi-analytical models, finding excellent agreement between velocity and displacement solutions for all three terms to the tidal potential. Time averaged energy flux is within 2-6% of the analytical values. Quadratic (bottom) friction is then incorporated into the model, replacing linear friction. This approach is commonly applied to terrestrial ocean dissipation studies where dissipation scales nonlinearly with velocity. A suite of simulations are also run for the quadratic friction case which are then compared to and analysed against recent scaling laws developed by Chen and Nimmo (2013).

  17. Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

    NASA Technical Reports Server (NTRS)

    Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

    2009-01-01

    The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

  18. Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Adamian, A.

    1988-01-01

    An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

  19. Quadratic and H∞ switching control for discrete-time linear systems with multiplicative noises

    NASA Astrophysics Data System (ADS)

    Costa, O. L. V.; Gonzaga, C. A. C.

    2014-11-01

    The goal of this paper is to study the switched stochastic control problem of discrete-time linear systems with multiplicative noises. We consider both the quadratic and the H∞ criteria for the performance evaluation. Initially we present a sufficient condition based on some Lyapunov-Metzler inequalities to guarantee the stochastic stability of the switching system. Moreover, we derive a sufficient condition for obtaining a Metzler matrix that will satisfy the Lyapunov-Metzler inequalities by directly solving a set of linear matrix inequalities, and not bilinear matrix inequalities as usual in the literature of switched systems. We believe that this result is an interesting contribution on its own. In the sequel we present sufficient conditions, again based on Lyapunov-Metzler inequalities, to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and H∞ performance costs are bounded above by a constant value. These results are illustrated with some numerical examples.

  20. Optimal piecewise linear schedules for LSGP- and LPGS-decomposed array processors via quadratic programming

    NASA Astrophysics Data System (ADS)

    Zimmermann, Karl-Heinz; Achtziger, Wolfgang

    2001-09-01

    The size of a systolic array synthesized from a uniform recurrence equation, whose computations are mapped by a linear function to the processors, matches the problem size. In practice, however, there exist several limiting factors on the array size. There are two dual schemes available to derive arrays of smaller size from large-size systolic arrays based on the partitioning of the large-size arrays into subarrays. In LSGP, the subarrays are clustered one-to-one into the processors of a small-size array, while in LPGS, the subarrays are serially assigned to a reduced-size array. In this paper, we propose a common methodology for both LSGP and LPGS based on polyhedral partitionings of large-size k-dimensional systolic arrays which are synthesized from n-dimensional uniform recurrences by linear mappings for allocation and timing. In particular, we address the optimization problem of finding optimal piecewise linear timing functions for small-size arrays. These are mappings composed of linear timing functions for the computations of the subarrays. We study a continuous approximation of this problem by passing from piecewise linear to piecewise quasi-linear timing functions. The resultant problem formulation is then a quadratic programming problem which can be solved by standard algorithms for nonlinear optimization problems.

  1. Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design

    NASA Technical Reports Server (NTRS)

    Turso, James A.; Litt, Jonathan S.

    2004-01-01

    A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

  2. Regions of attraction and ultimate boundedness for linear quadratic regulators with nonlinearities

    NASA Technical Reports Server (NTRS)

    Joshi, S. M.

    1984-01-01

    The closed-loop stability of multivariable linear time-invariant systems controlled by optimal linear quadratic (LQ) regulators is investigated for the case when the feedback loops have nonlinearities N(sigma) that violate the standard stability condition, sigma N(sigma) or = 0.5 sigma(2). The violations of the condition are assumed to occur either (1) for values of sigma away from the origin (sigma = 0) or (2) for values of sigma in a neighborhood of the origin. It is proved that there exists a region of attraction for case (1) and a region of ultimate boundedness for case (2), and estimates are obtained for these regions. The results provide methods for selecting the performance function parameters to design LQ regulators with better tolerance to nonlinearities. The results are demonstrated by application to the problem of attitude and vibration control of a large, flexible space antenna in the presence of actuator nonlinearities.

  3. Estimation of regions of attraction and ultimate boundedness for multiloop LQ regulators. [Linear Quadratic

    NASA Technical Reports Server (NTRS)

    Joshi, S. M.

    1984-01-01

    Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.

  4. Projection-free parallel quadratic programming for linear model predictive control

    NASA Astrophysics Data System (ADS)

    Di Cairano, S.; Brand, M.; Bortoff, S. A.

    2013-08-01

    A key component in enabling the application of model predictive control (MPC) in fields such as automotive, aerospace, and factory automation is the availability of low-complexity fast optimisation algorithms to solve the MPC finite horizon optimal control problem in architectures with reduced computational capabilities. In this paper, we introduce a projection-free iterative optimisation algorithm and discuss its application to linear MPC. The algorithm, originally developed by Brand for non-negative quadratic programs, is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum. An acceleration technique based on a projection-free line search is also introduced, to speed-up the convergence to the optimum. The algorithm is applied to MPC through the dual of the quadratic program (QP) formulated from the MPC finite time optimal control problem. We discuss how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algorithm performance can be optimised by pre-computing the matrices in a parametric form. We show computational results of the algorithm in three common case studies and we compare such results with the results obtained by other available free and commercial QP solvers.

  5. Improved control using PFC and modified linear quadratic regulator for a kind of nonlinear systems

    NASA Astrophysics Data System (ADS)

    Zhang, Ridong; Lu, Renquan; Wang, Shuqing

    2016-04-01

    This paper describes the combination design of predictive functional control (PFC) and optimal linear quadratic (LQ) method for a kind of nonlinear process with output feedback coupling. In many existing control methods for this kind of nonlinear systems, the nonlinear part is either ignored or represented as a rough linear one when corresponding predictive control methods are designed. However, by assuming that the nonlinearity can be ignored or simplified to a linear time-varying part may not lead to the good control performance of subsequent linear control designs. The paper is a further investigation on this kind of systems, in which a procedure of PFC plus a modified optimal LQ control is developed. With respect to the proposed control strategy and the corresponding processes, the closed-loop performance is improved concerning tracking ability and disturbance rejection compared with previous predictive control methods. In addition, the proposed control is easy to implement as it selects a simple structure and a modification of the classical control scheme.

  6. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.

    1988-01-01

    The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

  7. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.

    1987-01-01

    The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

  8. Observer based output feedback tuning for underwater remotely operated vehicle based on linear quadratic performance

    NASA Astrophysics Data System (ADS)

    Aras, Mohd Shahrieel Mohd; Abdullah, Shahrum Shah; Kamarudin, Muhammad Nizam; Rahman, Ahmad Fadzli Nizam Abdul; Azis, Fadilah Abd; Jaafar, Hazriq Izzuan

    2015-05-01

    This paper describes the effectiveness of observer-based output feedback for Unmanned Underwater Vehicle (UUV) with Linear Quadratic Regulation (LQR) performance. Tuning of observer parameters is crucial for tracking purpose. Prior to tuning facility, the ranges of observer and LQR parameters are obtained via system output cum error. The validation of this technique using unmanned underwater vehicles called Remotely Operated Vehicle (ROV) modelling helps to improve steady state performance of system response. The ROV modeling is focused for depth control using ROV 1 developed by the Underwater Technology Research Group (UTeRG). The results are showing that this technique improves steady state performances in term of overshoot and settling time of the system response.

  9. The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery.

    PubMed

    Kirkpatrick, John P; Meyer, Jeffrey J; Marks, Lawrence B

    2008-10-01

    The linear-quadratic (LQ) model is widely used to model the effect of total dose and dose per fraction in conventionally fractionated radiotherapy. Much of the data used to generate the model are obtained in vitro at doses well below those used in radiosurgery. Clinically, the LQ model often underestimates tumor control observed at radiosurgical doses. The underlying mechanisms implied by the LQ model do not reflect the vascular and stromal damage produced at the high doses per fraction encountered in radiosurgery and ignore the impact of radioresistant subpopulations of cells. The appropriate modeling of both tumor control and normal tissue toxicity in radiosurgery requires the application of emerging understanding of molecular-, cellular-, and tissue-level effects of high-dose/fraction-ionizing radiation and the role of cancer stem cells.

  10. A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators

    NASA Technical Reports Server (NTRS)

    Houpt, P. K.; Wahid, J.; Johnson, T. L.; Ward, S. A.

    1978-01-01

    A laboratory design facility for digital microprocessor implementation of linear-quadratic-Gaussian feedback compensators is described. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems were conditioned for implementation on the laboratory microcomputer system. The software consisted of two parts: an offline high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains and a cross compiler/macro assembler which generates object code for the target microprocessor system. A PDP 11/70 with a UNIX operating system was used for all high level program and data management, and the target microprocessor system is an Intel MDS (8080-based processor). Application to the control of a two dimensional inverted pendulum is presented and issues in expanding the design/prototyping system to other target machine architectures are discussed.

  11. Space shuttle active-pogo-suppressor control design using linear quadratic regulator techniques

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.; Lorenz, C. F.

    1979-01-01

    Two methods of active pogo suppression (stabilization) for the space shuttle vehicle were studied analytically. The basis for both approaches was the linear quadratic regulator, state space technique. The first approach minimized root-mean-square pump inlet pressure by using either fullstate feedback, partial-state feedback, or output feedback with a Kalman filter. The second approach increased the modal damping associated with the critical structural modes by using either full-state feedback or reconstructed state feedback. A number of implementable controls were found by both approaches. The designs were analyzed with respect to sensitivity, complexity, and controller energy requirements, as well as controller performance. Practical controllers resulting from the two design approaches tended to use pressure and flow as feedback variables for the minimum-rms method and structural accelerations or velocities for the modal control method. Both approaches are suitable for the design of active pogo-suppression controllers.

  12. Decoupled control analysis of a large flexible space antenna with linear quadratic regulator comparisons

    NASA Technical Reports Server (NTRS)

    Young, J. W.; Hamer, H. A.; Johnson, K. G.

    1984-01-01

    A decoupled-control analysis was performed for a large flexible space antenna. Control involved commanding changes in the rigid-body modes or nulling disturbances in the flexible modes. The study provides parametric-type data which could be useful in the final design of a large space antenna control system. Results are presented to illustrate the effect on control requirements of (1) the number of modes controlled; (2) the number, type, and location of control actuators; and (3) variations in the closed-loop dynamics of the control system. Comparisons are given between the decoupled-control results and those obtained by using a linear quadratic regulator approach. Time history responses are presented to illustrate the effects of the control procedures.

  13. A linear quadratic Gaussian with loop transfer recovery proximity operations autopilot for spacecraft. M.S. Thesis - MIT

    NASA Technical Reports Server (NTRS)

    Chen, George T.

    1987-01-01

    An automatic control scheme for spacecraft proximity operations is presented. The controller is capable of holding the vehicle at a prescribed location relative to a target, or maneuvering it to a different relative position using straight line-of-sight translations. The autopilot uses a feedforward loop to initiate and terminate maneuvers, and for operations at nonequilibrium set-points. A multivariate feedback loop facilitates precise position and velocity control in the presence of sensor noise. The feedback loop is formulated using the Linear Quadratic Gaussian (LQG) with Loop Transfer Recovery (LTR) design procedure. Linear models of spacecraft dynamics, adapted from Clohessey-Wiltshire Equations, are augmented and loop shaping techniques are applied to design a target feedback loop. The loop transfer recovery procedure is used to recover the frequency domain properties of the target feedback loop. The resulting compensator is integrated into an autopilot which is tested in a high fidelity Space Shuttle Simulator. The autopilot performance is evaluated for a variety of proximity operations tasks envisioned for future Shuttle flights.

  14. Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control

    USGS Publications Warehouse

    Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.

    1997-01-01

    One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.

  15. Linear quadratic Gaussian and feedforward controllers for the DSS-13 antenna

    NASA Technical Reports Server (NTRS)

    Gawronski, W. K.; Racho, C. S.; Mellstrom, J. A.

    1994-01-01

    The controller development and the tracking performance evaluation for the DSS-13 antenna are presented. A trajectory preprocessor, linear quadratic Gaussian (LQG) controller, feedforward controller, and their combination were designed, built, analyzed, and tested. The antenna exhibits nonlinear behavior when the input to the antenna and/or the derivative of this input exceeds the imposed limits; for slewing and acquisition commands, these limits are typically violated. A trajectory preprocessor was designed to ensure that the antenna behaves linearly, just to prevent nonlinear limit cycling. The estimator model for the LQG controller was identified from the data obtained from the field test. Based on an LQG balanced representation, a reduced-order LQG controller was obtained. The feedforward controller and the combination of the LQG and feedforward controller were also investigated. The performance of the controllers was evaluated with the tracking errors (due to following a trajectory) and the disturbance errors (due to the disturbances acting on the antenna). The LQG controller has good disturbance rejection properties and satisfactory tracking errors. The feedforward controller has small tracking errors but poor disturbance rejection properties. The combined LQG and feedforward controller exhibits small tracking errors as well as good disturbance rejection properties. However, the cost for this performance is the complexity of the controller.

  16. Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1987-01-01

    In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

  17. AESOP: An interactive computer program for the design of linear quadratic regulators and Kalman filters

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.; Geyser, L. C.

    1984-01-01

    AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.

  18. Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1985-01-01

    In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

  19. Twin boundary profiles with linear-quadratic coupling between order parameters.

    PubMed

    Pöttker, Henning; Salje, Ekhard K H

    2014-08-27

    A new type of twin boundary was found when two order parameters interact by linear-quadratic coupling QP(2). In this solution, we find that a domain wall consists of two layers in which in one layer both order parameters Q and P are active while in the second layer only Q is active. The adjacent domains are equally asymmetric (Q, P) and (Q, 0) so that one phase could be polar and/or magnetic and contain a ferroelastic strain while the second layer is ferroelastic only without polar or magnetic properties. The two layers represent a stepwise transition between the two domains.We analyze the full phase diagram depending on the coupling constant and anisotropy of the gradient term, and show that in a certain regime the order parameter Q becomes activated only in the interfacial region. A common solution contains kinks and breathers whereby the width of the interface can be very wide in agreement with the first order character of the transition.

  20. Antenna Linear-Quadratic-Gaussian (LQG) Controllers: Properties, Limits of Performance, and Tuning Procedure

    NASA Technical Reports Server (NTRS)

    Gawronski, W.

    2004-01-01

    Wind gusts are the main disturbances that depreciate tracking precision of microwave antennas and radiotelescopes. The linear-quadratic-Gaussian (LQG) controllers - as compared with the proportional-and-integral (PI) controllers significantly improve the tracking precision in wind disturbances. However, their properties have not been satisfactorily understood; consequently, their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller model and the selection of weights of the LQG performance index. This article analyzes properties of an open- and closed-loop antenna. It shows that the proper choice of coordinates of the open-loop model simplifies the shaping of the closed-loop performance. The closed-loop properties are influenced by the LQG weights. The article shows the impact of the weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. The bandwidth and the disturbance rejection characterize the antenna performance, while the acceleration represents the performance limit set by the antenna hardware (motors). The article presents the controller tuning procedure, based on the coordinate selection and the weight properties. The procedure rationally shapes the closed-loop performance, as an alternative to the trial-and-error approach.

  1. Spacecraft Formation Flying Maneuvers Using Linear-Quadratic Regulation with No Radial Axis Inputs

    NASA Technical Reports Server (NTRS)

    Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)

    2001-01-01

    Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame ' propulsion system simplifications and weight reduction may be accomplished. Several linear-quadratic regulators (LQR) are explored and compared based on performance measures likely to be important to many missions, but not directly optimized in the LQR designs. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. This work focusses on formations in which the controlled satellite has a relative trajectory which projects onto the local horizon of the uncontrolled satellite as a circle. This formation has potential uses for distributed remote sensing systems.

  2. Linear quadratic modeling of increased late normal-tissue effects in special clinical situations

    SciTech Connect

    Jones, Bleddyn . E-mail: b.jones.1@bham.ac.uk; Dale, Roger G.; Gaya, Andrew M.

    2006-03-01

    Purpose: To extend linear quadratic theory to allow changes in normal-tissue radiation tolerance after exposure to cytotoxic chemotherapy, after surgery, and in elderly patients. Methods: Examples of these situations are analyzed by use of the biologic effective dose (BED) concept. Changes in tolerance can be allowed for by: estimation of either the contribution of the additional factor as an equivalent BED or the equivalent dose in 2-Gy fractions or by the degree of radiosensitization by a mean dose-modifying factor (x). Results: The estimated x value is 1.063 (95% confidence limits for the mean, 1.056 to 1.070) for subcutaneous fibrosis after cyclophosphamide, methotrexate, and fluorouracil (CMF) chemotherapy and radiotherapy in breast cancer. The point estimate of x is 1.18 for the additional risk of gastrointestinal late-radiation effects after abdominal surgery in lymphoma patients (or 10.62 Gy at 2 Gy per fraction). For shoulder fibrosis in patients older than 60 years after breast and nodal irradiation, x is estimated to be 1.033 (95% confidence limits for the mean, 1.028 to 1.0385). The equivalent BED values were CMF chemotherapy (6.48 Gy{sub 3}), surgery (17.73 Gy{sub 3}), and age (3.61 Gy{sub 3}). Conclusions: The LQ model can, in principle, be extended to quantify reduced normal-tissue tolerance in special clinical situations.

  3. Radiobiological assessment of non-standard and novel radiotherapy treatments using the linear-quadratic model.

    PubMed

    Dale, R G

    1993-01-01

    The linear-quadratic (LQ) model is useful in the radiobiological assessment of a wide variety of radiotherapy treatment techniques, not being confined to analysis of fractionated treatments alone. The model uses parameters that must be separately specified for tumours and dose-limiting normal tissues, and may therefore be used to help identify treatments that are most likely to maximise tumour cell kill while minimising the risk of severe normal-tissue damage. Additionally, the model is capable of making tentative allowance for the tumour repopulation that can occur during extended treatments. Intercomparisons between different types of treatment are made through the concept of the Extrapolated Response Dose (ERD). The ERD is calculated for each critical tissue and takes account of both the radiobiological parameters and the dose/time pattern of radiation delivery. Known tolerance doses for specified organs may be expressed as an ERDtolerance value, and, if a proposed 'new' treatment is to be successful, its associated ERD value must not exceed ERDtolerance. Examples of this procedure are given in this paper. It is particularly important that medical physicists fully appreciate the scope and limitations of LQ equations, as the analysis of radiobiology problems using the model often requires a degree of mathematical understanding that clinicians may not possess.

  4. Irrigation Control in the Presence of Salinity: Extended Linear Quadratic Approach

    NASA Astrophysics Data System (ADS)

    Bras, Rafael L.; Seo, Dong-Jun

    1987-07-01

    An intraseasonal irrigation scheduling problem is dealt with via extended linear quadratic (ELQ) control. The ELQ control is well-suited for constrained multidimensional problems and provides openloop feedback control rules over the control horizon. A conceptual model is developed to describe the dynamics of water allocation and salt movement in the root zone of a crop. Moisture stress and osmotic stress are combined to obtain the integrated inhibitory effect of salinity on transpiration. For the intraseasonal model to be effective against perennial salt accumulation in the root zone, it should be able to yield control laws which will lead to favorable root zone conditions at the end of an irrigation season, thus avoiding any significant leaching prior to the next growing season. This long-term aspect of salinity control is handled via probabilistic state constraints which impose desired salinity and moisture levels with desired confidence level. The ELQ control is employed in a case study of expected net benefit maximization over an irrigation season of corn in Fort Morgan, Colorado. The results, in general, correspond well with expected irrigation schedules under different conditions and provide valuable information on both short- and long-term aspects of irrigation control under saline conditions. The ELQ control, being an analytic iterative solution scheme with theoretically guaranteed fast convergence, has a distinct computational advantage over state-of-the-art procedures.

  5. Linear Quadratic Tracking Design for a Generic Transport Aircraft with Structural Load Constraints

    NASA Technical Reports Server (NTRS)

    Burken, John J.; Frost, Susan A.; Taylor, Brian R.

    2011-01-01

    When designing control laws for systems with constraints added to the tracking performance, control allocation methods can be utilized. Control allocations methods are used when there are more command inputs than controlled variables. Constraints that require allocators are such task as; surface saturation limits, structural load limits, drag reduction constraints or actuator failures. Most transport aircraft have many actuated surfaces compared to the three controlled variables (such as angle of attack, roll rate & angle of side slip). To distribute the control effort among the redundant set of actuators a fixed mixer approach can be utilized or online control allocation techniques. The benefit of an online allocator is that constraints can be considered in the design whereas the fixed mixer cannot. However, an online control allocator mixer has a disadvantage of not guaranteeing a surface schedule, which can then produce ill defined loads on the aircraft. The load uncertainty and complexity has prevented some controller designs from using advanced allocation techniques. This paper considers actuator redundancy management for a class of over actuated systems with real-time structural load limits using linear quadratic tracking applied to the generic transport model. A roll maneuver example of an artificial load limit constraint is shown and compared to the same no load limitation maneuver.

  6. Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs

    NASA Technical Reports Server (NTRS)

    Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)

    2001-01-01

    Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.

  7. Effect of Fractionation in Stereotactic Body Radiation Therapy Using the Linear Quadratic Model

    SciTech Connect

    Yang, Jun; Lamond, John; Fowler, Jack; Lanciano, Rachelle; Feng, Jing; Brady, Luther

    2013-05-01

    Purpose: To examine the fractionation effect of stereotactic body radiation therapy with a heterogeneous dose distribution. Methods: Derived from the linear quadratic formula with measurements from a hypothetical 2-cm radiosurgical tumor, the threshold percentage was defined as (α/β{sub tissue}/α/β{sub tumor}), the balance α/β ratio was defined as (prescription dose/tissue tolerance*α/β{sub tumor}), and the balance dose was defined as (tissue tolerance/threshold percentage). Results: With increasing fractions and equivalent peripheral dose to the target, the biological equivalent dose of “hot spots” in a target decreases. The relative biological equivalent doses of serial organs decrease only when the relative percentage of its dose to the prescription dose is above the threshold percentage. The volume of parallel organs at risk decreases only when the tumor's α/β ratio is above the balance α/β ratio and the prescription dose is lower than balance dose. Conclusions: The potential benefits of fractionation in stereotactic body radiation therapy depend on the complex interplay between the total dose, α/β ratios, and dose differences between the target and the surrounding normal tissues.

  8. On relating the generalized equivalent uniform dose formalism to the linear-quadratic model.

    PubMed

    Djajaputra, David; Wu, Qiuwen

    2006-12-01

    Two main approaches are commonly used in the literature for computing the equivalent uniform dose (EUD) in radiotherapy. The first approach is based on the cell-survival curve as defined in the linear-quadratic model. The second approach assumes that EUD can be computed as the generalized mean of the dose distribution with an appropriate fitting parameter. We have analyzed the connection between these two formalisms by deriving explicit formulas for the EUD which are applicable to normal distributions. From these formulas we have established an explicit connection between the two formalisms. We found that the EUD parameter has strong dependence on the parameters that characterize the distribution, namely the mean dose and the standard deviation around the mean. By computing the corresponding parameters for clinical dose distributions, which in general do not follow the normal distribution, we have shown that our results are also applicable to actual dose distributions. Our analysis suggests that caution should be used in using generalized EUD approach for reporting and analyzing dose distributions.

  9. Isobio software: biological dose distribution and biological dose volume histogram from physical dose conversion using linear-quadratic-linear model

    PubMed Central

    Jaikuna, Tanwiwat; Khadsiri, Phatchareewan; Chawapun, Nisa; Saekho, Suwit

    2017-01-01

    Purpose To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL) model. Material and methods The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR), and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2) was calculated using biological effective dose (BED) based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit). Results Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS) in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV) determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT) and 0.240, 0.320, and 0.849 for brachytherapy (BT) in HR-CTV, bladder, and rectum, respectively. Conclusions The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT. PMID:28344603

  10. Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls.

    PubMed

    de Pillis, L G; Gu, W; Fister, K R; Head, T; Maples, K; Murugan, A; Neal, T; Yoshida, K

    2007-09-01

    We investigate a mathematical model of tumor-immune interactions with chemotherapy, and strategies for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form of the model allows us to test and compare various optimal control strategies, including a quadratic control, a linear control, and a state-constraint. We establish the existence of the optimal control, and solve for the control in both the quadratic and linear case. In the linear control case, we show that we cannot rule out the possibility of a singular control. An interesting aspect of this paper is that we provide a graphical representation of regions on which the singular control is optimal.

  11. Optimal Linear Quadratic Regulators for Control of Nonlinear Mechanical Systems with Redundant Degrees-of-Freedom

    NASA Astrophysics Data System (ADS)

    Arimoto, Suguru

    An optimal regulator problem for endpoint position control of a robot arm with (or without) redundancy in its total degrees-of-freedom (DOF) is solved by combining Riemannian geometry with nonlinear control theory. Given a target point, within the task-space, that the arm endpoint should reach, a task-space position feedback with joint damping is shown to asymptotically stabilize reaching movements even if the number of DOF of the arm is greater than the dimension of the task space and thereby the inverse kinematics is ill-posed. Usually the speed of convergence of the endpoint trajectory is unsatisfactory, depending on the choice of feedback gains for joint damping. Hence, to speed up the convergence without incurring further energy consumption, an optimal control design for minimizing a performance index composed of an integral of joint dissipation energy plus a linear quadratic form of the task-space control input and output is introduced. It is then shown that the Hamilton-Jacobi-Bellman equation derived from the principle of optimality is solvable in control variables and the Hamilton-Jacobi equation itself has an explicit solution. Although the state of the original dynamics (the Euler-Lagrange equation) with DOF-redundancy contains uncontrollable and unobservable manifolds, the dynamics satisfies a nonlinear version of the Kalman-Yakubovich-Popov lemma and the task-space input-output passivity. An inverse problem of optimal regulator design for robotic arms under the effect of gravity is also tackled by combining Riemannian geometry with passivity-based control theory.

  12. Revealing a quantum feature of dimensionless uncertainty in linear and quadratic potentials by changing potential intervals

    NASA Astrophysics Data System (ADS)

    Kheiri, R.

    2016-09-01

    As an undergraduate exercise, in an article (2012 Am. J. Phys. 80 780-14), quantum and classical uncertainties for dimensionless variables of position and momentum were evaluated in three potentials: infinite well, bouncing ball, and harmonic oscillator. While original quantum uncertainty products depend on {{\\hslash }} and the number of states (n), a dimensionless approach makes the comparison between quantum uncertainty and classical dispersion possible by excluding {{\\hslash }}. But the question is whether the uncertainty still remains dependent on quantum number n. In the above-mentioned article, there lies this contrast; on the one hand, the dimensionless quantum uncertainty of the potential box approaches classical dispersion only in the limit of large quantum numbers (n\\to ∞ )—consistent with the correspondence principle. On the other hand, similar evaluations for bouncing ball and harmonic oscillator potentials are equal to their classical counterparts independent of n. This equality may hide the quantum feature of low energy levels. In the current study, we change the potential intervals in order to make them symmetric for the linear potential and non-symmetric for the quadratic potential. As a result, it is shown in this paper that the dimensionless quantum uncertainty of these potentials in the new potential intervals is expressed in terms of quantum number n. In other words, the uncertainty requires the correspondence principle in order to approach the classical limit. Therefore, it can be concluded that the dimensionless analysis, as a useful pedagogical method, does not take away the quantum feature of the n-dependence of quantum uncertainty in general. Moreover, our numerical calculations include the higher powers of the position for the potentials.

  13. Lifespan estimates for the semi-linear Klein-Gordon equation with a quadratic potential in dimension one

    NASA Astrophysics Data System (ADS)

    Zhang, Qidi

    2016-12-01

    We show for almost every m > 0, the solution to the semi-linear Klein-Gordon equation with a quadratic potential in dimension one, exists over a longer time interval than the one given by local existence theory, using the normal form method. By using an Lp -Lq estimate for eigenfunctions of the harmonic oscillator and by carefully analysis on the nonlinearity, we improve the result obtained by the author before.

  14. Linear ubiquitination signals in adaptive immune responses.

    PubMed

    Ikeda, Fumiyo

    2015-07-01

    Ubiquitin can form eight different linkage types of chains using the intrinsic Met 1 residue or one of the seven intrinsic Lys residues. Each linkage type of ubiquitin chain has a distinct three-dimensional topology, functioning as a tag to attract specific signaling molecules, which are so-called ubiquitin readers, and regulates various biological functions. Ubiquitin chains linked via Met 1 in a head-to-tail manner are called linear ubiquitin chains. Linear ubiquitination plays an important role in the regulation of cellular signaling, including the best-characterized tumor necrosis factor (TNF)-induced canonical nuclear factor-κB (NF-κB) pathway. Linear ubiquitin chains are specifically generated by an E3 ligase complex called the linear ubiquitin chain assembly complex (LUBAC) and hydrolyzed by a deubiquitinase (DUB) called ovarian tumor (OTU) DUB with linear linkage specificity (OTULIN). LUBAC linearly ubiquitinates critical molecules in the TNF pathway, such as NEMO and RIPK1. The linear ubiquitin chains are then recognized by the ubiquitin readers, including NEMO, which control the TNF pathway. Accumulating evidence indicates an importance of the LUBAC complex in the regulation of apoptosis, development, and inflammation in mice. In this article, I focus on the role of linear ubiquitin chains in adaptive immune responses with an emphasis on the TNF-induced signaling pathways.

  15. Threshold and other departures from linear-quadratic curvature in the non-cancer mortality dose-response curve in the Japanese atomic bomb survivors.

    PubMed

    Little, Mark P

    2004-07-01

    Recently released data on non-cancer mortality in Japanese atomic bomb survivors are analysed using a variety of generalised relative risk models that take account of errors in estimates of dose to assess the dose-response at low doses. If linear-threshold, quadratic-threshold or linear-quadratic-threshold relative risk models (the dose-response is assumed to be linear, quadratic or linear-quadratic above the threshold, respectively) are fitted to the non-cancer data there are no statistically significant ( p>0.10) indications of threshold departures from linearity, quadratic curvature or linear-quadratic curvature. These findings are true irrespective of the assumed magnitude of dosimetric error, between 25%-45% geometric standard deviations. In general, increasing the assumed magnitude of dosimetric error had little effect on the central estimates of the threshold, but somewhat widened the associated confidence intervals. If a power of dose model is fitted, there is little evidence ( p>0.10) that the power of dose in the dose-response is statistically significantly different from 1, again irrespective of the assumed magnitude of dosimetric errors in the range 25%-45%. Again, increasing the size of the errors resulted in wider confidence intervals on the power of dose, without marked effect on the central estimates. In general these findings remain true for various non-cancer disease subtypes.

  16. Observation of linear and quadratic magnetic field-dependence of magneto-photocurrents in InAs/GaSb superlattice

    PubMed Central

    2014-01-01

    We experimentally studied the magneto-photocurrents generated by direct interband transition in InAs/GaSb type II superlattice. By varying the magnetic field direction, we observed that an in-plane magnetic field induces a photocurrent linearly proportional to the magnetic field; however, a magnetic field tilted to the sample plane induces a photocurrent presenting quadratic magnetic field dependence. The magneto-photocurrents in both conditions are insensitive to the polarization state of the incident light. Theoretical models involving excitation, relaxation and Hall effect are utilized to explain the experimental results. PMID:24936166

  17. A reformulation of the Linear-Quadratic-Gaussian stochastic control problem for application to low thrust navigation analysis

    NASA Technical Reports Server (NTRS)

    Jacobson, R. A.

    1978-01-01

    The formulation of the classical Linear-Quadratic-Gaussian stochastic control problem as employed in low thrust navigation analysis is reviewed. A reformulation is then presented which eliminates a potentially unreliable matrix subtraction in the control calculations, improves the computational efficiency, and provides for a cleaner computational interface between the estimation and control processes. Lastly, the application of the U-D factorization method to the reformulated equations is examined with the objective of achieving a complete set of factored equations for the joint estimation and control problem.

  18. CAD of control systems: Application of nonlinear programming to a linear quadratic formulation

    NASA Technical Reports Server (NTRS)

    Fleming, P.

    1983-01-01

    The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

  19. Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities

    NASA Astrophysics Data System (ADS)

    Vaidyanathan, S.

    2014-06-01

    This paper proposes a eight-term 3-D polynomial chaotic system with three quadratic nonlinearities and describes its properties. The maximal Lyapunov exponent (MLE) of the proposed 3-D chaotic system is obtained as L 1 = 6.5294. Next, new results are derived for the global chaos synchronization of the identical eight-term 3-D chaotic systems with unknown system parameters using adaptive control. Lyapunov stability theory has been applied for establishing the adaptive synchronization results. Numerical simulations are shown using MATLAB to describe the main results derived in this paper.

  20. Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Boskovic, Jovan D.

    2008-01-01

    This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.

  1. The increase in animal mortality risk following exposure to sparsely ionizing radiation is not linear quadratic with dose

    SciTech Connect

    Haley, Benjamin M.; Paunesku, Tatjana; Grdina, David J.; Woloschak, Gayle E.; Aravindan, Natarajan

    2015-12-09

    The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREFLSS). As a result, it was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limited number of animal studies.

  2. The increase in animal mortality risk following exposure to sparsely ionizing radiation is not linear quadratic with dose

    DOE PAGES

    Haley, Benjamin M.; Paunesku, Tatjana; Grdina, David J.; ...

    2015-12-09

    The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII), which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREFLSS). As a result, it was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limitedmore » number of animal studies.« less

  3. Neural-genetic synthesis for state-space controllers based on linear quadratic regulator design for eigenstructure assignment.

    PubMed

    da Fonseca Neto, João Viana; Abreu, Ivanildo Silva; da Silva, Fábio Nogueira

    2010-04-01

    Toward the synthesis of state-space controllers, a neural-genetic model based on the linear quadratic regulator design for the eigenstructure assignment of multivariable dynamic systems is presented. The neural-genetic model represents a fusion of a genetic algorithm and a recurrent neural network (RNN) to perform the selection of the weighting matrices and the algebraic Riccati equation solution, respectively. A fourth-order electric circuit model is used to evaluate the convergence of the computational intelligence paradigms and the control design method performance. The genetic search convergence evaluation is performed in terms of the fitness function statistics and the RNN convergence, which is evaluated by landscapes of the energy and norm, as a function of the parameter deviations. The control problem solution is evaluated in the time and frequency domains by the impulse response, singular values, and modal analysis.

  4. On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.; Wang, C.

    1990-01-01

    The convergence of solutions to the discrete or sampled time linear quadratic regulator problem and associated Riccati equation for infinite dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite and infinite time horizon problems are studied. In the finite time horizon case, strong continuity of the operators which define the control system and performance index together with a stability and consistency condition on the sampling scheme are required. For the infinite time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary of delay system, and a flexible beam are presented and discussed.

  5. Adaptive log-quadratic approach for target detection in nonhomogeneous backgrounds perturbed with speckle fluctuations.

    PubMed

    Magraner, Eric; Bertaux, Nicolas; Réfrégier, Philippe

    2008-12-01

    An approach for point target detection in the presence of speckle fluctuations with nonhomogeneous backgrounds is proposed. This approach is based on an automatic selection between the standard constant background model and a quadratic model for the logarithm of the background values. An improvement of the regulation of the false alarm probability in nonhomogeneous backgrounds is demonstrated.

  6. Reducing the model-data misfit in a marine ecosystem model using periodic parameters and linear quadratic optimal control

    NASA Astrophysics Data System (ADS)

    El Jarbi, M.; Rückelt, J.; Slawig, T.; Oschlies, A.

    2013-02-01

    This paper presents the application of the Linear Quadratic Optimal Control (LQOC) method to a parameter optimization problem for a one-dimensional marine ecosystem model of NPZD (N for dissolved inorganic nitrogen, P for phytoplankton, Z for zooplankton and D for detritus) type. This ecosystem model, developed by Oschlies and Garcon, simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column and is driven by ocean circulation data. The LQOC method is used to introduce annually periodic model parameters in a linearized version of the model. We show that the obtained version of the model gives a significant reduction of the model-data misfit, compared to the one obtained for the original model with optimized constant parameters. The found inner-annual variability of the optimized parameters provides hints for improvement of the original model. We use the obtained optimal periodic parameters also in validation and prediction experiments with the original non-linear version of the model. In both cases, the results are significantly better than those obtained with optimized constant parameters.

  7. AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

    USGS Publications Warehouse

    Lefkoff, L.J.; Gorelick, S.M.

    1987-01-01

    A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

  8. Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective

    NASA Astrophysics Data System (ADS)

    Ayvaz, Muzaffer; Demiralp, Metin

    2011-09-01

    In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.

  9. Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective

    SciTech Connect

    Ayvaz, Muzaffer; Demiralp, Metin

    2011-09-14

    In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.

  10. Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

    PubMed

    Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

    2015-04-01

    Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy.

  11. Multivariable control of a twin lift helicopter system using the LQG/LTR design methodology. [Linear Quadratic Gaussian/Loop Transfer Recovery method

    NASA Technical Reports Server (NTRS)

    Rodriguez, A. A.; Athans, M.

    1986-01-01

    Guidelines for developing a multivariable centralized automatic flight control system (AFCS) for a twin lift helicopter system (TLHS) are presented. Singular value ideas are used to formulate performance and stability robustness specifications. A linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) design is obtained and evaluated.

  12. Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control

    NASA Astrophysics Data System (ADS)

    Na, Xiaoxiang; Cole, David J.

    2013-02-01

    This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy.

  13. Decoupled and linear quadratic regulator control of a large, flexible space antenna with an observer in the control loop

    NASA Technical Reports Server (NTRS)

    Hamer, H. A.; Johnson, K. G.; Young, J. W.

    1985-01-01

    An analysis is performed to compare decoupled and linear quadratic regulator (LQR) procedures for the control of a large, flexible space antenna. Control objectives involve: (1) commanding changes in the rigid-body modes, (2) nulling initial disturbances in the rigid-body modes, or (3) nulling initial disturbances in the first three flexible modes. Control is achieved with two three-axis control-moment gyros located on the antenna column. Results are presented to illustrate various effects on control requirements for the two procedures. These effects include errors in the initial estimates of state variables, variations in the type, number, and location of sensors, and deletions of state-variable estimates for certain flexible modes after control activation. The advantages of incorporating a time lag in the control feedback are also illustrated. In addition, the effects of inoperative-control situations are analyzed with regard to control requirements and resultant modal responses. Comparisons are included which show the effects of perfect state feedback with no residual modes (ideal case). Time-history responses are presented to illustrate the various effects on the control procedures.

  14. Resistive Wall Mode feedback on DIII-D using Linear Quadratic Gaussian control and a GPU powered control system

    NASA Astrophysics Data System (ADS)

    Clement, M. D.; Navratil, G. A.; Hanson, J. M.; Bialek, J.; Piglowski, D. A.; Penaflor, B. G.

    2015-11-01

    A Graphics Processing Unit (GPU) based control system has been installed on the DIII-D tokamak for Resistive Wall Mode (RWM) control similar to one implemented at the HBT-EP tokamak. DIII-D can excite RWMs, which are strong, locked or nearly locked kink modes whose rotation frequencies do not evolve quickly and are slow compared to their growth rates. Simulations have predicted that modern control techniques like Linear Quadratic Gaussian (LQG) control will perform better than classical control techniques when using control coils external to the vacuum vessel. An LQG control algorithm based on the VALEN model for the RWM has been developed and tested on this system. Early tests have shown the algorithm is able to track and suppress with external control coils the plasma response of an n=1 perturbation driven by internal control coils. An overview of the control hardware, VALEN model, control algorithm and initial results will be presented. Supported by the US DOE under DE-FG02-04ER54761 and DE-FC02-04ER54698.

  15. PATTERN RECOGNITION AND CLASSIFICATION USING ADAPTIVE LINEAR NEURON DEVICES

    DTIC Science & Technology

    adaption by an adaptive linear neuron ( Adaline ), as applied to the pattern recognition and classification problem; (2) Four possible iterative adaption...schemes which may be used to train as Adaline ; (3) Use of Multiple Adalines (Madaline) and two logic layers to increase system capability; and (4) Use...of Adaline in the practical fields of Speech Recognition, Weather Forecasting and Adaptive Control Systems and the possible use of Madaline in the Character Recognition field.

  16. Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

    NASA Astrophysics Data System (ADS)

    McAneney, H.; O'Rourke, S. F. C.

    2007-02-01

    The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning.Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and α/β ratio, where α and β are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth

  17. Biological equivalence between LDR and PDR in cervical cancer: multifactor analysis using the linear-quadratic model

    PubMed Central

    Bravo, Isabel; Pirraco, Rui

    2011-01-01

    Purpose The purpose of this work was the biological comparison between Low Dose Rate (LDR) and Pulsed Dose Rate (PDR) in cervical cancer regarding the discontinuation of the afterloading system used for the LDR treatments at our Institution since December 2009. Material and methods In the first phase we studied the influence of the pulse dose and the pulse time in the biological equivalence between LDR and PDR treatments using the Linear Quadratic Model (LQM). In the second phase, the equivalent dose in 2 Gy/fraction (EQD2) for the tumor, rectum and bladder in treatments performed with both techniques was evaluated and statistically compared. All evaluated patients had stage IIB cervical cancer and were treated with External Beam Radiotherapy (EBRT) plus two Brachytherapy (BT) applications. Data were collected from 48 patients (26 patients treated with LDR and 22 patients with PDR). Results In the analyses of the influence of PDR parameters in the biological equivalence between LDR and PDR treatments (Phase 1), it was calculated that if the pulse dose in PDR was kept equal to the LDR dose rate, a small the-rapeutic loss was expected. If the pulse dose was decreased, the therapeutic window became larger, but a correction in the prescribed dose was necessary. In PDR schemes with 1 hour interval between pulses, the pulse time did not influence significantly the equivalent dose. In the comparison between the groups treated with LDR and PDR (Phase 2) we concluded that they were not equivalent, because in the PDR group the total EQD2 for the tumor, rectum and bladder was smaller than in the LDR group; the LQM estimated that a correction in the prescribed dose of 6% to 10% was ne-cessary to avoid therapeutic loss. Conclusions A correction in the prescribed dose was necessary; this correction should be achieved by calculating the PDR dose equivalent to the desired LDR total dose. PMID:23346123

  18. High-speed spiral imaging technique for an atomic force microscope using a linear quadratic Gaussian controller.

    PubMed

    Habibullah, H; Pota, H R; Petersen, I R

    2014-03-01

    This paper demonstrates a high-speed spiral imaging technique for an atomic force microscope (AFM). As an alternative to traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFM's piezoelectric tube scanner (PTS). Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoids from the X and Y-PTSs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. As part of the post-processing of the experimental data, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors and a Gaussian image filter is used to filter the images. A comparison of images scanned using the proposed controller (spiral) and the AFM PI controller (raster) shows improvement in the scanning rate using the proposed method.

  19. Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

    NASA Technical Reports Server (NTRS)

    Folta, David C.; Carpenter, J. Russell

    1999-01-01

    A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and

  20. Quadratic Damping

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2012-01-01

    Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

  1. Multi-variable control of the GE T700 engine using the LQG/LTR design methodology. [Linear Quadratic Gaussian/Loop Transfer Recovery method

    NASA Technical Reports Server (NTRS)

    Pfeil, W. H.; Athans, M.; Spang, H. A., III

    1986-01-01

    The design of scalar and multi-variable feedback control systems for the GE T700 turboshaft engine coupled to a helicopter rotor system is examined. A series of linearized models are presented and analyzed. Robustness and performance specifications are posed in the frequency domain. The linear-quadratic-Gaussian with loop-transfer-recovery (LQG/LTR) methodology is used to obtain a sequence of three feedback designs. Even in the single-input/single-output case, comparison of the current control system with that derived from the LQG/LTR approach shows significant performance improvement. The multi-variable designs, evaluated using linear and nonlinear simulations, show even more potential for performance improvement.

  2. Observables of a test mass along an inclined orbit in a post-Newtonian-approximated Kerr spacetime including the linear and quadratic spin terms.

    PubMed

    Hergt, Steven; Shah, Abhay; Schäfer, Gerhard

    2013-07-12

    The orbital motion is derived for a nonspinning test mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is represented by the Kerr metric, expanded to second post-Newtonian order including the linear and quadratic spin terms. The orbital period, the intrinsic periastron advance, and the precession of the orbital plane are derived with the aid of novel canonical variables and action-based methods.

  3. Self-characterization of linear and nonlinear adaptive optics systems

    NASA Astrophysics Data System (ADS)

    Hampton, Peter J.; Conan, Rodolphe; Keskin, Onur; Bradley, Colin; Agathoklis, Pan

    2008-01-01

    We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM.

  4. Fast HDR image upscaling using locally adapted linear filters

    NASA Astrophysics Data System (ADS)

    Talebi, Hossein; Su, Guan-Ming; Yin, Peng

    2015-02-01

    A new method for upscaling high dynamic range (HDR) images is introduced in this paper. Overshooting artifact is the common problem when using linear filters such as bicubic interpolation. This problem is visually more noticeable while working on HDR images where there exist more transitions from dark to bright. Our proposed method is capable of handling these artifacts by computing a simple gradient map which enables the filter to be locally adapted to the image content. This adaptation consists of first, clustering pixels into regions with similar edge structures and second, learning the shape and length of our symmetric linear filter for each of these pixel groups. This new filter can be implemented in a separable fashion which perfectly fits hardware implementations. Our experimental results show that training our filter with HDR images can effectively reduce the overshooting artifacts and improve upon the visual quality of the existing linear upscaling approaches.

  5. Linear adaptive control of a single-tether system

    NASA Technical Reports Server (NTRS)

    Greene, M. E.; Carter, J. T.; Walls, J. L.

    1992-01-01

    A control law for a single-tether orbiting satellite system based on a reduced order linear adaptive control technique is presented. The main advantages of this technique are its design simplicity and the facts that specific system parameters and model linearization are not required when designing the controller. Two controllers are developed: one which uses only tension in the tether as control actuation and one which uses both tension and in-plane thrusters as control actuation. Both a sixth-order nonlinear and an 11th-order bead model of a tethered satellite system are used for simulation purposes, demonstrating the ability of the controller to manage an uncertain system. Retrieval and stationkeeping results using these nonlinear models and the linear adaptive controller demonstrate the feasibility of the method. The robustness of the controller with respect to parameter uncertainties is also demonstrated by changing the nonlinear model and parameters within the model without redesigning the controller.

  6. Hierarchical transformation of Hamiltonians with linear and quadratic couplings for nonadiabatic quantum dynamics: application to the ππ∗∕nπ∗ internal conversion in thymine.

    PubMed

    Picconi, David; Lami, Alessandro; Santoro, Fabrizio

    2012-06-28

    We face with the general problem of defining a reduced number of effective collective coordinates to describe accurately the short-time nonadiabatic dynamics of large semirigid systems, amenable to a description in terms of coupled harmonic potential energy surfaces. We present a numeric iterative protocol to define a hierarchical representation of the Hamiltonian taking into account both linear and quadratic intra- and inter-state couplings (QVC, quadratic vibronic coupling model), thus generalizing the method introduced recently in the literature [E. Gindensperger, H. Köppel, and L. S. Cederbaum, J. Chem. Phys. 126, 034106 (2007)] for the linear vibronic coupling (LVC) model. This improvement allows to take into account the effect of harmonic frequency changes and Duschinsky mixings among the different electronic states, providing a route to upgrade the models for nonadiabatic harmonic systems to those nowadays routinely used for the simulation of vibronic spectra of adiabatic systems (negligible nonadiabatic couplings). We apply our method to the study of ππ∗ → nπ∗ internal conversion in thymine, analysing the differences in LVC and QVC predictions both for the absorption spectrum and the dynamics of electronic populations.

  7. Robustness of linear quadratic state feedback designs in the presence of system uncertainty. [application to Augmentor Wing Jet STOL Research Aircraft flare control autopilot design

    NASA Technical Reports Server (NTRS)

    Patel, R. V.; Toda, M.; Sridhar, B.

    1977-01-01

    The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

  8. Linear Matrix Inequality Method for a Quadratic Performance Index Minimization Problem with a class of Bilinear Matrix Inequality Conditions

    NASA Astrophysics Data System (ADS)

    Tanemura, M.; Chida, Y.

    2016-09-01

    There are a lot of design problems of control system which are expressed as a performance index minimization under BMI conditions. However, a minimization problem expressed as LMIs can be easily solved because of the convex property of LMIs. Therefore, many researchers have been studying transforming a variety of control design problems into convex minimization problems expressed as LMIs. This paper proposes an LMI method for a quadratic performance index minimization problem with a class of BMI conditions. The minimization problem treated in this paper includes design problems of state-feedback gain for switched system and so on. The effectiveness of the proposed method is verified through a state-feedback gain design for switched systems and a numerical simulation using the designed feedback gains.

  9. Visual discrimination and adaptation using non-linear unsupervised learning

    NASA Astrophysics Data System (ADS)

    Jiménez, Sandra; Laparra, Valero; Malo, Jesus

    2013-03-01

    Understanding human vision not only involves empirical descriptions of how it works, but also organization principles that explain why it does so. Identifying the guiding principles of visual phenomena requires learning algorithms to optimize specific goals. Moreover, these algorithms have to be flexible enough to account for the non-linear and adaptive behavior of the system. For instance, linear redundancy reduction transforms certainly explain a wide range of visual phenomena. However, the generality of this organization principle is still in question:10 it is not only that and additional constraints such as energy cost may be relevant as well, but also, statistical independence may not be the better solution to make optimal inferences in squared error terms. Moreover, linear methods cannot account for the non-uniform discrimination in different regions of the image and color space: linear learning methods necessarily disregard the non-linear nature of the system. Therefore, in order to account for the non-linear behavior, principled approaches commonly apply the trick of using (already non-linear) parametric expressions taken from empirical models. Therefore these approaches are not actually explaining the non-linear behavior, but just fitting it to image statistics. In summary, a proper explanation of the behavior of the system requires flexible unsupervised learning algorithms that (1) are tunable to different, perceptually meaningful, goals; and (2) make no assumption on the non-linearity. Over the last years we have worked on these kind of learning algorithms based on non-linear ICA,18 Gaussianization, 19 and principal curves. In this work we stress the fact that these methods can be tuned to optimize different design strategies, namely statistical independence, error minimization under quantization, and error minimization under truncation. Then, we show (1) how to apply these techniques to explain a number of visual phenomena, and (2) suggest the

  10. Feedforward and output feedback control of a highly oscillating and nonlinear 2-DOF piezoelectric actuator by using input shaping compensator and a linear quadratic regulator

    NASA Astrophysics Data System (ADS)

    Al Hamidi, Yasser; Rakotondrabe, Micky

    2016-05-01

    This paper deals with the control of a two degrees of freedom (2-DOF) piezoelectric cantilever actuator which is characterized by badly damped oscillations, hysteresis nonlinearity and cross-couplings. First, a feedforward control scheme based on the zero placement technique is introduced to annihilate the oscillations. Then a disturbance observer and a disturbance compensator are introduced to reduce the effects of low frequencies phenomena (hysteresis and creep) which were approximated by a fictive disturbance. Finally an output feedback scheme based on the linear quadratic regulator is added in order to reduce the cross-couplings effects to improve the tracking performances, and eventually to add robustness. Experiments were carried out and confirm the predicted performances.

  11. Quadratic spline subroutine package

    USGS Publications Warehouse

    Rasmussen, Lowell A.

    1982-01-01

    A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)

  12. Adaptive local linear regression with application to printer color management.

    PubMed

    Gupta, Maya R; Garcia, Eric K; Chin, Erika

    2008-06-01

    Local learning methods, such as local linear regression and nearest neighbor classifiers, base estimates on nearby training samples, neighbors. Usually, the number of neighbors used in estimation is fixed to be a global "optimal" value, chosen by cross validation. This paper proposes adapting the number of neighbors used for estimation to the local geometry of the data, without need for cross validation. The term enclosing neighborhood is introduced to describe a set of neighbors whose convex hull contains the test point when possible. It is proven that enclosing neighborhoods yield bounded estimation variance under some assumptions. Three such enclosing neighborhood definitions are presented: natural neighbors, natural neighbors inclusive, and enclosing k-NN. The effectiveness of these neighborhood definitions with local linear regression is tested for estimating lookup tables for color management. Significant improvements in error metrics are shown, indicating that enclosing neighborhoods may be a promising adaptive neighborhood definition for other local learning tasks as well, depending on the density of training samples.

  13. Effects of model error on control of large flexible space antenna with comparisons of decoupled and linear quadratic regulator control procedures

    NASA Technical Reports Server (NTRS)

    Hamer, H. A.; Johnson, K. G.

    1986-01-01

    An analysis was performed to determine the effects of model error on the control of a large flexible space antenna. Control was achieved by employing two three-axis control-moment gyros (CMG's) located on the antenna column. State variables were estimated by including an observer in the control loop that used attitude and attitude-rate sensors on the column. Errors were assumed to exist in the individual model parameters: modal frequency, modal damping, mode slope (control-influence coefficients), and moment of inertia. Their effects on control-system performance were analyzed either for (1) nulling initial disturbances in the rigid-body modes, or (2) nulling initial disturbances in the first three flexible modes. The study includes the effects on stability, time to null, and control requirements (defined as maximum torque and total momentum), as well as on the accuracy of obtaining initial estimates of the disturbances. The effects on the transients of the undisturbed modes are also included. The results, which are compared for decoupled and linear quadratic regulator (LQR) control procedures, are shown in tabular form, parametric plots, and as sample time histories of modal-amplitude and control responses. Results of the analysis showed that the effects of model errors on the control-system performance were generally comparable for both control procedures. The effect of mode-slope error was the most serious of all model errors.

  14. Dosimetric characteristics of a newly designed grid block for megavoltage photon radiation and its therapeutic advantage using a linear quadratic model

    SciTech Connect

    Meigooni, Ali S.; Dou Kai; Meigooni, Navid J.; Gnaster, Michael; Awan, Shahid; Dini, Sharifeh; Johnson, Ellis L.

    2006-09-15

    Grid radiation therapy with megavoltage x-ray beam has been proven to be an effective technique for management of large, bulky malignant tumors. The clinical advantage of GRID therapy, combined with conventional radiation therapy, has been demonstrated using a prototype GRID block [Mohiuddin, Curtis, Grizos, and Komarnicky, Cancer 66, 114-118 (1990)]. Recently, a new GRID block design with improved dosimetric properties has become commercially available from Radiation Product Design, Inc. (Albertive, MN). This GRID collimator consists of an array of focused apertures in a cerrobend block arranged in a hexagonal pattern having a circular cross-section with a diameter and center-to-center spacing of 14.3 and 21.1 mm, respectively, in the plane of isocenter. In this project, dosimetric characteristics of the newly redesigned GRID block have been investigated for a Varian 21EX linear accelerator (Varian Associates, Palo Alto, CA). These determinations were performed using radiographic films, thermoluminescent dosimeters in Solid Water trade mark sign phantom materials, and an ionization chamber in water. The output factor, percentage depth dose, beam profiles, and isodose distributions of the GRID radiation as a function of field size and beam energy have been measured using both 6 and 18 MV x-ray beams. In addition, the therapeutic advantage obtained from this treatment modality with the new GRID block design for a high, single fraction of dose has been calculated using the linear quadratic model with {alpha}/{beta} ratios for typical tumor and normal cells. These biological characteristics of the new GRID block design will also be presented.

  15. Estimation of Errors Associated With Use of Linear-Quadratic Formalism for Evaluation of Biologic Equivalence Between Single and Hypofractionated Radiation Doses: An In Vitro Study

    SciTech Connect

    Iwata, Hiromitsu Shibamoto, Yuta; Murata, Rumi; Tomita, Natsuo; Ayakawa, Shiho; Ogino, Hiroyuki; Ito, Masato

    2009-10-01

    Purpose: To investigate the reliability of the linear-quadratic (LQ) formalism and the magnitude of errors associated with its use in assessing biologic equivalence between single, high radiation doses and hypofractionated radiation doses. Methods and Materials: V79 and EMT6 single cells received single doses of 2-12 Gy or two or three fractions of 4 or 5 Gy, each at 4-h intervals. Single and fractionated doses to actually reduce the cell survival to the same level were determined by a colony assay. The {alpha}/{beta} ratio was obtained from the cell survival curves. Using the {alpha}/{beta} ratio and the LQ formalism, equivalent single doses for the hypofractionated doses were calculated. They were then compared with the actually determined equivalent single doses for the hypofractionated doses. The V79 spheroids received single doses of 5-26 Gy or two to five fractions of 5-12 Gy at 2 or 4-h interval, and then were assayed for cell survival. Next, equivalent single doses for the hypofractionated doses were determined, as were done for the single cells. Results: The {alpha}/{beta} ratio was 5.1 Gy for the V79 single cells and 0.36 Gy for EMT6. In V79, the equivalent single doses for the hypofractionated doses calculated using the LQ formalism were 12-19% lower than the actually measured biologically equivalent single doses. In the EMT6 cells, this trend was also seen, but the differences were not significant. In the V79 spheroids, the calculated doses were 18-30% lower than the measured doses. Conclusion: Conversion of hypofractionated radiation doses to single doses using the LQ formalism could underestimate the effect of hypofractionated radiation by {<=}30%.

  16. Adaptive and Optimal Control of Stochastic Dynamical Systems

    DTIC Science & Technology

    2015-09-14

    control and stochastic differential games . Stochastic linear-quadratic, continuous time, stochastic control problems are solved for systems with noise...control problems for systems with arbitrary correlated n 15. SUBJECT TERMS Adaptive control, optimal control, stochastic differential games 16. SECURITY...explicit results have been obtained for problems of stochastic control and stochastic differential games . Stochastic linear- quadratic, continuous time

  17. Adaptive Error Estimation in Linearized Ocean General Circulation Models

    NASA Technical Reports Server (NTRS)

    Chechelnitsky, Michael Y.

    1999-01-01

    Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large

  18. Some Randomized Algorithms for Convex Quadratic Programming

    SciTech Connect

    Goldbach, R.

    1999-01-15

    We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a unified and elegant presentation and analysis. We also show that LP-type problems include minimization of a convex quadratic function subject to convex quadratic constraints as a special case, for which the algorithms can be implemented efficiently, if only linear constraints are present. We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical results. Even though the framework of LP-type problems may appear rather abstract at first, application of the methods considered in this paper to a given problem of that type is easy and efficient. Moreover, our proofs are in fact rather simple, since many technical details of more explicit problem representations are handled in a uniform manner by our approach. In particular, we do not assume boundedness of the feasible set as required in related methods.

  19. Compatibility of the Linear-Quadratic Formalism and Biologically Effective Dose Concept to High-Dose-Per-Fraction Irradiation in a Murine Tumor

    SciTech Connect

    Otsuka, Shinya; Shibamoto, Yuta; Iwata, Hiromitsu; Murata, Rumi; Sugie, Chikao; Ito, Masato; Ogino, Hiroyuki

    2011-12-01

    Purpose: To evaluate the compliance of linear-quadratic (LQ) model calculations in the high-dose range as used in stereotactic irradiation in a murine tumor model. Methods and Materials: Female 10-week-old Balb/c mice bearing 1-cm-diameter EMT6 tumors in the hind legs were used. Single doses of 10-25 Gy were compared with 2-5 fractions of 4-13 Gy given at 4-hour intervals. Cell survival after irradiation was determined by an in vivo-in vitro assay. Using an {alpha}/{beta} ratio determined for in vitro EMT6 cells and the LQ formalism, equivalent single doses for the hypofractionated doses were calculated. They were then compared with actually measured equivalent single doses for the hypofractionated doses. These fractionation schedules were also compared simultaneously to investigate the concordance/divergence of dose-survival curves plotted against actual radiation doses and biologically effective doses (BED). Results: Equivalent single doses for hypofractionated doses calculated from LQ formalism were lower than actually measured doses by 21%-31% in the 2- or 3-fraction experiments and by 27%-42% in the 4- or 5-fraction experiments. The differences were all significant. When a higher {alpha}/{beta} ratio was assumed, the discrepancy became smaller. In direct comparison of the 2- to 5-fraction schedules, respective dose-response curves almost overlapped when cell survival was plotted against actual radiation doses. However, the curves tended to shift downward by increasing the fraction number when cell survival was plotted against BED calculated using an {alpha}/{beta} ratio of 3.5 Gy for in vitro EMT6 cells. Conclusion: Conversion of hypofractionated radiation doses to single doses using the LQ formalism underestimated the in vivo effect of hypofractionated radiation by approximately 20%-40%. The discrepancy appeared to be larger than that seen in the previous in vitro study and tended to increase with the fraction number. BED appeared to be an unreliable measure

  20. Effects of oxygen on intrinsic radiation sensitivity: A test of the relationship between aerobic and hypoxic linear-quadratic (LQ) model parameters

    SciTech Connect

    Carlson, David J.; Stewart, Robert D.; Semenenko, Vladimir A.

    2006-09-15

    The poor treatment prognosis for tumors with high levels of hypoxia is usually attributed to the decreased sensitivity of hypoxic cells to ionizing radiation. Mechanistic considerations suggest that linear quadratic (LQ) survival model radiosensitivity parameters for hypoxic (H) and aerobic (A) cells are related by {alpha}{sub H}={alpha}{sub A}/oxygen enhancement ratio (OER) and ({alpha}/{beta}){sub H}=OER({alpha}/{beta}){sub A}. The OER parameter may be interpreted as the ratio of the dose to the hypoxic cells to the dose to the aerobic cells required to produce the same number of DSBs per cell. The validity of these expressions is tested against survival data for mammalian cells irradiated in vitro with low- and high-LET radiation. Estimates of hypoxic and aerobic radiosensitivity parameters are derived from independent and simultaneous least-squares fits to the survival data. An external bootstrap procedure is used to test whether independent fits to the survival data give significantly better predictions than simultaneous fits to the aerobic and hypoxic data. For low-LET radiation, estimates of the OER derived from the in vitro data are between 2.3 and 3.3 for extreme levels of hypoxia. The estimated range for the OER is similar to the oxygen enhancement ratios reported in the literature for the initial yield of DSBs. The half-time for sublethal damage repair was found to be independent of oxygen concentration. Analysis of patient survival data for cervix cancer suggests an average OER less than or equal to 1.5, which corresponds to a pO{sub 2} of 5 mm Hg (0.66%) in the in vitro experiments. Because the OER derived from the cervix cancer data is averaged over cells at all oxygen levels, cells irradiated in vivo under extreme levels of hypoxia (<0.5 mm Hg) may have an OER substantially higher than 1.5. The reported analyses of in vitro data, as well as mechanistic considerations, provide strong support for the expressions relating hypoxic and aerobic

  1. Asymptotic Linearity of Optimal Control Modification Adaptive Law with Analytical Stability Margins

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.

    2010-01-01

    Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained. Using the gradient projection operator, a free design parameter of the adaptive law can be selected to satisfy stability margins.

  2. On Quantization of Quadratic Poisson Structures

    NASA Astrophysics Data System (ADS)

    Manchon, D.; Masmoudi, M.; Roux, A.

    Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.

  3. Bounded Linear Stability Analysis - A Time Delay Margin Estimation Approach for Adaptive Control

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Ishihara, Abraham K.; Krishnakumar, Kalmanje Srinlvas; Bakhtiari-Nejad, Maryam

    2009-01-01

    This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.

  4. Linear and Angolar Moment of a general spherical TEM and DEM beam radio wave detection with a quadratic order system processor in state of art technology implementation: a three axis sensors array quadratic order correlator for the 21cm radiation radio detection coming from Early Universe

    NASA Astrophysics Data System (ADS)

    Romano, Francesco; Trifiletti, Alessandro; Cimmino, Rosario F.

    2016-07-01

    The paper focuses on an innovative spherical wave beam quadratic order processor, HSCS-1. It is an IP, Coulob Gauge based, to directly mesure, ∀t and in any single P ∀P (along the propagation axis too) the quadratic order Poynting Vector, with both the complex Linear Momentum (LiM) and Angolar Momentum (AnM) contributions, as well as the mutual quadratic order coherence function of any total or pseudo monochromatic observed beam wave. The focoused spherical quadratic order method, directly mesure the spherical complex OAM (time and propagation axsis invariant) which is composed by the observed beam wave modes. Such solenoidal energy modes, becomes relevant to mesure far distance (as exemple: distance greater than billions of light years away) sources radiations. Furthermore, HSCS-1 contemporary and directly measure the mutual (spatial as well as temporal) complex coherence of any general complex divergent or not strictly TEM (as example: TEM+DEM) observed radiations. Tipically TEM+DEM radiations are characterized by N=LPM+1 complex wave beam modes. N is the number of considered EM fields modes, as great as requested; N and L are integer, which values are internal to a closed interval [0; ∞] P and M are integer, which values are internal to a closed interval [1; ∞] n=0,1,…,N is the mode or beam channel index; with l=0, 1,…,L; p= 1,…, P; and m = 1,…,M; n=l=0 is the fundamental mode index). Here are considered only the wave beam modes which satisfy the related Helmoltz monochromatic wave equation soluctions. As well known in Physics, only adopting a quadratic order energy processor it is possible ∀t to contemporary and directely mesure in P, ∀P(θ Φ z) and ∀(P-P0), both the proper P0 position and quantity of motion (proper space time variations), or by a Fourier Transformation to contemporary and directely mesure proper phase and frequency spectrum variations, of the observed general radiation source.

  5. Self-Replicating Quadratics

    ERIC Educational Resources Information Center

    Withers, Christopher S.; Nadarajah, Saralees

    2012-01-01

    We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

  6. Differential adaptation of the linear and nonlinear components of the horizontal vestibuloocular reflex in squirrel monkeys

    NASA Technical Reports Server (NTRS)

    Clendaniel, Richard A.; Lasker, David M.; Minor, Lloyd B.; Shelhamer, M. J. (Principal Investigator)

    2002-01-01

    Previous work in squirrel monkeys has demonstrated the presence of linear and nonlinear components to the horizontal vestibuloocular reflex (VOR) evoked by high-acceleration rotations. The nonlinear component is seen as a rise in gain with increasing velocity of rotation at frequencies more than 2 Hz (a velocity-dependent gain enhancement). We have shown that there are greater changes in the nonlinear than linear component of the response after spectacle-induced adaptation. The present study was conducted to determine if the two components of the response share a common adaptive process. The gain of the VOR, in the dark, to sinusoidal stimuli at 4 Hz (peak velocities: 20-150 degrees /s) and 10 Hz (peak velocities: 20 and 100 degrees /s) was measured pre- and postadaptation. Adaptation was induced over 4 h with x0.45 minimizing spectacles. Sum-of-sines stimuli were used to induce adaptation, and the parameters of the stimuli were adjusted to invoke only the linear or both linear and nonlinear components of the response. Preadaptation, there was a velocity-dependent gain enhancement at 4 and 10 Hz. In postadaptation with the paradigms that only recruited the linear component, there was a decrease in gain and a persistent velocity-dependent gain enhancement (indicating adaptation of only the linear component). After adaptation with the paradigm designed to recruit both the linear and nonlinear components, there was a decrease in gain and no velocity-dependent gain enhancement (indicating adaptation of both components). There were comparable changes in the response to steps of acceleration. We interpret these results to indicate that separate processes drive the adaptation of the linear and nonlinear components of the response.

  7. [Evaluation of an adaptive filter for CT under low-CNR condition: comparison with linear filter].

    PubMed

    Mori, Issei; Uchida, Miho; Sato, Ami; Sato, Shingo; Tamura, Hajime; Takai, Yoshihiro; Ishibashi, Tadashi; Saito, Haruo; Hosokai, Yoshiyuki; Ogura, Takahide; Chida, Koichi; Machida, Yoshio

    2009-01-20

    The use of an adaptive filter for CT images is becoming a common procedure and is said to reduce image noise while preserving sharpness and helping to reduce the required X-ray dose. Although many reports support this view, the validity of such evaluations is arguable. When the linearity of a system is in question, physical performance indexes should be measured under conditions similar to those of clinical use. Evaluations of diagnosis using clinical images may be fallible because the non-filtered image used as the reference might not have been optimally reconstructed. We have chosen simple, but commonly used, adaptive filters for our evaluation. As a reference for comparing performance, we designed linear filters that best approximate the noise characteristics of the adaptive filters. MTF is measured through observation of the edge-spread function. Clinical abdominal images are used to compare the performance of adaptive filters and linear filters. We conclude that the performance of the type of adaptive filter we have chosen is virtually the same as that of the linear filter, as long as the image quality of soft tissues is our interest. Both the noise SD and MTF are virtually the same if the contrast of the object is not substantially higher than 150 HU. Images of soft tissues obtained with the use of adaptive filters are also virtually the same as those obtained by linear filters. The edge-preservation characteristic of this adaptive filter is not observable for soft tissues.

  8. A Self-Adaptive Projection and Contraction Method for Linear Complementarity Problems

    SciTech Connect

    Liao Lizhi Wang Shengli

    2003-10-15

    In this paper we develop a self-adaptive projection and contraction method for the linear complementarity problem (LCP). This method improves the practical performance of the modified projection and contraction method by adopting a self-adaptive technique. The global convergence of our new method is proved under mild assumptions. Our numerical tests clearly demonstrate the necessity and effectiveness of our proposed method.

  9. Model reference adaptive control for linear time varying and nonlinear systems

    NASA Technical Reports Server (NTRS)

    Abida, L.; Kaufman, H.

    1982-01-01

    Model reference adaptive control is applied to linear time varying systems and to nonlinear systems amenable to virtual linearization. Asymptotic stability is guaranteed even if the perfect model following conditions do not hold, provided that some sufficient conditions are satisfied. Simulations show the scheme to be capable of effectively controlling certain nonlinear systems.

  10. Adjustment of Adaptive Gain with Bounded Linear Stability Analysis to Improve Time-Delay Margin for Metrics-Driven Adaptive Control

    NASA Technical Reports Server (NTRS)

    Bakhtiari-Nejad, Maryam; Nguyen, Nhan T.; Krishnakumar, Kalmanje Srinvas

    2009-01-01

    This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a linear damaged twin-engine generic transport model of aircraft. The analysis shows that the system with the adjusted adaptive gain becomes more robust to unmodeled dynamics or time delay.

  11. Linear and quadratic magneto-optical Kerr effect investigation of Co2Mn1.30Si0.84 epitaxially grown on MgO

    NASA Astrophysics Data System (ADS)

    Liu, Jihong; Qiao, Shuang; Wang, Shufang; Fu, Guangsheng

    2017-01-01

    We investigated the magneto-optical properties of a L21 ordered nonstoichiometric Co2Mn1.30Si0.84 film epitaxially grown on a MgO-buffered MgO (001) single-crystal substrate. Longitudinal magneto-optical Kerr effects (LMOKE) and rotating magneto-optical Kerr effect (ROT-MOKE) measurements suggest that the film exhibits a cubic magnetic anisotropy with the extracted cubic anisotropy constant of KC = 6.7 ×104 erg / cm3 . Orientation-dependent ROT-MOKE suggest that the quadratic magneto-optical Kerr effects (QMOKE) components also show fourfold symmetry with a modest amplitude of 3 mdeg, which is in accordance with complex Kerr angle expression for cubic symmetry systems. Our results suggest that ROT-MOKE is not only an efficient method to determine magnetic anisotropy parameters but also a good method to extract QMOKE components.

  12. Adaptive superposition of finite element meshes in linear and nonlinear dynamic analysis

    NASA Astrophysics Data System (ADS)

    Yue, Zhihua

    2005-11-01

    The numerical analysis of transient phenomena in solids, for instance, wave propagation and structural dynamics, is a very important and active area of study in engineering. Despite the current evolutionary state of modern computer hardware, practical analysis of large scale, nonlinear transient problems requires the use of adaptive methods where computational resources are locally allocated according to the interpolation requirements of the solution form. Adaptive analysis of transient problems involves obtaining solutions at many different time steps, each of which requires a sequence of adaptive meshes. Therefore, the execution speed of the adaptive algorithm is of paramount importance. In addition, transient problems require that the solution must be passed from one adaptive mesh to the next adaptive mesh with a bare minimum of solution-transfer error since this form of error compromises the initial conditions used for the next time step. A new adaptive finite element procedure (s-adaptive) is developed in this study for modeling transient phenomena in both linear elastic solids and nonlinear elastic solids caused by progressive damage. The adaptive procedure automatically updates the time step size and the spatial mesh discretization in transient analysis, achieving the accuracy and the efficiency requirements simultaneously. The novel feature of the s-adaptive procedure is the original use of finite element mesh superposition to produce spatial refinement in transient problems. The use of mesh superposition enables the s-adaptive procedure to completely avoid the need for cumbersome multipoint constraint algorithms and mesh generators, which makes the s-adaptive procedure extremely fast. Moreover, the use of mesh superposition enables the s-adaptive procedure to minimize the solution-transfer error. In a series of different solid mechanics problem types including 2-D and 3-D linear elastic quasi-static problems, 2-D material nonlinear quasi-static problems

  13. Quadratic Generalized Scale Invariance

    NASA Astrophysics Data System (ADS)

    Lovejoy, S.; Schertzer, D.; Addor, J. B.

    Nearly twenty years ago, two of us argued that in order to account for the scaling strat- ification of the atmosphere, that an anisotropic "unified scaling model" of the atmo- sphere was required with elliptical dimension 23/9=2.555... "in between" the standard 3-D (small scale) and 2-D large scale model. This model was based on the formal- ism of generalized scale invariance (GSI). Physically, GSI is justified by arguing that various conserved fluxes (energy, buoyancy force variance etc.) should define the ap- propriate notion of scale. In a recent large scale satellite cloud image analysis, we directly confirmed this model by studying the isotropic (angle averaged) horizontal cloud statistics. Mathematically, GSI is based on a a group of scale changing opera- tors and their generators but to date, both analyses (primarily of cloud images) and nu- merical (multifractal) simulations, have been limited to the special case of linear GSI. This has shown that cloud texture can plausibly be associated with local linearizations. However realistic morphologies involve spatially avarying textures; the full non linear GSI is clearly necessary. In this talk, we first show that the observed angle averaged (multi)scaling statistics only give a realtively weak constraint on the nonlinear gner- ator: that the latter can be expressed by self-similar (isotropic) part, and a deviatoric part described (in two dimensions) by an arbitrary scalar potential which contains all the information about the cloud morphology. We then show (using a theorem due to Poincaré) how to reduce nonlinear GSI to linear GSI plus a nonlinear coordinate trans- formation numerically, using this to take multifractal GSI modelling to the next level of approximation: quadratic GSI. We show many examples of the coresponding simu- lations which include transitions from various morphologies (including cyclones) and we discuss the results in relation to satellite cloud images.

  14. Unmasking the linear behaviour of slow motor adaptation to prolonged convergence.

    PubMed

    Erkelens, Ian M; Thompson, Benjamin; Bobier, William R

    2016-06-01

    Adaptation to changing environmental demands is central to maintaining optimal motor system function. Current theories suggest that adaptation in both the skeletal-motor and oculomotor systems involves a combination of fast (reflexive) and slow (recalibration) mechanisms. Here we used the oculomotor vergence system as a model to investigate the mechanisms underlying slow motor adaptation. Unlike reaching with the upper limbs, vergence is less susceptible to changes in cognitive strategy that can affect the behaviour of motor adaptation. We tested the hypothesis that mechanisms of slow motor adaptation reflect early neural processing by assessing the linearity of adaptive responses over a large range of stimuli. Using varied disparity stimuli in conflict with accommodation, the slow adaptation of tonic vergence was found to exhibit a linear response whereby the rate (R(2)  = 0.85, P < 0.0001) and amplitude (R(2)  = 0.65, P < 0.0001) of the adaptive effects increased proportionally with stimulus amplitude. These results suggest that this slow adaptive mechanism is an early neural process, implying a fundamental physiological nature that is potentially dominated by subcortical and cerebellar substrates.

  15. Adaptive inverse control of linear and nonlinear systems using dynamic neural networks.

    PubMed

    Plett, G L

    2003-01-01

    In this paper, we see adaptive control as a three-part adaptive-filtering problem. First, the dynamical system we wish to control is modeled using adaptive system-identification techniques. Second, the dynamic response of the system is controlled using an adaptive feedforward controller. No direct feedback is used, except that the system output is monitored and used by an adaptive algorithm to adjust the parameters of the controller. Third, disturbance canceling is performed using an additional adaptive filter. The canceler does not affect system dynamics, but feeds back plant disturbance in a way that minimizes output disturbance power. The techniques work to control minimum-phase or nonminimum-phase, linear or nonlinear, single-input-single-output (SISO) or multiple-input-multiple-ouput (MIMO), stable or stabilized systems. Constraints may additionally be placed on control effort for a practical implementation. Simulation examples are presented to demonstrate that the proposed methods work very well.

  16. Adaptive stabilization of discrete-time systems using linear periodically time varying controllers

    NASA Technical Reports Server (NTRS)

    Ortega, Romeo; Albertos, Pedro; Lozano, Rogelio

    1988-01-01

    A direct adaptive scheme based on the use of linear time-varying periodic controllers is proposed which estimates online the periodic coefficients of the controller. It is shown that adaptive stabilization is attained for all possibly nonstably invertible plants of known order but unknown delay. Although no appeal is made to persistency of excitation arguments, a provision is needed to avoid the singularity of an estimated matrix, this property being required only for the analysis and not the control calculations.

  17. Quadratic eigenvalue problems.

    SciTech Connect

    Walsh, Timothy Francis; Day, David Minot

    2007-04-01

    In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.

  18. Tandem time-of-flight mass spectrometer for photodissociation of biopolymer ions generated by matrix-assisted laser desorption ionization (MALDI-TOF-PD-TOF) using a linear-plus-quadratic potential reflectron.

    PubMed

    Oh, Joo Yeon; Moon, Jeong Hee; Kim, Myung Soo

    2004-08-01

    A tandem time-of-flight mass spectrometer for the study of photodissociation of biopolymer ions generated by matrix-assisted laser desorption ionization was designed and constructed. A reflectron with linear and quadratic (LPQ) potential components was used. Characteristics of the LPQ reflectron and its utility as the second stage analyzer of the tandem mass spectrometer were investigated. Performance of the instrument was tested by observing photodissociation of [M + H](+) from angiotensin II, a prototype polypeptide. Quality of the photodissociation tandem mass spectrum was almost comparable to that of the post-source decay spectrum. Monoisotopic selection of the parent ion was possible, which was achieved through the ion beam-laser beam synchronization. General theoretical considerations needed for a successful photodissociation of large biopolymer ions are also presented.

  19. Adaptive Control for Linear Uncertain Systems with Unmodeled Dynamics Revisited via Optimal Control Modification

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan

    2013-01-01

    This paper presents the optimal control modification for linear uncertain plants. The Lyapunov analysis shows that the modification parameter has a limiting value depending on the nature of the uncertainty. The optimal control modification exhibits a linear asymptotic property that enables it to be analyzed in a linear time invariant framework for linear uncertain plants. The linear asymptotic property shows that the closed-loop plants in the limit possess a scaled input-output mapping. Using this property, we can derive an analytical closed-loop transfer function in the limit as the adaptive gain tends to infinity. The paper revisits the Rohrs counterexample problem that illustrates the nature of non-robustness of model-reference adaptive control in the presence of unmodeled dynamics. An analytical approach is developed to compute exactly the modification parameter for the optimal control modification that stabilizes the plant in the Rohrs counterexample. The linear asymptotic property is also used to address output feedback adaptive control for non-minimum phase plants with a relative degree 1.

  20. An adaptive observer for single-input single-output linear systems

    NASA Technical Reports Server (NTRS)

    Carroll, R. L.; Lindorff, D. P.

    1972-01-01

    It is shown that the full order adaptive observer for single input, single output, observable, continuous, stable, linear differential systems in the absence of a deterministic or random disturbance vector guarantees the vanishing of observation error, regardless of the size of the constant or slowly varying parameter ignorance. The observer parameters are directly changed in a Liapunov adaptive way so as to eventually yield the unknown full order Luenberger observer. The observer poles throughout may be placed freely in the stable region and no derivatives are required in the adaptive law.

  1. Intelligent control of non-linear dynamical system based on the adaptive neurocontroller

    NASA Astrophysics Data System (ADS)

    Engel, E.; Kovalev, I. V.; Kobezhicov, V.

    2015-10-01

    This paper presents an adaptive neuro-controller for intelligent control of non-linear dynamical system. The formed as the fuzzy selective neural net the adaptive neuro-controller on the base of system's state, creates the effective control signal under random perturbations. The validity and advantages of the proposed adaptive neuro-controller are demonstrated by numerical simulations. The simulation results show that the proposed controller scheme achieves real-time control speed and the competitive performance, as compared to PID, fuzzy logic controllers.

  2. Using quadratic simplicial elements for hierarchical approximation and visualization

    NASA Astrophysics Data System (ADS)

    Wiley, David F.; Childs, Henry R.; Hamann, Bernd; Joy, Kenneth I.; Max, Nelson

    2002-03-01

    Best quadratic simplicial spline approximations can be computed, using quadratic Bernstein-Bezier basis functions, by identifying and bisecting simplicial elements with largest errors. Our method begins with an initial triangulation of the domain; a best quadratic spline approximation is computed; errors are computed for all simplices; and simplices of maximal error are subdivided. This process is repeated until a user-specified global error tolerance is met. The initial approximations for the unit square and cube are given by two quadratic triangles and five quadratic tetrahedra, respectively. Our more complex triangulation and approximation method that respects field discontinuities and geometrical features allows us to better approximate data. Data is visualized by using the hierarchy of increasingly better quadratic approximations generated by this process. Many visualization problems arise for quadratic elements. First tessellating quadratic elements with smaller linear ones and then rendering the smaller linear elements is one way to visualize quadratic elements. Our results show a significant reduction in the number of simplices required to approximate data sets when using quadratic elements as compared to using linear elements.

  3. Incremental harmonic balance method for predicting amplitudes of a multi-d.o.f. non-linear wheel shimmy system with combined Coulomb and quadratic damping

    NASA Astrophysics Data System (ADS)

    Zhou, J. X.; Zhang, L.

    2005-01-01

    Incremental harmonic balance (IHB) formulations are derived for general multiple degrees of freedom (d.o.f.) non-linear autonomous systems. These formulations are developed for a concerned four-d.o.f. aircraft wheel shimmy system with combined Coulomb and velocity-squared damping. A multi-harmonic analysis is performed and amplitudes of limit cycles are predicted. Within a large range of parametric variations with respect to aircraft taxi velocity, the IHB method can, at a much cheaper cost, give results with high accuracy as compared with numerical results given by a parametric continuation method. In particular, the IHB method avoids the stiff problems emanating from numerical treatment of aircraft wheel shimmy system equations. The development is applicable to other vibration control systems that include commonly used dry friction devices or velocity-squared hydraulic dampers.

  4. Digital redesign of the decentralised adaptive tracker for linear large-scale systems

    NASA Astrophysics Data System (ADS)

    Lin, Ming-Hong; Sheng-Hong Tsai, Jason; Chen, Chia-Wei; Guo, Shu-Mei; Chu, Che-An

    2010-02-01

    A novel digital redesign of the analogue model-reference-based decentralized adaptive tracker is proposed for the sampled-data large scale system consisting of N interconnected linear subsystems, so that the system output will follow any trajectory specified at sampling instant which may not be presented by the analytic reference initially, and shows that the proposed decentralized controller induces a good robustness on the decoupling of the closed-loop controlled system. The adaptation of the analogue controller gain is derived by using the model-reference adaptive control theory based on Lyapunov's method. In this article, it is shown that using the sampled-data decentralized adaptive control system it is theoretically possible to asymptotically track the desired output with a desired performance. It is assumed that all the controllers share their prior information and the principal result is derived when they cooperate implicitly. Based on the prediction-based digital redesign methodology, the optimal digital redesigned tracker for the sampled-data decentralised adaptive control systems is newly proposed. An illustrative example of interconnected linear system is presented to demonstrate the effectiveness of the proposed design methodology.

  5. Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems

    NASA Technical Reports Server (NTRS)

    Downie, John D.; Goodman, Joseph W.

    1989-01-01

    The accuracy requirements of optical processors in adaptive optics systems are determined by estimating the required accuracy in a general optical linear algebra processor (OLAP) that results in a smaller average residual aberration than that achieved with a conventional electronic digital processor with some specific computation speed. Special attention is given to an error analysis of a general OLAP with regard to the residual aberration that is created in an adaptive mirror system by the inaccuracies of the processor, and to the effect of computational speed of an electronic processor on the correction. Results are presented on the ability of an OLAP to compete with a digital processor in various situations.

  6. An adaptive locally linear embedding manifold learning approach for hyperspectral target detection

    NASA Astrophysics Data System (ADS)

    Ziemann, Amanda K.; Messinger, David W.

    2015-05-01

    Algorithms for spectral analysis commonly use parametric or linear models of the data. Research has shown, however, that hyperspectral data -- particularly in materially cluttered scenes -- are not always well-modeled by statistical or linear methods. Here, we propose an approach to hyperspectral target detection that is based on a graph theory model of the data and a manifold learning transformation. An adaptive nearest neighbor (ANN) graph is built on the data, and then used to implement an adaptive version of locally linear embedding (LLE). We artificially induce a target manifold and incorporate it into the adaptive LLE transformation. The artificial target manifold helps to guide the separation of the target data from the background data in the new, transformed manifold coordinates. Then, target detection is performed in the manifold space using Spectral Angle Mapper. This methodology is an improvement over previous iterations of this approach due to the incorporation of ANN, the artificial target manifold, and the choice of detector in the transformed space. We implement our approach in a spatially local way: the image is delineated into square tiles, and the detection maps are normalized across the entire image. Target detection results will be shown using laboratory-measured and scene-derived target data from the SHARE 2012 collect.

  7. A new adaptive multiple modelling approach for non-linear and non-stationary systems

    NASA Astrophysics Data System (ADS)

    Chen, Hao; Gong, Yu; Hong, Xia

    2016-07-01

    This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.

  8. Multiple linear combination (MLC) regression tests for common variants adapted to linkage disequilibrium structure

    PubMed Central

    Yoo, Yun Joo; Sun, Lei; Poirier, Julia G.; Paterson, Andrew D.

    2016-01-01

    ABSTRACT By jointly analyzing multiple variants within a gene, instead of one at a time, gene‐based multiple regression can improve power, robustness, and interpretation in genetic association analysis. We investigate multiple linear combination (MLC) test statistics for analysis of common variants under realistic trait models with linkage disequilibrium (LD) based on HapMap Asian haplotypes. MLC is a directional test that exploits LD structure in a gene to construct clusters of closely correlated variants recoded such that the majority of pairwise correlations are positive. It combines variant effects within the same cluster linearly, and aggregates cluster‐specific effects in a quadratic sum of squares and cross‐products, producing a test statistic with reduced degrees of freedom (df) equal to the number of clusters. By simulation studies of 1000 genes from across the genome, we demonstrate that MLC is a well‐powered and robust choice among existing methods across a broad range of gene structures. Compared to minimum P‐value, variance‐component, and principal‐component methods, the mean power of MLC is never much lower than that of other methods, and can be higher, particularly with multiple causal variants. Moreover, the variation in gene‐specific MLC test size and power across 1000 genes is less than that of other methods, suggesting it is a complementary approach for discovery in genome‐wide analysis. The cluster construction of the MLC test statistics helps reveal within‐gene LD structure, allowing interpretation of clustered variants as haplotypic effects, while multiple regression helps to distinguish direct and indirect associations. PMID:27885705

  9. The Mystical "Quadratic Formula."

    ERIC Educational Resources Information Center

    March, Robert H.

    1993-01-01

    Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

  10. A Quadratic Spring Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  11. Adaptive iterative learning control for a class of non-linearly parameterised systems with input saturations

    NASA Astrophysics Data System (ADS)

    Zhang, Ruikun; Hou, Zhongsheng; Ji, Honghai; Yin, Chenkun

    2016-04-01

    In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov-Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L2[0, T] convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.

  12. Adaptive H∞ nonlinear velocity tracking using RBFNN for linear DC brushless motor

    NASA Astrophysics Data System (ADS)

    Tsai, Ching-Chih; Chan, Cheng-Kain; Li, Yi Yu

    2012-01-01

    This article presents an adaptive H ∞ nonlinear velocity control for a linear DC brushless motor. A simplified model of this motor with friction is briefly recalled. The friction dynamics is described by the Lu Gre model and the online tuning radial basis function neural network (RBFNN) is used to parameterise the nonlinear friction function and un-modelled errors. An adaptive nonlinear H ∞ control method is then proposed to achieve velocity tracking, by assuming that the upper bounds of the ripple force, the changeable load and the nonlinear friction can be learned by the RBFNN. The closed-loop system is proven to be uniformly bounded using the Lyapunov stability theory. The feasibility and the efficacy of the proposed control are exemplified by conducting two velocity tracking experiments.

  13. Model-free adaptive fractional order control of stable linear time-varying systems.

    PubMed

    Yakoub, Z; Amairi, M; Chetoui, M; Saidi, B; Aoun, M

    2017-03-01

    This paper presents a new model-free adaptive fractional order control approach for linear time-varying systems. An online algorithm is proposed to determine some frequency characteristics using a selective filtering and to design a fractional PID controller based on the numerical optimization of the frequency-domain criterion. When the system parameters are time-varying, the controller is updated to keep the same desired performances. The main advantage of the proposed approach is that the controller design depends only on the measured input and output signals of the process. The effectiveness of the proposed method is assessed through a numerical example.

  14. Stability of Wilkinson's linear model of prism adaptation over time for various targets.

    PubMed

    Wallace, B

    1977-01-01

    Prism adaptation as measured by negative aftereffects (NA), proprioceptive shifts (PS), and visual shifts (VS) was assessed as a function of amount of exposure time and target specificity, whether an exposure and a test target background were the same or different, to determine the validity of Wilkinson's linear model (NA = PS + VS). With few exceptions the model was found to hold well up to 40 min of prism viewing regardless of type of exposure background. In addition target specificity affected magnitude of the NA component of adapation but not the PS and the VS components.

  15. Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

    NASA Technical Reports Server (NTRS)

    Balas, M. J.; Kaufman, H.; Wen, J.

    1985-01-01

    A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

  16. Optimisation of substrate blends in anaerobic co-digestion using adaptive linear programming.

    PubMed

    García-Gen, Santiago; Rodríguez, Jorge; Lema, Juan M

    2014-12-01

    Anaerobic co-digestion of multiple substrates has the potential to enhance biogas productivity by making use of the complementary characteristics of different substrates. A blending strategy based on a linear programming optimisation method is proposed aiming at maximising COD conversion into methane, but simultaneously maintaining a digestate and biogas quality. The method incorporates experimental and heuristic information to define the objective function and the linear restrictions. The active constraints are continuously adapted (by relaxing the restriction boundaries) such that further optimisations in terms of methane productivity can be achieved. The feasibility of the blends calculated with this methodology was previously tested and accurately predicted with an ADM1-based co-digestion model. This was validated in a continuously operated pilot plant, treating for several months different mixtures of glycerine, gelatine and pig manure at organic loading rates from 1.50 to 4.93 gCOD/Ld and hydraulic retention times between 32 and 40 days at mesophilic conditions.

  17. Single-photon quadratic optomechanics

    PubMed Central

    Liao, Jie-Qiao; Nori, Franco

    2014-01-01

    We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon. PMID:25200128

  18. AdS waves as exact solutions to quadratic gravity

    SciTech Connect

    Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin

    2011-04-15

    We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.

  19. L1-norm locally linear representation regularization multi-source adaptation learning.

    PubMed

    Tao, Jianwen; Wen, Shiting; Hu, Wenjun

    2015-09-01

    In most supervised domain adaptation learning (DAL) tasks, one has access only to a small number of labeled examples from target domain. Therefore the success of supervised DAL in this "small sample" regime needs the effective utilization of the large amounts of unlabeled data to extract information that is useful for generalization. Toward this end, we here use the geometric intuition of manifold assumption to extend the established frameworks in existing model-based DAL methods for function learning by incorporating additional information about the target geometric structure of the marginal distribution. We would like to ensure that the solution is smooth with respect to both the ambient space and the target marginal distribution. In doing this, we propose a novel L1-norm locally linear representation regularization multi-source adaptation learning framework which exploits the geometry of the probability distribution, which has two techniques. Firstly, an L1-norm locally linear representation method is presented for robust graph construction by replacing the L2-norm reconstruction measure in LLE with L1-norm one, which is termed as L1-LLR for short. Secondly, considering the robust graph regularization, we replace traditional graph Laplacian regularization with our new L1-LLR graph Laplacian regularization and therefore construct new graph-based semi-supervised learning framework with multi-source adaptation constraint, which is coined as L1-MSAL method. Moreover, to deal with the nonlinear learning problem, we also generalize the L1-MSAL method by mapping the input data points from the input space to a high-dimensional reproducing kernel Hilbert space (RKHS) via a nonlinear mapping. Promising experimental results have been obtained on several real-world datasets such as face, visual video and object.

  20. Linear-scaling symmetry-adapted perturbation theory with scaled dispersion

    SciTech Connect

    Maurer, Simon A.; Beer, Matthias; Lambrecht, Daniel S.; Ochsenfeld, Christian

    2013-11-14

    We present a linear-scaling symmetry-adapted perturbation theory (SAPT) method that is based on an atomic orbital (AO) formulation of zeroth-order SAPT (SAPT0). The non-dispersive terms are realized with linear-scaling cost using both the continuous fast multipole method (CFMM) and the linear exchange (LinK) approach for integral contractions as well as our efficient Laplace-based coupled-perturbed self-consistent field method (DL-CPSCF) for evaluating response densities. The reformulation of the dispersion term is based on our linear-scaling AO Møller-Plesset second-order perturbation theory (AO-MP2) method, that uses our recently introduced QQR-type screening [S. A. Maurer, D. S. Lambrecht, J. Kussmann, and C. Ochsenfeld, J. Chem. Phys. 138, 014101 (2013)] for preselecting numerically significant energy contributions. Similar to scaled opposite-spin MP2, we neglect the exchange-dispersion term in SAPT and introduce a scaling factor for the dispersion term, which compensates for the error and at the same time accounts for basis set incompleteness effects and intramonomer correlation. We show in extensive benchmark calculations that the new scaled-dispersion (sd-)SAPT0 approach provides reliable results for small and large interacting systems where the results with a small 6-31G** basis are roughly comparable to supermolecular MP2 calculations in a triple-zeta basis. The performance of our method is demonstrated with timings on cellulose fragments, DNA systems, and cutouts of a protein-ligand complex with up to 1100 atoms on a single computer core.

  1. Linear hypergeneralization of learned dynamics across movement speeds reveals anisotropic, gain-encoding primitives for motor adaptation.

    PubMed

    Joiner, Wilsaan M; Ajayi, Obafunso; Sing, Gary C; Smith, Maurice A

    2011-01-01

    The ability to generalize learned motor actions to new contexts is a key feature of the motor system. For example, the ability to ride a bicycle or swing a racket is often first developed at lower speeds and later applied to faster velocities. A number of previous studies have examined the generalization of motor adaptation across movement directions and found that the learned adaptation decays in a pattern consistent with the existence of motor primitives that display narrow Gaussian tuning. However, few studies have examined the generalization of motor adaptation across movement speeds. Following adaptation to linear velocity-dependent dynamics during point-to-point reaching arm movements at one speed, we tested the ability of subjects to transfer this adaptation to short-duration higher-speed movements aimed at the same target. We found near-perfect linear extrapolation of the trained adaptation with respect to both the magnitude and the time course of the velocity profiles associated with the high-speed movements: a 69% increase in movement speed corresponded to a 74% extrapolation of the trained adaptation. The close match between the increase in movement speed and the corresponding increase in adaptation beyond what was trained indicates linear hypergeneralization. Computational modeling shows that this pattern of linear hypergeneralization across movement speeds is not compatible with previous models of adaptation in which motor primitives display isotropic Gaussian tuning of motor output around their preferred velocities. Instead, we show that this generalization pattern indicates that the primitives involved in the adaptation to viscous dynamics display anisotropic tuning in velocity space and encode the gain between motor output and motion state rather than motor output itself.

  2. Linear dichroism amplification: Adapting a long-known technique for ultrasensitive femtosecond IR spectroscopy

    SciTech Connect

    Rehault, Julien; Helbing, Jan; Zanirato, Vinicio; Olivucci, Massimo

    2011-03-28

    We demonstrate strong amplification of polarization-sensitive transient IR signals using a pseudo-null crossed polarizer technique first proposed by Keston and Lospalluto [Fed. Proc. 10, 207 (1951)] and applied for nanosecond flash photolysis in the visible by Che et al. [Chem. Phys. Lett. 224, 145 (1994)]. We adapted the technique to ultrafast pulsed laser spectroscopy in the infrared using photoelastic modulators, which allow us to measure amplified linear dichroism at kilohertz repetition rates. The method was applied to a photoswitch of the N-alkylated Schiff base family in order to demonstrate its potential of strongly enhancing sensitivity and signal to noise in ultrafast transient IR experiments, to simplify spectra and to determine intramolecular transition dipole orientations.

  3. Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems

    NASA Astrophysics Data System (ADS)

    Nguyen, Chuong Hoang; Leonessa, Alexander

    2017-02-01

    In this paper, the problem of characterizing adaptive output feedback control laws for a general class of unknown MIMO linear systems is considered. Specifically, the presented control approach relies on three components, i.e., a predictor, a reference model and a controller. The predictor is designed to predict the system's output with arbitrary accuracy, for any admissible control input. Subsequently, a full state feedback control law is designed to control the predictor output to approach the reference system, while the reference system tracks the desired trajectory. Ultimately, the control objective of driving the actual system output to track the desired trajectories is achieved by showing that the system output, the predictor output and the reference system trajectories all converge to each other.

  4. Long-range accelerated BOTDA sensor using adaptive linear prediction and cyclic coding.

    PubMed

    Muanenda, Yonas; Taki, Mohammad; Pasquale, Fabrizio Di

    2014-09-15

    We propose and experimentally demonstrate a long-range accelerated Brillouin optical time domain analysis (BOTDA) sensor that exploits the complementary noise reduction benefits of adaptive linear prediction and optical pulse coding. The combined technique allows using orders of magnitude less the number of averages of the backscattered BOTDA traces compared to a standard single pulse BOTDA, enabling distributed strain measurement over 10 km of a standard single mode fiber with meter-scale spatial resolution and 1.8 MHz Brillouin frequency shift resolution. By optimizing the system parameters, the measurement is achieved with only 20 averages for each Brillouin gain spectrum scanned frequency, allowing for an eight times faster strain measurement compared to the use of cyclic pulse coding alone.

  5. Missing pixels restoration for remote sensing images using adaptive search window and linear regression

    NASA Astrophysics Data System (ADS)

    Tai, Shen-Chuan; Chen, Peng-Yu; Chao, Chian-Yen

    2016-07-01

    The Consultative Committee for Space Data Systems proposed an efficient image compression standard that can do lossless compression (CCSDS-ICS). CCSDS-ICS is the most widely utilized standard for satellite communications. However, the original CCSDS-ICS is weak in terms of error resilience with even a single incorrect bit possibly causing numerous missing pixels. A restoration algorithm based on the neighborhood similar pixel interpolator is proposed to fill in missing pixels. The linear regression model is used to generate the reference image from other panchromatic or multispectral images. Furthermore, an adaptive search window is utilized to sieve out similar pixels from the pixels in the search region defined in the neighborhood similar pixel interpolator. The experimental results show that the proposed methods are capable of reconstructing missing regions with good visual quality.

  6. Quadratic algebras for three-dimensional superintegrable systems

    SciTech Connect

    Daskaloyannis, C. Tanoudis, Y.

    2010-02-15

    The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.

  7. Adapting Predictive Models for Cepheid Variable Star Classification Using Linear Regression and Maximum Likelihood

    NASA Astrophysics Data System (ADS)

    Gupta, Kinjal Dhar; Vilalta, Ricardo; Asadourian, Vicken; Macri, Lucas

    2014-05-01

    We describe an approach to automate the classification of Cepheid variable stars into two subtypes according to their pulsation mode. Automating such classification is relevant to obtain a precise determination of distances to nearby galaxies, which in addition helps reduce the uncertainty in the current expansion of the universe. One main difficulty lies in the compatibility of models trained using different galaxy datasets; a model trained using a training dataset may be ineffectual on a testing set. A solution to such difficulty is to adapt predictive models across domains; this is necessary when the training and testing sets do not follow the same distribution. The gist of our methodology is to train a predictive model on a nearby galaxy (e.g., Large Magellanic Cloud), followed by a model-adaptation step to make the model operable on other nearby galaxies. We follow a parametric approach to density estimation by modeling the training data (anchor galaxy) using a mixture of linear models. We then use maximum likelihood to compute the right amount of variable displacement, until the testing data closely overlaps the training data. At that point, the model can be directly used in the testing data (target galaxy).

  8. Optimization of an adaptive SPECT system with the scanning linear estimator

    NASA Astrophysics Data System (ADS)

    Ghanbari, Nasrin; Clarkson, Eric; Kupinski, Matthew A.; Li, Xin

    2015-08-01

    The adaptive single-photon emission computed tomography (SPECT) system studied here acquires an initial scout image to obtain preliminary information about the object. Then the configuration is adjusted by selecting the size of the pinhole and the magnification that optimize system performance on an ensemble of virtual objects generated to be consistent with the scout data. In this study the object is a lumpy background that contains a Gaussian signal with a variable width and amplitude. The virtual objects in the ensemble are imaged by all of the available configurations and the subsequent images are evaluated with the scanning linear estimator to obtain an estimate of the signal width and amplitude. The ensemble mean squared error (EMSE) on the virtual ensemble between the estimated and the true parameters serves as the performance figure of merit for selecting the optimum configuration. The results indicate that variability in the original object background, noise and signal parameters leads to a specific optimum configuration in each case. A statistical study carried out for a number of objects show that the adaptive system on average performs better than its nonadaptive counterpart.

  9. Degenerate nonlinear programming with a quadratic growth condition.

    SciTech Connect

    Anitescu, M.; Mathematics and Computer Science

    2000-01-01

    We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.

  10. Stable direct adaptive control of linear infinite-dimensional systems using a command generator tracker approach

    NASA Technical Reports Server (NTRS)

    Balas, Mark; Kaufman, Howard; Wen, John

    1984-01-01

    The topics are presented in view graph form and include the following: an adaptive model following control; adaptive control of a distributed parameter system (DPS) with a finite-dimensional controller; a direct adaptive controller; a closed-loop adaptively controlled DPS; Lyapunov stability; the asymptotic stability of the closed loop; and model control of a simply supported beam.

  11. Linear matrix inequality-based nonlinear adaptive robust control with application to unmanned aircraft systems

    NASA Astrophysics Data System (ADS)

    Kun, David William

    Unmanned aircraft systems (UASs) are gaining popularity in civil and commercial applications as their lightweight on-board computers become more powerful and affordable, their power storage devices improve, and the Federal Aviation Administration addresses the legal and safety concerns of integrating UASs in the national airspace. Consequently, many researchers are pursuing novel methods to control UASs in order to improve their capabilities, dependability, and safety assurance. The nonlinear control approach is a common choice as it offers several benefits for these highly nonlinear aerospace systems (e.g., the quadrotor). First, the controller design is physically intuitive and is derived from well known dynamic equations. Second, the final control law is valid in a larger region of operation, including far from the equilibrium states. And third, the procedure is largely methodical, requiring less expertise with gain tuning, which can be arduous for a novice engineer. Considering these facts, this thesis proposes a nonlinear controller design method that combines the advantages of adaptive robust control (ARC) with the powerful design tools of linear matrix inequalities (LMI). The ARC-LMI controller is designed with a discontinuous projection-based adaptation law, and guarantees a prescribed transient and steady state tracking performance for uncertain systems in the presence of matched disturbances. The norm of the tracking error is bounded by a known function that depends on the controller design parameters in a known form. Furthermore, the LMI-based part of the controller ensures the stability of the system while overcoming polytopic uncertainties, and minimizes the control effort. This can reduce the number of parameters that require adaptation, and helps to avoid control input saturation. These desirable characteristics make the ARC-LMI control algorithm well suited for the quadrotor UAS, which may have unknown parameters and may encounter external

  12. Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  13. Approximate non-linear multiparameter inversion with single and double scattering seismic wavefields in acoustic media

    NASA Astrophysics Data System (ADS)

    Ouyang, Wei; Mao, Weijian; Li, Wuqun; Zhang, Pan

    2017-02-01

    An approach for approximate direct quadratic non-linear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating non-linear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic non-linear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion.

  14. Adaptive tracking control of leader-following linear multi-agent systems with external disturbances

    NASA Astrophysics Data System (ADS)

    Lin, Hanquan; Wei, Qinglai; Liu, Derong; Ma, Hongwen

    2016-10-01

    In this paper, the consensus problem for leader-following linear multi-agent systems with external disturbances is investigated. Brownian motions are used to describe exogenous disturbances. A distributed tracking controller based on Riccati inequalities with an adaptive law for adjusting coupling weights between neighbouring agents is designed for leader-following multi-agent systems under fixed and switching topologies. In traditional distributed static controllers, the coupling weights depend on the communication graph. However, coupling weights associated with the feedback gain matrix in our method are updated by state errors between neighbouring agents. We further present the stability analysis of leader-following multi-agent systems with stochastic disturbances under switching topology. Most traditional literature requires the graph to be connected all the time, while the communication graph is only assumed to be jointly connected in this paper. The design technique is based on Riccati inequalities and algebraic graph theory. Finally, simulations are given to show the validity of our method.

  15. Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

    NASA Technical Reports Server (NTRS)

    Kincaid, D. R.; Young, D. M.

    1984-01-01

    Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

  16. Adaptation of the phase of the human linear vestibulo-ocular reflex (LVOR) and effects on the oculomotor neural integrator

    NASA Technical Reports Server (NTRS)

    Hegemann, S.; Shelhamer, M.; Kramer, P. D.; Zee, D. S.

    2000-01-01

    The phase of the translational linear VOR (LVOR) can be adaptively modified by exposure to a visual-vestibular mismatch. We extend here our earlier work on LVOR phase adaptation, and discuss the role of the oculomotor neural integrator. Ten subjects were oscillated laterally at 0.5 Hz, 0.3 g peak acceleration, while sitting upright on a linear sled. LVOR was assessed before and after adaptation with subjects tracking the remembered location of a target at 1 m in the dark. Phase and gain were measured by fitting sine waves to the desaccaded eye movements, and comparing sled and eye position. To adapt LVOR phase, the subject viewed a computer-generated stereoscopic visual display, at a virtual distance of 1 m, that moved so as to require either a phase lead or a phase lag of 53 deg. Adaptation lasted 20 min, during which subjects were oscillated at 0.5 Hz/0.3 g. Four of five subjects produced an adaptive change in the lag condition (range 4-45 deg), and each of five produced a change in the lead condition (range 19-56 deg), as requested. Changes in drift on eccentric gaze suggest that the oculomotor velocity-to-position integrator may be involved in the phase changes.

  17. A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

    SciTech Connect

    Jian Jinbao Hu Qingjie; Tang Chunming; Zheng Haiyan

    2007-12-15

    In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported.

  18. Distributed adaptive output consensus control of second-order systems containing unknown non-linear control gains

    NASA Astrophysics Data System (ADS)

    Wang, Gang; Wang, Chaoli; Du, Qinghui; Cai, Xuan

    2016-10-01

    In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.

  19. Quadratic Programming for Allocating Control Effort

    NASA Technical Reports Server (NTRS)

    Singh, Gurkirpal

    2005-01-01

    A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

  20. A study of passive and adaptive hydraulic engine mount systems with emphasis on non-linear characteristics

    NASA Astrophysics Data System (ADS)

    Kim, G.; Singh, R.

    1995-01-01

    Passive hydraulic mounts exhibit excitation frequency variant and deflection amplitude sensitive stiffness and damping properties. Such non-linear dynamic characteristics are examined by using analytical and experimental methods, both at the device level and within the context of a simplified vehicle model. A new lumped parameter non-linear mathematical model of the hydraulic mount is developed by simulating its decoupler switching mechanism and inertia track dynamics. The low frequency performance features and limitations of several passive mounts are made clear through the non-linear vehicle model simulation and comparable laboratory vibration tests. The high frequency performance problems of the passive hydraulic mount are identified by applying the quasi-linear analysis method. Based on these results, a new adaptive mount system is developed which exhibits broad bandwidth performance features up to 250 Hz. It implements an on-off damping control mode by using engine intake manifold vacuum and a microprocessor based solenoid valve controller. A laboratory bench set-up has already demonstrated its operational feasibility. Through analytical methods, it is observed that our adaptive mount provides superior dynamic performance to passive engine mounts and comparable performance to a small scale active mount over a wide frequency range, given the engine mounting resonance control, shock absorption and vibration isolation performance requirements. Although technical prospects of the proposed adaptive system appear promising, the in situperformance needs to be evaluated.

  1. Study of Interpolated Timing Recovery Phase-Locked Loop with Linearly Constrained Adaptive Prefilter for Higher-Density Optical Disc

    NASA Astrophysics Data System (ADS)

    Kajiwara, Yoshiyuki; Shiraishi, Junya; Kobayashi, Shoei; Yamagami, Tamotsu

    2009-03-01

    A digital phase-locked loop (PLL) with a linearly constrained adaptive filter (LCAF) has been studied for higher-linear-density optical discs. LCAF has been implemented before an interpolated timing recovery (ITR) PLL unit in order to improve the quality of phase error calculation by using an adaptively equalized partial response (PR) signal. Coefficient update of an asynchronous sampled adaptive FIR filter with a least-mean-square (LMS) algorithm has been constrained by a projection matrix in order to suppress the phase shift of the tap coefficients of the adaptive filter. We have developed projection matrices that are suitable for Blu-ray disc (BD) drive systems by numerical simulation. Results have shown the properties of the projection matrices. Then, we have designed the read channel system of the ITR PLL with an LCAF model on the FPGA board for experiments. Results have shown that the LCAF improves the tilt margins of 30 gigabytes (GB) recordable BD (BD-R) and 33 GB BD read-only memory (BD-ROM) with a sufficient LMS adaptation stability.

  2. An Improved Correction for Range Restricted Correlations Under Extreme, Monotonic Quadratic Nonlinearity and Heteroscedasticity.

    PubMed

    Culpepper, Steven Andrew

    2016-06-01

    Standardized tests are frequently used for selection decisions, and the validation of test scores remains an important area of research. This paper builds upon prior literature about the effect of nonlinearity and heteroscedasticity on the accuracy of standard formulas for correcting correlations in restricted samples. Existing formulas for direct range restriction require three assumptions: (1) the criterion variable is missing at random; (2) a linear relationship between independent and dependent variables; and (3) constant error variance or homoscedasticity. The results in this paper demonstrate that the standard approach for correcting restricted correlations is severely biased in cases of extreme monotone quadratic nonlinearity and heteroscedasticity. This paper offers at least three significant contributions to the existing literature. First, a method from the econometrics literature is adapted to provide more accurate estimates of unrestricted correlations. Second, derivations establish bounds on the degree of bias attributed to quadratic functions under the assumption of a monotonic relationship between test scores and criterion measurements. New results are presented on the bias associated with using the standard range restriction correction formula, and the results show that the standard correction formula yields estimates of unrestricted correlations that deviate by as much as 0.2 for high to moderate selectivity. Third, Monte Carlo simulation results demonstrate that the new procedure for correcting restricted correlations provides more accurate estimates in the presence of quadratic and heteroscedastic test score and criterion relationships.

  3. Adaptive Control of Linear Modal Systems Using Residual Mode Filters and a Simple Disturbance Estimator

    NASA Technical Reports Server (NTRS)

    Balas, Mark; Frost, Susan

    2012-01-01

    Flexible structures containing a large number of modes can benefit from adaptive control techniques which are well suited to applications that have unknown modeling parameters and poorly known operating conditions. In this paper, we focus on a direct adaptive control approach that has been extended to handle adaptive rejection of persistent disturbances. We extend our adaptive control theory to accommodate troublesome modal subsystems of a plant that might inhibit the adaptive controller. In some cases the plant does not satisfy the requirements of Almost Strict Positive Realness. Instead, there maybe be a modal subsystem that inhibits this property. This section will present new results for our adaptive control theory. We will modify the adaptive controller with a Residual Mode Filter (RMF) to compensate for the troublesome modal subsystem, or the Q modes. Here we present the theory for adaptive controllers modified by RMFs, with attention to the issue of disturbances propagating through the Q modes. We apply the theoretical results to a flexible structure example to illustrate the behavior with and without the residual mode filter.

  4. No Evidence for a Low Linear Energy Transfer Adaptive Response in Irradiated RKO Cells

    SciTech Connect

    Sowa, Marianne B.; Goetz, Wilfried; Baulch, Janet E.; Lewis, Adam J.; Morgan, William F.

    2011-01-06

    It has become increasingly evident from reports in the literature that there are many confounding factors that are capable of modulating radiation induced non-targeted responses such as the bystander effect and the adaptive response. In this paper we examine recent data that suggest that the observation of non-targeted responses may not be universally observable for differing radiation qualities. We have conducted a study of the adaptive response following low LET exposures for human colon carcinoma cells and failed to observe adaption for the endpoints of clonogenic survival or micronucleus formation.

  5. Students' understanding of quadratic equations

    NASA Astrophysics Data System (ADS)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  6. Digital image restoration using quadratic programming.

    PubMed

    Abdelmalek, N N; Kasvand, T

    1980-10-01

    The problem of digital image restoration is considered by obtaining an approximate solution to the Fredholm integral equation of the first kind in two variables. The system of linear equations resulting from the discretization of the integral equation is converted to a consistent system of linear equations. The problem is then solved as a quadratic programming problem with bounded variables where the unknown solution is minimized in the L(2) norm. In this method minimum computer storage is needed, and the repeated solutions are obtained in an efficient way. Also the rank of the consistent system which gives a best or near best solution is estimated. Computer simulated examples using spatially separable pointspread functions are presented. Comments and conclusion are given.

  7. Forced oscillations in quadratically damped systems

    NASA Technical Reports Server (NTRS)

    Bayliss, A.

    1978-01-01

    Bayliss (1975) has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations. In the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear. The properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution. By using the Lipschitz continuity of the mapping and the contracting mapping principle, almost periodic solutions can be found for perturbations of the considered equation. Attention is also given to the Lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory.

  8. Reconceptualizing Family Adaptation to Developmental Delay.

    PubMed

    Pedersen, Anita L; Crnic, Keith A; Baker, Bruce L; Blacher, Jan

    2015-07-01

    This study explores accurate conceptualization of the adaptation construct in families of children with developmental delay aged 3 to 8 years. Parents' self-reported measures of adaptation and observed dyadic relationship variables were examined. Confirmatory factor analysis and longitudinal growth modeling were used to evaluate the nature of adaptational processes. Results indicate that adaptational processes vary across adaptation index, child developmental level, and parent gender. Adaptation indices did not load onto a single construct at any time point. Several adaptational processes remained stable across time, although others showed linear or quadratic change. The findings of the current study indicate that it is time for a change in how adaptation is conceived for families of children with developmental delay.

  9. Biohybrid Control of General Linear Systems Using the Adaptive Filter Model of Cerebellum

    PubMed Central

    Wilson, Emma D.; Assaf, Tareq; Pearson, Martin J.; Rossiter, Jonathan M.; Dean, Paul; Anderson, Sean R.; Porrill, John

    2015-01-01

    The adaptive filter model of the cerebellar microcircuit has been successfully applied to biological motor control problems, such as the vestibulo-ocular reflex (VOR), and to sensory processing problems, such as the adaptive cancelation of reafferent noise. It has also been successfully applied to problems in robotics, such as adaptive camera stabilization and sensor noise cancelation. In previous applications to inverse control problems, the algorithm was applied to the velocity control of a plant dominated by viscous and elastic elements. Naive application of the adaptive filter model to the displacement (as opposed to velocity) control of this plant results in unstable learning and control. To be more generally useful in engineering problems, it is essential to remove this restriction to enable the stable control of plants of any order. We address this problem here by developing a biohybrid model reference adaptive control (MRAC) scheme, which stabilizes the control algorithm for strictly proper plants. We evaluate the performance of this novel cerebellar-inspired algorithm with MRAC scheme in the experimental control of a dielectric electroactive polymer, a class of artificial muscle. The results show that the augmented cerebellar algorithm is able to accurately control the displacement response of the artificial muscle. The proposed solution not only greatly extends the practical applicability of the cerebellar-inspired algorithm, but may also shed light on cerebellar involvement in a wider range of biological control tasks. PMID:26257638

  10. Biohybrid Control of General Linear Systems Using the Adaptive Filter Model of Cerebellum.

    PubMed

    Wilson, Emma D; Assaf, Tareq; Pearson, Martin J; Rossiter, Jonathan M; Dean, Paul; Anderson, Sean R; Porrill, John

    2015-01-01

    The adaptive filter model of the cerebellar microcircuit has been successfully applied to biological motor control problems, such as the vestibulo-ocular reflex (VOR), and to sensory processing problems, such as the adaptive cancelation of reafferent noise. It has also been successfully applied to problems in robotics, such as adaptive camera stabilization and sensor noise cancelation. In previous applications to inverse control problems, the algorithm was applied to the velocity control of a plant dominated by viscous and elastic elements. Naive application of the adaptive filter model to the displacement (as opposed to velocity) control of this plant results in unstable learning and control. To be more generally useful in engineering problems, it is essential to remove this restriction to enable the stable control of plants of any order. We address this problem here by developing a biohybrid model reference adaptive control (MRAC) scheme, which stabilizes the control algorithm for strictly proper plants. We evaluate the performance of this novel cerebellar-inspired algorithm with MRAC scheme in the experimental control of a dielectric electroactive polymer, a class of artificial muscle. The results show that the augmented cerebellar algorithm is able to accurately control the displacement response of the artificial muscle. The proposed solution not only greatly extends the practical applicability of the cerebellar-inspired algorithm, but may also shed light on cerebellar involvement in a wider range of biological control tasks.

  11. Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems

    NASA Technical Reports Server (NTRS)

    Downie, John D.

    1990-01-01

    A ground-based adaptive optics imaging telescope system attempts to improve image quality by detecting and correcting for atmospherically induced wavefront aberrations. The required control computations during each cycle will take a finite amount of time. Longer time delays result in larger values of residual wavefront error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper presents a study of the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for the adaptive optics application. An optimization of the adaptive optics correction algorithm with respect to an optical processor's degree of accuracy is also briefly discussed.

  12. Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems.

    PubMed

    Downie, J D; Goodman, J W

    1989-10-15

    A ground-based adaptive optics imaging telescope system attempts to improve image quality by measuring and correcting for atmospherically induced wavefront aberrations. The necessary control computations during each cycle will take a finite amount of time, which adds to the residual error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper investigates this possibility by studying the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for adaptive optics use.

  13. Quadratic programming-based approach for autonomous vehicle path planning in space

    NASA Astrophysics Data System (ADS)

    Chen, Yang; Han, Jianda; Wu, Huaiyu

    2012-07-01

    Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades. The major difficulties are that most of existing methods only adapt to static environment instead of dynamic one, and also can not solve the inherent constraints arising from the robot body and the exterior environment. To address these difficulties, this research aims to provide a feasible trajectory based on quadratic programming(QP) for path planning in three-dimensional space where an autonomous vehicle is requested to pursue a target while avoiding static or dynamic obstacles. First, the objective function is derived from the pursuit task which is defined in terms of the relative distance to the target, as well as the angle between the velocity and the position in the relative velocity coordinates(RVCs). The optimization is in quadratic polynomial form according to QP formulation. Then, the avoidance task is modeled with linear constraints in RVCs. Some other constraints, such as kinematics, dynamics, and sensor range, are included. Last, simulations with typical multiple obstacles are carried out, including in static and dynamic environments and one of human-in-the-loop. The results indicate that the optimal trajectories of the autonomous robot in three-dimensional space satisfy the required performances. Therefore, the QP model proposed in this paper not only adapts to dynamic environment with uncertainty, but also can satisfy all kinds of constraints, and it provides an efficient approach to solve the problems of path planning in three-dimensional space.

  14. Detection of spatial variations in temporal trends with a quadratic function.

    PubMed

    Moraga, Paula; Kulldorff, Martin

    2016-08-01

    Methods for the assessment of spatial variations in temporal trends (SVTT) are important tools for disease surveillance, which can help governments to formulate programs to prevent diseases, and measure the progress, impact, and efficacy of preventive efforts already in operation. The linear SVTT method is designed to detect areas with unusual different disease linear trends. In some situations, however, its estimation trend procedure can lead to wrong conclusions. In this article, the quadratic SVTT method is proposed as alternative of the linear SVTT method. The quadratic method provides better estimates of the real trends, and increases the power of detection in situations where the linear SVTT method fails. A performance comparison between the linear and quadratic methods is provided to help illustrate their respective properties. The quadratic method is applied to detect unusual different cervical cancer trends in white women in the United States, over the period 1969 to 1995.

  15. Error-based adaptive non-linear control and regions of feasibility

    NASA Technical Reports Server (NTRS)

    Teel, Andrew R.

    1992-01-01

    The nonlinear adaptive algorithm of Kanellakopoulos et al. (1991) was modified to produce an error-based algorithm. This permits global stabilizability for a large subset of pure-feedback nonlinear systems. The algorithm was demonstrated on the single-input stabilization problem, but extends easily to the multiple input tracking problems.

  16. Concretising Factorisation of Quadratic Expressions

    ERIC Educational Resources Information Center

    Hoong, Leong Yew; Fwe, Yap Sook; Yvonne, Teo Mei Lin; Subramaniam, Thilagam d/o; Zaini, Irni Karen Bte Mohd; Chiew, Quek Eng; Karen, Tan Kang Ling

    2010-01-01

    The way quadratic factorisation was usually taught to students in Bukit View Secondary was through the familiar "cross-method." However, some teachers felt that a significant number of students could not use the method effectively even after careful demonstration through repeated examples. In addition, many secondary mathematics teachers…

  17. Mixed linear model approach adapted for genome-wide association studies

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Mixed linear model (MLM) methods have proven useful in controlling for population structure and relatedness within genome-wide association studies. However, MLM-based methods can be computationally challenging for large datasets. We report a compression approach, called ‘compressed MLM,’ that decrea...

  18. Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner

    NASA Astrophysics Data System (ADS)

    Akhunov, R. R.; Gazizov, T. R.; Kuksenko, S. P.

    2016-08-01

    The mean time needed to solve a series of systems of linear algebraic equations (SLAEs) as a function of the number of SLAEs is investigated. It is proved that this function has an extremum point. An algorithm for adaptively determining the time when the preconditioner matrix should be recalculated when a series of SLAEs is solved is developed. A numerical experiment with multiply solving a series of SLAEs using the proposed algorithm for computing 100 capacitance matrices with two different structures—microstrip when its thickness varies and a modal filter as the gap between the conductors varies—is carried out. The speedups turned out to be close to the optimal ones.

  19. Online optimal tracking control of continuous-time linear systems with unknown dynamics by using adaptive dynamic programming

    NASA Astrophysics Data System (ADS)

    Qin, Chunbin; Zhang, Huaguang; Luo, Yanhong

    2014-05-01

    In this paper, a novel theoretic formulation based on adaptive dynamic programming (ADP) is developed to solve online the optimal tracking problem of the continuous-time linear system with unknown dynamics. First, the original system dynamics and the reference trajectory dynamics are transformed into an augmented system. Then, under the same performance index with the original system dynamics, an augmented algebraic Riccati equation is derived. Furthermore, the solutions for the optimal control problem of the augmented system are proven to be equal to the standard solutions for the optimal tracking problem of the original system dynamics. Moreover, a new online algorithm based on the ADP technique is presented to solve the optimal tracking problem of the linear system with unknown system dynamics. Finally, simulation results are given to verify the effectiveness of the theoretic results.

  20. A transient, quadratic nodal method for triangular-Z geometry

    SciTech Connect

    DeLorey, T.F.

    1993-06-01

    Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.

  1. A Projection Neural Network for Constrained Quadratic Minimax Optimization.

    PubMed

    Liu, Qingshan; Wang, Jun

    2015-11-01

    This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

  2. The generalized quadratic knapsack problem. A neuronal network approach.

    PubMed

    Talaván, Pedro M; Yáñez, Javier

    2006-05-01

    The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

  3. Linear adaptive noise-reduction filters for tomographic imaging: Optimizing for minimum mean square error

    SciTech Connect

    Sun, W Y

    1993-04-01

    This thesis solves the problem of finding the optimal linear noise-reduction filter for linear tomographic image reconstruction. The optimization is data dependent and results in minimizing the mean-square error of the reconstructed image. The error is defined as the difference between the result and the best possible reconstruction. Applications for the optimal filter include reconstructions of positron emission tomographic (PET), X-ray computed tomographic, single-photon emission tomographic, and nuclear magnetic resonance imaging. Using high resolution PET as an example, the optimal filter is derived and presented for the convolution backprojection, Moore-Penrose pseudoinverse, and the natural-pixel basis set reconstruction methods. Simulations and experimental results are presented for the convolution backprojection method.

  4. Security analysis of quadratic phase based cryptography

    NASA Astrophysics Data System (ADS)

    Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.

    2016-09-01

    The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.

  5. On Coupled Rate Equations with Quadratic Nonlinearities

    PubMed Central

    Montroll, Elliott W.

    1972-01-01

    Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013

  6. Compact stars with quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi

    2015-05-01

    We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.

  7. Orthogonality preserving infinite dimensional quadratic stochastic operators

    SciTech Connect

    Akın, Hasan; Mukhamedov, Farrukh

    2015-09-18

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

  8. Minerals detection for hyperspectral images using adapted linear unmixing: LinMin

    NASA Astrophysics Data System (ADS)

    Schmidt, Frédéric; Legendre, Maxime; Le Mouëlic, Stéphane

    2014-07-01

    Minerals detection over large volume of spectra is the challenge addressed by current hyperspectral imaging spectrometer in Planetary Science. Instruments such OMEGA (Mars Express), CRISM (Mars Reconnaissance Orbiter), M3 (Chandrayaan-1), VIRTIS (Rosetta) and many more, have been producing very large datasets since one decade. We propose here a fast supervised detection algorithm called LinMin, in the framework of linear unmixing, with innovative arrangement in order to treat non-linear cases due to radiative transfer in both atmosphere and surface. We use reference laboratory and synthetic spectral library. Additional spectra are used in order to mimic the effect of Martian aerosols, grain size, and observation geometry discrepancies between reference and observed spectra. The proposed algorithm estimates the uncertainty on “mixing coefficient” from the uncertainty of observed spectra. Both numerical and observational tests validate the approach. Fast parallel implementation of the best algorithm (IPLS) on Graphics Processing Units (GPU) allows to significantly reduce the computation cost by a factor of ∼40.

  9. Adaptive vision-based control of an unmanned aerial vehicle without linear velocity measurements.

    PubMed

    Jabbari Asl, Hamed; Yoon, Jungwon

    2016-11-01

    In this paper, an image-based visual servo controller is designed for an unmanned aerial vehicle. The main objective is to use flow of image features as the velocity cue to compensate for the low quality of linear velocity information obtained from accelerometers. Nonlinear observers are designed to estimate this flow. The proposed controller is bounded, which can help to keep the target points in the field of view of the camera. The main advantages over the previous full dynamic observer-based methods are that, the controller is robust with respect to unknown image depth, and also no yaw information is required. The complete stability analysis is presented and asymptotic convergence of the error signals is guaranteed. Simulation results show the effectiveness of the proposed approach.

  10. Performance analysis of structured gradient algorithm. [for adaptive beamforming linear arrays

    NASA Technical Reports Server (NTRS)

    Godara, Lal C.

    1990-01-01

    The structured gradient algorithm uses a structured estimate of the array correlation matrix (ACM) to estimate the gradient required for the constrained least-mean-square (LMS) algorithm. This structure reflects the structure of the exact array correlation matrix for an equispaced linear array and is obtained by spatial averaging of the elements of the noisy correlation matrix. In its standard form the LMS algorithm does not exploit the structure of the array correlation matrix. The gradient is estimated by multiplying the array output with the receiver outputs. An analysis of the two algorithms is presented to show that the covariance of the gradient estimated by the structured method is less sensitive to the look direction signal than that estimated by the standard method. The effect of the number of elements on the signal sensitivity of the two algorithms is studied.

  11. A new adaptation of linear reservoir models in parallel sets to assess actual hydrological events

    NASA Astrophysics Data System (ADS)

    Mateo Lázaro, Jesús; Sánchez Navarro, José Ángel; García Gil, Alejandro; Edo Romero, Vanesa

    2015-05-01

    A methodology based on Parallel Linear Reservoir (PLR) models is presented. To carry it out has been implemented within the software SHEE (Simulation of Hydrological Extreme Events), which is a tool for the analysis of hydrological processes in catchments with the management and display of DEM and datasets. The algorithms of the models pass throughout the cells and drainage network, by means of the Watershed Traversal Algorithm (WTA) that runs the entire drainage network of a basin in both directions, upwards and downwards, which is ideal for incorporating the models of the hydrological processes of the basins into its structure. The WTA methodology is combined with another one based on models of Parallel Linear Reservoirs (PLR) whose main qualities include: (1) the models are defined by observing the recession curves of actual hydrographs, i.e., the watershed actual responses; (2) the models serve as a way to simulate the routing through the watershed and its different reservoirs; and (3) the models allow calculating the water balance, which is essential to the study of actual events in the watershed. A complete hydrometeorological event needs the combination of several models, each one of which represents a hydrological process. The PLR model is a routing model, but it also contributes to the adjustment of other models (e.g., the rainfall-runoff model) and allows establishing a distributed model of effective rainfall for an actual event occurred in a basin. On the other hand, the proposed formulation solves the rainfall distribution problem for each deposit in the reservoir combination models.

  12. Properties of surjective real quadratic maps

    NASA Astrophysics Data System (ADS)

    Arutyunov, A. V.; Zhukovskiy, S. E.

    2016-09-01

    The properties of surjective real quadratic maps are investigated. Sufficient conditions for the property of surjectivity to be stable under various perturbations are obtained. Examples of surjective quadratic maps whose surjectivity breaks down after an arbitrarily small perturbation are constructed. Sufficient conditions for quadratic maps to have nontrivial zeros are obtained. For a smooth even map in a neighbourhood of the origin an inverse function theorem in terms of the degree of the corresponding quadratic map is obtained. A canonical form of surjective quadratic maps from {R}^3 to {R}^3 is constructed. Bibliography: 27 titles.

  13. "Adapted Linear Interaction Energy": A Structure-Based LIE Parametrization for Fast Prediction of Protein-Ligand Affinities.

    PubMed

    Linder, Mats; Ranganathan, Anirudh; Brinck, Tore

    2013-02-12

    We present a structure-based parametrization of the Linear Interaction Energy (LIE) method and show that it allows for the prediction of absolute protein-ligand binding energies. We call the new model "Adapted" LIE (ALIE) because the α and β coefficients are defined by system-dependent descriptors and do therefore not require any empirical γ term. The best formulation attains a mean average deviation of 1.8 kcal/mol for a diverse test set and depends on only one fitted parameter. It is robust with respect to additional fitting and cross-validation. We compare this new approach with standard LIE by Åqvist and co-workers and the LIE + γSASA model (initially suggested by Jorgensen and co-workers) against in-house and external data sets and discuss their applicabilities.

  14. Asymptotic Normality of Quadratic Estimators.

    PubMed

    Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad

    2016-12-01

    We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.

  15. Optimizing the general linear model for functional near-infrared spectroscopy: an adaptive hemodynamic response function approach

    PubMed Central

    Uga, Minako; Dan, Ippeita; Sano, Toshifumi; Dan, Haruka; Watanabe, Eiju

    2014-01-01

    Abstract. An increasing number of functional near-infrared spectroscopy (fNIRS) studies utilize a general linear model (GLM) approach, which serves as a standard statistical method for functional magnetic resonance imaging (fMRI) data analysis. While fMRI solely measures the blood oxygen level dependent (BOLD) signal, fNIRS measures the changes of oxy-hemoglobin (oxy-Hb) and deoxy-hemoglobin (deoxy-Hb) signals at a temporal resolution severalfold higher. This suggests the necessity of adjusting the temporal parameters of a GLM for fNIRS signals. Thus, we devised a GLM-based method utilizing an adaptive hemodynamic response function (HRF). We sought the optimum temporal parameters to best explain the observed time series data during verbal fluency and naming tasks. The peak delay of the HRF was systematically changed to achieve the best-fit model for the observed oxy- and deoxy-Hb time series data. The optimized peak delay showed different values for each Hb signal and task. When the optimized peak delays were adopted, the deoxy-Hb data yielded comparable activations with similar statistical power and spatial patterns to oxy-Hb data. The adaptive HRF method could suitably explain the behaviors of both Hb parameters during tasks with the different cognitive loads during a time course, and thus would serve as an objective method to fully utilize the temporal structures of all fNIRS data. PMID:26157973

  16. Application of Heisenberg's S matrix program to the angular scattering of the H + D2(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D reaction: piecewise S matrix elements using linear, quadratic, step-function, and top-hat parametrizations.

    PubMed

    Shan, Xiao; Connor, J N L

    2012-11-26

    A previous paper by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392) reported the surprising result that four simple parametrized S matrices can reproduce the forward-angle glory scattering of the H + D(2)(v(i)=0,j(i)=0) → HD(v(f)=3,j(f)=0) + D reaction, whose differential cross section (DCS) had been computed in a state-of-the-art scattering calculation for a state-of-the-art potential energy surface. Here, v and j are vibrational and rotational quantum numbers, respectively, and the translational energy is 1.81 eV. This paper asks the question: Can we replace the analytic functions (of class C(ω)) used by Shan-Connor with simpler mathematical functions and still reproduce the forward-angle glory scattering? We first construct S matrix elements (of class C(0)) using a quadratic phase and a piecewise-continuous pre-exponential factor consisting of three pieces. Two of the pieces are constants, with one taking the value N (a real normalization constant) at small values of the total angular momentum number, J; the other piece has the value 0 at large J. These two pieces are joined at intermediate values of J by either a straight line, giving rise to the linear parametrization (denoted param L), or a quadratic curve, which defines the quadratic parametrization (param Q). We find that both param L and param Q can reproduce the glory scattering for center-of-mass reactive scattering angles, θ(R) ≲ 30°. Second, we use a piecewise-discontinuous pre-exponential factor and a quadratic phase, giving rise to a step-function parametrization (param SF) and a top-hat parametrization (param TH). We find that both param SF and param TH can reproduce the forward-angle scattering, even though these class C(-1) parametrizations are usually considered too simplistic to be useful for calculations of DCSs. We find that an ultrasimplistic param THz, which is param TH with a phase of zero, can also reproduce the glory scattering at forward angles. The S matrix elements for

  17. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  18. Quadratic performance index generation for optimal regular design.

    NASA Technical Reports Server (NTRS)

    Bullock, T. E.; Elder, J. M.

    1971-01-01

    Application of optimal control theory to practical problems has been limited by the difficulty of prescribing a performance index which accurately reflects design requirements. The task of deriving equivalent performance indices is considered in the present paper for a plant that is a completely controllable, scalar linear system with state feedback. A quadratic index is developed which leads to an optimal design performance satisfying some of the classical performance criteria.

  19. Evaluating the Contributions of Individual Variables to a Quadratic Form.

    PubMed

    Garthwaite, Paul H; Koch, Inge

    2016-03-01

    Quadratic forms capture multivariate information in a single number, making them useful, for example, in hypothesis testing. When a quadratic form is large and hence interesting, it might be informative to partition the quadratic form into contributions of individual variables. In this paper it is argued that meaningful partitions can be formed, though the precise partition that is determined will depend on the criterion used to select it. An intuitively reasonable criterion is proposed and the partition to which it leads is determined. The partition is based on a transformation that maximises the sum of the correlations between individual variables and the variables to which they transform under a constraint. Properties of the partition, including optimality properties, are examined. The contributions of individual variables to a quadratic form are less clear-cut when variables are collinear, and forming new variables through rotation can lead to greater transparency. The transformation is adapted so that it has an invariance property under such rotation, whereby the assessed contributions are unchanged for variables that the rotation does not affect directly. Application of the partition to Hotelling's one- and two-sample test statistics, Mahalanobis distance and discriminant analysis is described and illustrated through examples. It is shown that bootstrap confidence intervals for the contributions of individual variables to a partition are readily obtained.

  20. Piecewise linear approximations to model the dynamics of adaptation to osmotic stress by food-borne pathogens.

    PubMed

    Métris, Aline; George, Susie M; Ropers, Delphine

    2017-01-02

    Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available

  1. Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

    PubMed

    Wang, Di; Kleinberg, Robert D

    2009-11-28

    Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

  2. Optimization with quadratic support functions in nonconvex smooth optimization

    NASA Astrophysics Data System (ADS)

    Khamisov, O. V.

    2016-10-01

    Problem of global minimization of twice continuously differentiable function with Lipschitz second derivatives over a polytope is considered. We suggest a branch and bound method with polytopes as partition elements. Due to the Lipschitz property of the objective function we can construct a quadratic support minorant at each point of the feasible set. Global minimum of of this minorant provides a lower bound of the objective over given partition subset. The main advantage of the suggested method consists in the following. First quadratic minorants usually are nonconvex and we have to solve auxiliary global optimization problem. This problem is reduced to a mixed 0-1 linear programming problem and can be solved by an advanced 0-1 solver. Then we show that the quadratic minorants are getting convex as soon as partition elements are getting smaller in diameter. Hence, at the final steps of the branch and bound method we solve convex auxiliary quadratic problems. Therefore, the method accelerates when we are close to the global minimum of the initial problem.

  3. The Random Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Paul, Gerald; Shao, Jia; Stanley, H. Eugene

    2011-11-01

    The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.

  4. Adaptation.

    PubMed

    Broom, Donald M

    2006-01-01

    The term adaptation is used in biology in three different ways. It may refer to changes which occur at the cell and organ level, or at the individual level, or at the level of gene action and evolutionary processes. Adaptation by cells, especially nerve cells helps in: communication within the body, the distinguishing of stimuli, the avoidance of overload and the conservation of energy. The time course and complexity of these mechanisms varies. Adaptive characters of organisms, including adaptive behaviours, increase fitness so this adaptation is evolutionary. The major part of this paper concerns adaptation by individuals and its relationships to welfare. In complex animals, feed forward control is widely used. Individuals predict problems and adapt by acting before the environmental effect is substantial. Much of adaptation involves brain control and animals have a set of needs, located in the brain and acting largely via motivational mechanisms, to regulate life. Needs may be for resources but are also for actions and stimuli which are part of the mechanism which has evolved to obtain the resources. Hence pigs do not just need food but need to be able to carry out actions like rooting in earth or manipulating materials which are part of foraging behaviour. The welfare of an individual is its state as regards its attempts to cope with its environment. This state includes various adaptive mechanisms including feelings and those which cope with disease. The part of welfare which is concerned with coping with pathology is health. Disease, which implies some significant effect of pathology, always results in poor welfare. Welfare varies over a range from very good, when adaptation is effective and there are feelings of pleasure or contentment, to very poor. A key point concerning the concept of individual adaptation in relation to welfare is that welfare may be good or poor while adaptation is occurring. Some adaptation is very easy and energetically cheap and

  5. Flight Control System Design by Quadratic Stabilization with Partial Pole Placement

    NASA Astrophysics Data System (ADS)

    Satoh, Atsushi; Sugimoto, Kenji

    The most fundamental requirements for flight control system are ensuring robust stability and improving flying quality. Quadratic stabilization is a powerful technique ensuring robust stability against parameter change of aircraft due to flight condition. Furthermore, flying quality requirements are regarded as eigenstructure assignment specifications. This paper proposes a new design method of feedback gain which simultaneously achieves quadratic stabilization and partial pole placement. This design method is reduced to a numerical optimization problem including linear matrix inequality (LMI) constraints.

  6. Controller design for nonlinear quadratic Markov jumping systems with input saturation

    NASA Astrophysics Data System (ADS)

    Chen, Fu; Xu, Shengyuan; Zou, Yun; Xu, Huiling

    2014-01-01

    This paper deals with the controller design problem of nonlinear quadratic Markov jumping systems with input saturation. Both mode-dependent and mode-independent state feedback controllers are designed. By using the concept of domain of attraction in mean square sense, sufficient conditions for stochastic stabilisation for nonlinear quadratic systems are derived in terms of linear matrix inequalities. Certain existing results are improved. Simulation examples are presented to illustrate the effectiveness of the proposed technique.

  7. QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

    PubMed

    Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

    2014-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

  8. Integer-Linear-Programing Optimization in Scalable Video Multicast with Adaptive Modulation and Coding in Wireless Networks

    PubMed Central

    Lee, Chaewoo

    2014-01-01

    The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC) with adaptive modulation and coding (AMC) provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs) to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP) and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm. PMID:25276862

  9. Integer-linear-programing optimization in scalable video multicast with adaptive modulation and coding in wireless networks.

    PubMed

    Lee, Dongyul; Lee, Chaewoo

    2014-01-01

    The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC) with adaptive modulation and coding (AMC) provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs) to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP) and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm.

  10. Pre-Service Teachers' Linear and Quadratic Inequalities Understandings

    ERIC Educational Resources Information Center

    Bicer, Ali; Capraro, Robert M.; Capraro, Mary M.

    2014-01-01

    The National Council of Teachers of Mathematics [NCTM] noted that middle and high school students are expected to be able to both explain inequalities by using mathematical symbols and understand meanings by interpreting the solutions of inequalities. Unfortunately, research has revealed that not only do middle and high school students hold…

  11. Adapt

    NASA Astrophysics Data System (ADS)

    Bargatze, L. F.

    2015-12-01

    Active Data Archive Product Tracking (ADAPT) is a collection of software routines that permits one to generate XML metadata files to describe and register data products in support of the NASA Heliophysics Virtual Observatory VxO effort. ADAPT is also a philosophy. The ADAPT concept is to use any and all available metadata associated with scientific data to produce XML metadata descriptions in a consistent, uniform, and organized fashion to provide blanket access to the full complement of data stored on a targeted data server. In this poster, we present an application of ADAPT to describe all of the data products that are stored by using the Common Data File (CDF) format served out by the CDAWEB and SPDF data servers hosted at the NASA Goddard Space Flight Center. These data servers are the primary repositories for NASA Heliophysics data. For this purpose, the ADAPT routines have been used to generate data resource descriptions by using an XML schema named Space Physics Archive, Search, and Extract (SPASE). SPASE is the designated standard for documenting Heliophysics data products, as adopted by the Heliophysics Data and Model Consortium. The set of SPASE XML resource descriptions produced by ADAPT includes high-level descriptions of numerical data products, display data products, or catalogs and also includes low-level "Granule" descriptions. A SPASE Granule is effectively a universal access metadata resource; a Granule associates an individual data file (e.g. a CDF file) with a "parent" high-level data resource description, assigns a resource identifier to the file, and lists the corresponding assess URL(s). The CDAWEB and SPDF file systems were queried to provide the input required by the ADAPT software to create an initial set of SPASE metadata resource descriptions. Then, the CDAWEB and SPDF data repositories were queried subsequently on a nightly basis and the CDF file lists were checked for any changes such as the occurrence of new, modified, or deleted

  12. Primal-Dual Interior Methods for Quadratic Programming

    NASA Astrophysics Data System (ADS)

    Shustrova, Anna

    Interior methods are a class of computational methods for solving a con- strained optimization problem. Interior methods follow a continuous path to the solution that passes through the interior of the feasible region (i.e., the set of points that satisfy the constraints). Interior-point methods may also be viewed as methods that replace the constrained problem by a sequence of unconstrained problems in which the objective function is augmented by a weighted "barrier" term that is infinite at the boundary of the feasible region. Convergence to a solution of the constrained problem is achieved by solving a sequence of unconstrained problems in which the weight on the barrier term is steadily reduced to zero. This thesis concerns the formulation and analysis of interior methods for the solution of a quadratic programming (QP) problem, which is an optimization problem with a quadratic objective function and linear constraints. The linear constraints may include an arbitrary mixture of equality and inequality constraints, where the inequality constraints may be subject to lower and/or upper bounds. QP problems arise in a wide variety of applications. An important application is in sequential quadratic programming methods for nonlinear optimization, which involve minimizing a sequence of QP subproblems based on a quadratic approximation of the nonlinear objective function and a set of linearized nonlinear constraints. Two new interior methods for QP are proposed. Each is based on the properties of a barrier function defined in terms of both the primal and dual variables. The first method is suitable for a QP with all inequality constraints. At each iteration, the Newton equations for minimizing a quadratic model of the primal-dual barrier function are reformulated in terms of a symmetric indefinite system of equations that is solved using an inertia controlling factorization. This factorization provides an effective method for the detection and convexification of

  13. Seven Wonders of the Ancient and Modern Quadratic World.

    ERIC Educational Resources Information Center

    Taylor, Sharon E.; Mittag, Kathleen Cage

    2001-01-01

    Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

  14. Measurement of quadratic electrogyration effect in castor oil

    NASA Astrophysics Data System (ADS)

    Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

    2015-07-01

    This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

  15. WHAT IS A SATISFACTORY QUADRATIC EQUATION SOLVER?

    DTIC Science & Technology

    The report discusses precise requirements for a satisfactory computer program to solve a quadratic equation with floating - point coefficients. The principal practical problem is coping with overflow and underflow.

  16. Schur Stability Regions for Complex Quadratic Polynomials

    ERIC Educational Resources Information Center

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  17. Test spaces and characterizations of quadratic spaces

    NASA Astrophysics Data System (ADS)

    Dvurečenskij, Anatolij

    1996-10-01

    We show that a test space consisting of nonzero vectors of a quadratic space E and of the set all maximal orthogonal systems in E is algebraic iff E is Dacey or, equivalently, iff E is orthomodular. In addition, we present another orthomodularity criteria of quadratic spaces, and using the result of Solèr, we show that they can imply that E is a real, complex, or quaternionic Hilbert space.

  18. Analysing the mechanical performance and growth adaptation of Norway spruce using a non-linear finite-element model and experimental data.

    PubMed

    Lundström, T; Jonas, T; Volkwein, A

    2008-01-01

    Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.

  19. Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results.

    PubMed

    Gray, Morgan; Petit, Cyril; Rodionov, Sergey; Bocquet, Marc; Bertino, Laurent; Ferrari, Marc; Fusco, Thierry

    2014-08-25

    We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).

  20. The Factorability of Quadratics: Motivation for More Techniques

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Nandakumar, N. R.

    2005-01-01

    Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

  1. Fast Approximate Quadratic Programming for Graph Matching

    PubMed Central

    Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624

  2. Limit cycles near hyperbolas in quadratic systems

    NASA Astrophysics Data System (ADS)

    Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume

    In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics DI2a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability.

  3. Fast approximate quadratic programming for graph matching.

    PubMed

    Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.

  4. Qualitative analysis of certain generalized classes of quadratic oscillator systems

    SciTech Connect

    Bagchi, Bijan Ghosh, Samiran Pal, Barnali Poria, Swarup

    2016-02-15

    We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56, 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ, the other points to a centre for λ < 0 but a saddle λ > 0. On the other hand, the second potential reveals only a center for both the signs of λ from a linear stability analysis. We carry out our study by extending Quesne’s scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term fcosωt.

  5. PSQP -- Puzzle Solving by Quadratic Programming.

    PubMed

    Andalo, Fernanda; Taubin, Gabriel; Goldenstein, Siome

    2016-03-25

    In this article we present the first effective global method for the reconstruction of image puzzles comprising rectangle pieces - Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

  6. PSQP: Puzzle Solving by Quadratic Programming.

    PubMed

    Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

    2017-02-01

    In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

  7. Quintessence with quadratic coupling to dark matter

    SciTech Connect

    Boehmer, Christian G.; Chan, Nyein; Caldera-Cabral, Gabriela; Lazkoz, Ruth; Maartens, Roy

    2010-04-15

    We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.

  8. Guises and disguises of quadratic divergences

    SciTech Connect

    Cherchiglia, A.L.; Vieira, A.R.; Hiller, Brigitte; Baêta Scarpelli, A.P.; Sampaio, Marcos

    2014-12-15

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  9. Guises and disguises of quadratic divergences

    NASA Astrophysics Data System (ADS)

    Cherchiglia, A. L.; Vieira, A. R.; Hiller, Brigitte; Baêta Scarpelli, A. P.; Sampaio, Marcos

    2014-12-01

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  10. On orthogonality preserving quadratic stochastic operators

    SciTech Connect

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  11. Effects of quadrat size and shape, initial epidemic conditions, and spore dispersal gradient on spatial statistics of plant disease epidemics.

    PubMed

    Xu, X M; Ridout, M S

    2000-07-01

    ABSTRACT The spatiotemporal spread of plant diseases was simulated using a stochastic model to study the effects of initial conditions (number of plants initially infected and their spatial pattern), spore dispersal gradient, and size and shape of sampling quadrats on statistics describing the spatiotemporal dynamics of epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance mu (units of distance). A total of 54 different quadrat types, including 23 distinct sizes ranging from 4 to 144 plants, were used to sample the simulated epidemics. A symmetric form of the binary power law with two parameters (alpha, beta) was fitted to the sampled epidemic data using each of the 54 quadrats for each replicate simulation run. The alpha and beta estimates were highly correlated positively with each other, and their estimates were comparable to those estimated from observed epidemics. Intraclass correlation (kappa) was calculated for each quadrat type; kappa decreased exponentially with increasing quadrat size. An asymmetric form of the binary power law with three parameters (alpha (1), beta(1), beta(2)) was used to relate kappa to the disease incidence (p); beta1 was highly correlated to beta: beta1 approximately beta - 1. In general, initial conditions and quadrat size affected alpha, beta, alpha(1), beta(1), and beta(2) greatly. The parameter estimates increased as quadrat size increased, and the relationships were described well by a linear regression model on the logarithm of quadrat size with the slope or intercept parameters dependent on initial conditions and mu. Compared with initial conditions and quadrat size, the overall effects of mu and quadrat shape were generally small, although within each quadrat size and initial condition they could be substantial. Quadrat shape had the greatest effect when the quadrat was long and thin. The relationship of the index of dispersion (D) to p and quadrat size was

  12. Projected sequential quadratic programming methods

    SciTech Connect

    Heinkenschloss, M.

    1994-12-31

    In this talk we investigate projected SQP methods for the solution of min f(y, u). s.t. c(y, u) = 0 a {<=} u {<=} b. These methods combine the ideas of (reduced) SQP methods and projected Newton methods. The problem formulation and the design of these solution methods is motivated by optimal control problems. In this case y and u are the state and the control, respectively, and c(y, u) = 0 represents the state equation. Projected SQP methods use the simple projection onto the set {l_brace}a {<=} u {<=} b{r_brace} and maintain feasibility with respect to the inequality constraints. In each iteration only linearized constraint equations need to be solved. Global convergence of the method is enforced using a constrained merit function and an Armijo-like line search. We discuss global and local convergence properties of these methods, the identification of active indices, and implementation details for optimal control problems. Numerical examples of projected SQP methods applied to optimal control problems are presented.

  13. Electricity Consumption in the Industrial Sector of Jordan: Application of Multivariate Linear Regression and Adaptive Neuro-Fuzzy Techniques

    NASA Astrophysics Data System (ADS)

    Samhouri, M.; Al-Ghandoor, A.; Fouad, R. H.

    2009-08-01

    In this study two techniques, for modeling electricity consumption of the Jordanian industrial sector, are presented: (i) multivariate linear regression and (ii) neuro-fuzzy models. Electricity consumption is modeled as function of different variables such as number of establishments, number of employees, electricity tariff, prevailing fuel prices, production outputs, capacity utilizations, and structural effects. It was found that industrial production and capacity utilization are the most important variables that have significant effect on future electrical power demand. The results showed that both the multivariate linear regression and neuro-fuzzy models are generally comparable and can be used adequately to simulate industrial electricity consumption. However, comparison that is based on the square root average squared error of data suggests that the neuro-fuzzy model performs slightly better for future prediction of electricity consumption than the multivariate linear regression model. Such results are in full agreement with similar work, using different methods, for other countries.

  14. Teacher Conceptions, Curriculum Ideologies, and Adaptations to Linear Change in River School District: Implications for Gifted and Talented

    ERIC Educational Resources Information Center

    Allen, William T., Jr.; Hunsaker, Scott L.

    2016-01-01

    Curriculum ideologies are educational theories applied in everyday pedagogical practice. In this study, to better meet the learning needs of their students, four middle school teachers used a variety of ideologies as a professional toolbox. When confronted with school district standardization, these teachers adapted; however, as predicted by…

  15. Development of flank wear model of cutting tool by using adaptive feedback linear control system on machining AISI D2 steel and AISI 4340 steel

    NASA Astrophysics Data System (ADS)

    Orra, Kashfull; Choudhury, Sounak K.

    2016-12-01

    The purpose of this paper is to build an adaptive feedback linear control system to check the variation of cutting force signal to improve the tool life. The paper discusses the use of transfer function approach in improving the mathematical modelling and adaptively controlling the process dynamics of the turning operation. The experimental results shows to be in agreement with the simulation model and error obtained is less than 3%. The state space approach model used in this paper successfully check the adequacy of the control system through controllability and observability test matrix and can be transferred from one state to another by appropriate input control in a finite time. The proposed system can be implemented to other machining process under varying range of cutting conditions to improve the efficiency and observability of the system.

  16. An adaptive panoramic filter bank as a qualitative model of the filtering system of the cochlea: the peculiarities in linear and nonlinear mode.

    PubMed

    Stasiunas, Antanas; Verikas, Antanas; Bacauskiene, Marija; Miliauskas, Rimvydas

    2012-03-01

    Outer hair cells in the cochlea of the ear, together with the local structures of the basilar membrane, reticular lamina and tectorial membrane constitute the adaptive primary filters (PF) of the second order. We used them for designing a serial-parallel signal filtering system. We determined a rational number of the PF included in Gaussian channels of the system, summation weights of the output signals, and distribution of the PF along the basilar membrane. A Gaussian panoramic filter bank each channel of which consists of five PF is presented as an example. The properties of the PF, the channel and the filter bank operating in the linear and nonlinear modes are determined during adaptation and under efferent control. The results suggest that application of biological filtering principles can be useful for designing cochlear implants with new speech encoding strategies.

  17. Quadratic Hadamard Memories 1: Adaptive Stochastic Content-Addressable Memory

    DTIC Science & Technology

    1989-12-01

    learning mechanisms", Phys. Rev. A34, 4217 (1986). [4] I. Kanter and H. Sompolinsky , "Associative recall of memory without errors", Phys. Rev, A35...Acad. Sei. USA 79, 2554 (1982). [2] D. J. Aalt, H. Gutfreund, and H, Sompolinski , "Informa- tion storage in neural networks with low levels of activity

  18. Quadratic Hadamard Memories II. Adaptive Stochastic Content. Addressable Memory

    DTIC Science & Technology

    1990-07-01

    Dreyfus, "Collective computational properties of neural networks: New learning mechanisms", Phys. Rev. A34, 4217 (1986) 5] 1. Kanter and H. Sompolinski ... Sompolinsky , "Information storage in neural networks with low levels of activity", Phys. Rev. A35, 2293 (1987) [4] L. Personnaz, I. Guyon, and G

  19. Analysis of quadratic nonlinearities in hydrodynamic transport systems employing numerical simulations

    NASA Astrophysics Data System (ADS)

    Bicken, Gurcan

    This dissertation deals with the analysis and identification of quadratic non-linearities in hydrodynamic transport problems arising in engineering and science. As representative application areas, homogenous oscillations of electron and ion plasmas in a 1-D periodic domain and the forced voltage-current dynamics of a semiconductor device are considered. The time series data obtained from numerical solutions of the associated hydrodynamic equations are used for the spectral analysis of the quadratic nonlinearities in these respective systems. More specifically, electron plasma oscillations are analyzed using power spectra and cross-bicoherency spectra to gain insight into the quadratic interactions predicted by a simple model of the energy transfer that cascades from lower modes to higher modes within a small amplitude range of oscillations. The efficiency of the bicoherency function in detecting the quadratic wave interactions from the complex time series of the mode amplitudes is observed. The difference in the modal interactions for isentropic and isothermal plasma models are investigated based on numerical 'experiments' simulating the modal dynamics in each case. Furthermore, the concentration oscillations of cold ion plasmas in a Lagrangian frame are analyzed for different Debye lengths. The detailed effects of linear and nonlinear mechanisms in the hydrodynamic model on the power spectra of the oscillations are investigated. Second-order Volterra models are considered for approximating the dynamics of input-output systems with quadratic nonlinear terms. The linear and quadratic kernels of the Volterra model are estimated using multi- tone inputs and least-squares minimization. The implications of the non-orthogonality of the model are investigated in detail. To circumvent the negative effects of non-orthogonality on the accuracy of the kernel estimation, an 'odd-even' separation technique is utilized in the kernel estimation. This approach for estimating an

  20. Investigating Students' Mathematical Difficulties with Quadratic Equations

    ERIC Educational Resources Information Center

    O'Connor, Bronwyn Reid; Norton, Stephen

    2016-01-01

    This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

  1. Target manifold formation using a quadratic SDF

    NASA Astrophysics Data System (ADS)

    Hester, Charles F.; Risko, Kelly K. D.

    2013-05-01

    Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.

  2. Curious Consequences of a Miscopied Quadratic

    ERIC Educational Resources Information Center

    Poet, Jeffrey L.; Vestal, Donald L., Jr.

    2005-01-01

    The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

  3. Haar wavelet operational matrix method for solving constrained nonlinear quadratic optimal control problem

    NASA Astrophysics Data System (ADS)

    Swaidan, Waleeda; Hussin, Amran

    2015-10-01

    Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.

  4. Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

    SciTech Connect

    Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

    2011-06-23

    This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.

  5. An Instability Index Theory for Quadratic Pencils and Applications

    NASA Astrophysics Data System (ADS)

    Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd

    2014-04-01

    Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.

  6. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

  7. Electric current quadratic in an applied electric field

    NASA Astrophysics Data System (ADS)

    Deyo, Eric

    The theory of the photogalvanic effect in a low frequency electric field is developed. We complete the semiclassical theory of the effect in bulk samples lacking inversion symmetry, taking into account contributions from the asymmetry of scattering, the shift current, and the effect of Berry's phase. We consider the effect in such samples both in the presence and absence of a constant magnetic field. It is found that by experimentally measuring this effect, that Berry's curvature and the average shift of the center of mass of an electron during a scattering event can be extracted. We also investigate the magnetic field dependence of the part of the electrical current which is quadratic in voltage in mesoscopic conductors. We find that the part of the current which is quadratic in bias voltage, and linear in an applied magnetic field can be related to the effective electron-electron interaction strength. We also find that in the case when the magnetic field is oriented parallel to the plane of a two dimensional sample, that the spin-orbit scattering rate can be measured.

  8. Geometric Approaches to Quadratic Equations from Other Times and Places.

    ERIC Educational Resources Information Center

    Allaire, Patricia R.; Bradley, Robert E.

    2001-01-01

    Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

  9. Use of quadratic components for buckling calculations

    SciTech Connect

    Dohrmann, C.R.; Segalman, D.J.

    1996-12-31

    A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.

  10. Bifurcations in biparametric quadratic potentials. II.

    PubMed

    Lanchares, V.; Elipe, A.

    1995-09-01

    Quadratic Hamiltonians with the phase space on the S (2) sphere represent numerous dynamical systems. There are only two classes of quadratic Hamiltonians depending on two parameters. We analyze the occurrence of bifurcations and we obtain the bifurcation lines in the parameter plane for one of these classes, thus complementing the work done in a previous paper where the other class was analyzed. As the parameters evolve, the appearance-disappearance of homoclinic orbits in the phase portrait is governed by four types of bifurcations: namely the pitchfork, the butterfly, the oyster and the pentadent bifurcations. We find also values where the system is degenerate, that is, there are nonisolated equilibria. (c) 1995 American Institute of Physics.

  11. Linear collider: a preview

    SciTech Connect

    Wiedemann, H.

    1981-11-01

    Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center.

  12. Schwarz and multilevel methods for quadratic spline collocation

    SciTech Connect

    Christara, C.C.; Smith, B.

    1994-12-31

    Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.

  13. A quadratic-shaped-finger comb parametric resonator

    NASA Astrophysics Data System (ADS)

    Guo, Congzhong; Fedder, Gary K.

    2013-09-01

    A large-stroke (8 µm) parametric resonator excited by an in-plane ‘shaped-finger’ electrostatic comb drive is fabricated using a 15 µm thick silicon-on-insulator microelectromechanical systems (SOI-MEMS) process. A quadratic capacitance-engagement response is synthesized by engineering a custom-shaped comb finger profile. A folded-flexure suspension allows lateral motion while constraining rotational modes. The excitation of the nonlinear parametric resonance is realized by selecting an appropriate combination of the linear and cubic electrostatic stiffness coefficients through a specific varying-gap comb-finger design. The large-amplitude parametric resonance promotes high signal-to-noise ratio for potential use in sensitive chemical gravimetric sensors, strain gauges, and mode-matched gyroscope applications.

  14. Wind turbine power tracking using an improved multimodel quadratic approach.

    PubMed

    Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

    2010-07-01

    In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables.

  15. Cosmology for quadratic gravity in generalized Weyl geometry

    SciTech Connect

    Jiménez, Jose Beltrán; Heisenberg, Lavinia; Koivisto, Tomi S.

    2016-04-26

    A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.

  16. Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

    ERIC Educational Resources Information Center

    Laine, A. D.

    2015-01-01

    There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

  17. THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

    EPA Science Inventory

    Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

  18. Characterization of a Quadratic Function in Rn

    ERIC Educational Resources Information Center

    Xu, Conway

    2010-01-01

    It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

  19. Monotone and convex quadratic spline interpolation

    NASA Technical Reports Server (NTRS)

    Lam, Maria H.

    1990-01-01

    A method for producing interpolants that preserve the monotonicity and convexity of discrete data is described. It utilizes the quadratic spline proposed by Schumaker (1983) which was subsequently characterized by De Vore and Yan (1986). The selection of first order derivatives at the given data points is essential to this spline. An observation made by De Vore and Yan is generalized, and an improved method to select these derivatives is proposed. The resulting spline is completely local, efficient, and simple to implement.

  20. Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.

    2012-01-01

    This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.

  1. Quadratic optimization in ill-posed problems

    NASA Astrophysics Data System (ADS)

    Ben Belgacem, F.; Kaber, S.-M.

    2008-10-01

    Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.

  2. A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

    PubMed

    Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

    2015-01-01

    It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

  3. A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

    PubMed Central

    Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

    2015-01-01

    It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. PMID:26381742

  4. Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity

    SciTech Connect

    Golubkov, A A; Makarov, Vladimir A

    2011-11-30

    We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.

  5. Modelling non-normal data: The relationship between the skew-normal factor model and the quadratic factor model.

    PubMed

    Smits, Iris A M; Timmerman, Marieke E; Stegeman, Alwin

    2016-05-01

    Maximum likelihood estimation of the linear factor model for continuous items assumes normally distributed item scores. We consider deviations from normality by means of a skew-normally distributed factor model or a quadratic factor model. We show that the item distributions under a skew-normal factor are equivalent to those under a quadratic model up to third-order moments. The reverse only holds if the quadratic loadings are equal to each other and within certain bounds. We illustrate that observed data which follow any skew-normal factor model can be so well approximated with the quadratic factor model that the models are empirically indistinguishable, and that the reverse does not hold in general. The choice between the two models to account for deviations of normality is illustrated by an empirical example from clinical psychology.

  6. Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method

    NASA Astrophysics Data System (ADS)

    Bizyaev, I. A.; Kozlov, V. V.

    2015-12-01

    We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.

  7. Variational viewpoint of the quadratic Markov measure field models: theory and algorithms.

    PubMed

    Rivera, Mariano; Dalmau, Oscar

    2012-03-01

    We present a framework for image segmentation based on quadratic programming, i.e., by minimization of a quadratic regularized energy linearly constrained. In particular, we present a new variational derivation of the quadratic Markov measure field (QMMF) models, which can be understood as a procedure for regularizing model preferences (memberships or likelihoods). We also present efficient optimization algorithms. In the QMMFs, the uncertainty in the computed regularized probability measure field is controlled by penalizing Gini's coefficient, and hence, it affects the convexity of the quadratic programming problem. The convex case is reduced to the solution of a positive definite linear system, and for that case, an efficient Gauss-Seidel (GS) scheme is presented. On the other hand, we present an efficient projected GS with subspace minimization for optimizing the nonconvex case. We demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two-class segmentation, as well as the simultaneous estimation of segmentation and (parametric and nonparametric) generative models. We present extensions to the original formulation for including color and texture clues, as well as imprecise user scribbles in an interactive framework.

  8. A new highly adaptable design of shear-flow device for orientation of macromolecules for Linear Dichroism (LD) measurement.

    PubMed

    Lundahl, P Johan; Kitts, Catherine C; Nordén, Bengt

    2011-08-21

    This article presents a new design of flow-orientation device for the study of bio-macromolecules, including DNA and protein complexes, as well as aggregates such as amyloid fibrils and liposome membranes, using Linear Dichroism (LD) spectroscopy. The design provides a number of technical advantages that should make the device inexpensive to manufacture, easier to use and more reliable than existing techniques. The degree of orientation achieved is of the same order of magnitude as that of the commonly used concentric cylinders Couette flow cell, however, since the device exploits a set of flat strain-free quartz plates, a number of problems associated with refraction and birefringence of light are eliminated, increasing the sensitivity and accuracy of measurement. The device provides similar shear rates to those of the Couette cell but is superior in that the shear rate is constant across the gap. Other major advantages of the design is the possibility to change parts and vary sample volume and path length easily and at a low cost.

  9. AN INTRODUCTION TO THE APPLICATION OF DYNAMIC PROGRAMMING TO LINEAR CONTROL SYSTEMS

    DTIC Science & Technology

    DYNAMIC PROGRAMMING APPLIED TO OPTIMIZE LINEAR CONTROL SYSTEMS WITH QUADRATIC PERFORMANCE MEASURES. MATHEMATICAL METHODS WHICH MAY BE APPLIED TO SPACE VEHICLE AND RELATED GUIDANCE AND CONTROL PROBLEMS.

  10. Performance of the Gemini Planet Imager's adaptive optics system.

    PubMed

    Poyneer, Lisa A; Palmer, David W; Macintosh, Bruce; Savransky, Dmitry; Sadakuni, Naru; Thomas, Sandrine; Véran, Jean-Pierre; Follette, Katherine B; Greenbaum, Alexandra Z; Ammons, S Mark; Bailey, Vanessa P; Bauman, Brian; Cardwell, Andrew; Dillon, Daren; Gavel, Donald; Hartung, Markus; Hibon, Pascale; Perrin, Marshall D; Rantakyrö, Fredrik T; Sivaramakrishnan, Anand; Wang, Jason J

    2016-01-10

    The Gemini Planet Imager's adaptive optics (AO) subsystem was designed specifically to facilitate high-contrast imaging. A definitive description of the system's algorithms and technologies as built is given. 564 AO telemetry measurements from the Gemini Planet Imager Exoplanet Survey campaign are analyzed. The modal gain optimizer tracks changes in atmospheric conditions. Science observations show that image quality can be improved with the use of both the spatially filtered wavefront sensor and linear-quadratic-Gaussian control of vibration. The error budget indicates that for all targets and atmospheric conditions AO bandwidth error is the largest term.

  11. White noise analysis of pace-maker-response interactions and non-linearities in slowly adapting crayfish stretch receptor.

    PubMed Central

    Buño, W; Bustamante, J; Fuentes, J

    1984-01-01

    Input-output relations were investigated in the slowly adapting stretch receptor organ of crayfish using a Gaussian white noise length input with a 0.03-12.5 Hz band width and the resulting action potential output. The noise input was presented to the de-efferented receptor in situ, at three mean elongations and at four different amplitudes. The three mean elongations were set within the normal range in vivo, two at the extremes close to the minimum and maximum physiological lengths and the other in the mid-range. With white noise inputs there is a finite probability that the system will be tested in all possible conditions within the chosen band width because white noise has the advantage that it contains, with a finite probability, all possible stimulus wave forms at random. The analysis indicated similarities between the effects of the input variables, namely white noise amplitude and mean elongation. With low input variables the activity was periodic. With larger inputs, impulse rates were higher and irregular. The average length trajectories leading to a spike (i.e. the average stimulus) were either biphasic with high inputs or multiphasic and periodic with lower input variables. The frequency of periodicity increased with mean elongation. Although for a given length and noise amplitude a variety of individual length trajectories preceded spikes, the final biphasic shortening-lengthening average stimulus sequence before a spike was similar in all cases irrespective of the input variables. The number of possible trajectories decreased with increments in the input variables. The standard deviation of length values for each average stimulus was computed and displayed as a function of time relative to the spike. It was first constant, and decreased gradually to a minimum value at the spike reference. Standard deviation values were lower for higher white noise amplitudes and mean elongation. Simple, short-lasting stimulus wave forms in the white noise were isolated

  12. Reduced order parameter estimation using quasilinearization and quadratic programming

    NASA Astrophysics Data System (ADS)

    Siade, Adam J.; Putti, Mario; Yeh, William W.-G.

    2012-06-01

    The ability of a particular model to accurately predict how a system responds to forcing is predicated on various model parameters that must be appropriately identified. There are many algorithms whose purpose is to solve this inverse problem, which is often computationally intensive. In this study, we propose a new algorithm that significantly reduces the computational burden associated with parameter identification. The algorithm is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters. The resulting inverse problem therefore becomes a linear regression or quadratic programming problem (QP) for minimizing the sum of squared residuals; the solution becomes an update on the parameter set. This process of linearization and regression is repeated until convergence takes place. This algorithm has not received much attention, as the QPs can become quite large, often infeasible for real-world systems. To alleviate this drawback, proper orthogonal decomposition is applied to reduce the size of the linearized model, thereby reducing the computational burden of solving each QP. In fact, this study shows that the snapshots need only be calculated once at the very beginning of the algorithm, after which no further calculations of the reduced-model subspace are required. The proposed algorithm therefore only requires one linearized full-model run per parameter at the first iteration followed by a series of reduced-order QPs. The method is applied to a groundwater model with about 30,000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated.

  13. Robust model reference adaptive output feedback tracking for uncertain linear systems with actuator fault based on reinforced dead-zone modification.

    PubMed

    Bagherpoor, H M; Salmasi, Farzad R

    2015-07-01

    In this paper, robust model reference adaptive tracking controllers are considered for Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) linear systems containing modeling uncertainties, unknown additive disturbances and actuator fault. Two new lemmas are proposed for both SISO and MIMO, under which dead-zone modification rule is improved such that the tracking error for any reference signal tends to zero in such systems. In the conventional approach, adaption of the controller parameters is ceased inside the dead-zone region which results tracking error, while preserving the system stability. In the proposed scheme, control signal is reinforced with an additive term based on tracking error inside the dead-zone which results in full reference tracking. In addition, no Fault Detection and Diagnosis (FDD) unit is needed in the proposed approach. Closed loop system stability and zero tracking error are proved by considering a suitable Lyapunov functions candidate. It is shown that the proposed control approach can assure that all the signals of the close loop system are bounded in faulty conditions. Finally, validity and performance of the new schemes have been illustrated through numerical simulations of SISO and MIMO systems in the presence of actuator faults, modeling uncertainty and output disturbance.

  14. Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.

    PubMed

    Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A

    2016-03-21

    Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics.

  15. Constrained neural approaches to quadratic assignment problems.

    PubMed

    Ishii, S; Sato, M

    1998-08-01

    In this paper, we discuss analog neural approaches to the quadratic assignment problem (QAP). These approaches employ a hard constraints scheme to restrict the domain space, and are able to obtain much improved solutions over conventional neural approaches. Since only a few strong heuristics for QAP have been known to date, our approaches are good alternatives, capable of obtaining fairly good solutions in a short period of time. Some of them can also be applied to large-scale problems, say of size N>/=300.

  16. Quadratic finite elements and incompressible viscous flows.

    SciTech Connect

    Dohrmann, Clark R.; Gartling, David K.

    2005-01-01

    Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.

  17. A quadratic analog-to-digital converter

    NASA Technical Reports Server (NTRS)

    Harrison, D. C.; Staples, M. H.

    1980-01-01

    An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.

  18. On the classification of elliptic foliations induced by real quadratic fields with center

    NASA Astrophysics Data System (ADS)

    Puchuri, Liliana; Bueno, Orestes

    2016-12-01

    Related to the study of Hilbert's infinitesimal problem, is the problem of determining the existence and estimating the number of limit cycles of the linear perturbation of Hamiltonian fields. A classification of the elliptic foliations in the projective plane induced by the fields obtained by quadratic fields with center was already studied by several authors. In this work, we devise a unified proof of the classification of elliptic foliations induced by quadratic fields with center. This technique involves using a formula due to Cerveau & Lins Neto to calculate the genus of the generic fiber of a first integral of foliations of these kinds. Furthermore, we show that these foliations induce several examples of linear families of foliations which are not bimeromorphically equivalent to certain remarkable examples given by Lins Neto.

  19. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1988-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

  20. Blind deconvolution estimation of fluorescence measurements through quadratic programming

    NASA Astrophysics Data System (ADS)

    Campos-Delgado, Daniel U.; Gutierrez-Navarro, Omar; Arce-Santana, Edgar R.; Skala, Melissa C.; Walsh, Alex J.; Jo, Javier A.

    2015-07-01

    Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.

  1. Adaptive SPECT

    PubMed Central

    Barrett, Harrison H.; Furenlid, Lars R.; Freed, Melanie; Hesterman, Jacob Y.; Kupinski, Matthew A.; Clarkson, Eric; Whitaker, Meredith K.

    2008-01-01

    Adaptive imaging systems alter their data-acquisition configuration or protocol in response to the image information received. An adaptive pinhole single-photon emission computed tomography (SPECT) system might acquire an initial scout image to obtain preliminary information about the radiotracer distribution and then adjust the configuration or sizes of the pinholes, the magnifications, or the projection angles in order to improve performance. This paper briefly describes two small-animal SPECT systems that allow this flexibility and then presents a framework for evaluating adaptive systems in general, and adaptive SPECT systems in particular. The evaluation is in terms of the performance of linear observers on detection or estimation tasks. Expressions are derived for the ideal linear (Hotelling) observer and the ideal linear (Wiener) estimator with adaptive imaging. Detailed expressions for the performance figures of merit are given, and possible adaptation rules are discussed. PMID:18541485

  2. Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube

    NASA Astrophysics Data System (ADS)

    Mittelmann, Hans; Peng, Jiming; Wu, Xiaolin

    2009-07-01

    In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs. Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.

  3. Mechanical cooling in single-photon optomechanics with quadratic nonlinearity

    NASA Astrophysics Data System (ADS)

    Gu, Wen-ju; Yi, Zhen; Sun, Li-hui; Xu, Da-hai

    2015-08-01

    In the paper we study the nonlinear mechanical cooling processes in an intrinsic quadratically optomechanical coupling system without linearizing the optomechanical interaction. We apply scattering theory to calculate the transition rates between different mechanical Fock states using the resolvent of the Hamiltonian, which allows for a direct identification of the underlying physical processes, where only even-phonon transitions are permitted and odd-phonon transitions are forbidden. We verify the feasibility of the approach by comparing the steady-state mean phonon number obtained from transition rates with the simulation of the full quantum master equation, and also discuss the analytical results in the weak coupling limit that coincide with two-phonon mechanical cooling processes. Furthermore, to evaluate the statistical properties of steady mechanical state, we respectively apply the Mandel Q parameter to show that the oscillator can be in nonclassical mechanical states, and the phonon number fluctuations F to display that the even-phonon transitions favor suppressing the phonon number fluctuations compared to the linear coupling optomechanical system.

  4. Adaptive support vector regression for UAV flight control.

    PubMed

    Shin, Jongho; Jin Kim, H; Kim, Youdan

    2011-01-01

    This paper explores an application of support vector regression for adaptive control of an unmanned aerial vehicle (UAV). Unlike neural networks, support vector regression (SVR) generates global solutions, because SVR basically solves quadratic programming (QP) problems. With this advantage, the input-output feedback-linearized inverse dynamic model and the compensation term for the inversion error are identified off-line, which we call I-SVR (inversion SVR) and C-SVR (compensation SVR), respectively. In order to compensate for the inversion error and the unexpected uncertainty, an online adaptation algorithm for the C-SVR is proposed. Then, the stability of the overall error dynamics is analyzed by the uniformly ultimately bounded property in the nonlinear system theory. In order to validate the effectiveness of the proposed adaptive controller, numerical simulations are performed on the UAV model.

  5. A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model.

    PubMed

    Endicott, Julia S; Joubert-Doriol, Loïc; Izmaylov, Artur F

    2014-07-21

    We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.

  6. Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence

    NASA Astrophysics Data System (ADS)

    Khaneja, Navin

    2017-03-01

    In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system. This article is part of the themed issue 'Horizons of cybernetical physics'.

  7. Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence.

    PubMed

    Khaneja, Navin

    2017-03-06

    In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system.This article is part of the themed issue 'Horizons of cybernetical physics'.

  8. A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model

    SciTech Connect

    Endicott, Julia S.; Joubert-Doriol, Loïc; Izmaylov, Artur F.

    2014-07-21

    We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.

  9. Some Aspects of Quadratic Generalized White Noise Functionals

    NASA Astrophysics Data System (ADS)

    Si, Si; Hida, Takeyuki

    2009-02-01

    We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.

  10. Development of a log-quadratic model to describe microbial inactivation, illustrated by thermal inactivation of Clostridium botulinum.

    PubMed

    Stone, G; Chapman, B; Lovell, D

    2009-11-01

    In the commercial food industry, demonstration of microbiological safety and thermal process equivalence often involves a mathematical framework that assumes log-linear inactivation kinetics and invokes concepts of decimal reduction time (D(T)), z values, and accumulated lethality. However, many microbes, particularly spores, exhibit inactivation kinetics that are not log linear. This has led to alternative modeling approaches, such as the biphasic and Weibull models, that relax strong log-linear assumptions. Using a statistical framework, we developed a novel log-quadratic model, which approximates the biphasic and Weibull models and provides additional physiological interpretability. As a statistical linear model, the log-quadratic model is relatively simple to fit and straightforwardly provides confidence intervals for its fitted values. It allows a D(T)-like value to be derived, even from data that exhibit obvious "tailing." We also showed how existing models of non-log-linear microbial inactivation, such as the Weibull model, can fit into a statistical linear model framework that dramatically simplifies their solution. We applied the log-quadratic model to thermal inactivation data for the spore-forming bacterium Clostridium botulinum and evaluated its merits compared with those of popular previously described approaches. The log-quadratic model was used as the basis of a secondary model that can capture the dependence of microbial inactivation kinetics on temperature. This model, in turn, was linked to models of spore inactivation of Sapru et al. and Rodriguez et al. that posit different physiological states for spores within a population. We believe that the log-quadratic model provides a useful framework in which to test vitalistic and mechanistic hypotheses of inactivation by thermal and other processes.

  11. Bones' adaptive response to mechanical loading is essentially linear between the low strains associated with disuse and the high strains associated with the lamellar/woven bone transition.

    PubMed

    Sugiyama, Toshihiro; Meakin, Lee B; Browne, William J; Galea, Gabriel L; Price, Joanna S; Lanyon, Lance E

    2012-08-01

    There is a widely held view that the relationship between mechanical loading history and adult bone mass/strength includes an adapted state or "lazy zone" where the bone mass/strength remains constant over a wide range of strain magnitudes. Evidence to support this theory is circumstantial. We investigated the possibility that the "lazy zone" is an artifact and that, across the range of normal strain experience, features of bone architecture associated with strength are linearly related in size to their strain experience. Skeletally mature female C57BL/6 mice were right sciatic neurectomized to minimize natural loading in their right tibiae. From the fifth day, these tibiae were subjected to a single period of external axial loading (40, 10-second rest interrupted cycles) on alternate days for 2 weeks, with a peak dynamic load magnitude ranging from 0 to 14 N (peak strain magnitude: 0-5000 µε) and a constant loading rate of 500 N/s (maximum strain rate: 75,000 µε/s). The left tibiae were used as internal controls. Multilevel regression analyses suggest no evidence of any discontinuity in the progression of the relationships between peak dynamic load and three-dimensional measures of bone mass/strength in both cortical and cancellous regions. These are essentially linear between the low-peak locomotor strains associated with disuse (∼300 µε) and the high-peak strains derived from artificial loading and associated with the lamellar/woven bone transition (∼5000 µε). The strain:response relationship and minimum effective strain are site-specific, probably related to differences in the mismatch in strain distribution between normal and artificial loading at the locations investigated.

  12. Large-scale sequential quadratic programming algorithms

    SciTech Connect

    Eldersveld, S.K.

    1992-09-01

    The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

  13. Null steering of adaptive beamforming using linear constraint minimum variance assisted by particle swarm optimization, dynamic mutated artificial immune system, and gravitational search algorithm.

    PubMed

    Darzi, Soodabeh; Kiong, Tiong Sieh; Islam, Mohammad Tariqul; Ismail, Mahamod; Kibria, Salehin; Salem, Balasem

    2014-01-01

    Linear constraint minimum variance (LCMV) is one of the adaptive beamforming techniques that is commonly applied to cancel interfering signals and steer or produce a strong beam to the desired signal through its computed weight vectors. However, weights computed by LCMV usually are not able to form the radiation beam towards the target user precisely and not good enough to reduce the interference by placing null at the interference sources. It is difficult to improve and optimize the LCMV beamforming technique through conventional empirical approach. To provide a solution to this problem, artificial intelligence (AI) technique is explored in order to enhance the LCMV beamforming ability. In this paper, particle swarm optimization (PSO), dynamic mutated artificial immune system (DM-AIS), and gravitational search algorithm (GSA) are incorporated into the existing LCMV technique in order to improve the weights of LCMV. The simulation result demonstrates that received signal to interference and noise ratio (SINR) of target user can be significantly improved by the integration of PSO, DM-AIS, and GSA in LCMV through the suppression of interference in undesired direction. Furthermore, the proposed GSA can be applied as a more effective technique in LCMV beamforming optimization as compared to the PSO technique. The algorithms were implemented using Matlab program.

  14. Conditions for Stabilizability of Linear Switched Systems

    NASA Astrophysics Data System (ADS)

    Minh, Vu Trieu

    2011-06-01

    This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence.

  15. Learning control for minimizing a quadratic cost during repetitions of a task

    NASA Technical Reports Server (NTRS)

    Longman, Richard W.; Chang, Chi-Kuang

    1990-01-01

    In many applications, control systems are asked to perform the same task repeatedly. Learning control laws have been developed over the last few years that allow the controller to improve its performance each repetition, and to converge to zero error in tracking a desired trajectory. This paper generates a new type of learning control law that learns to minimize a quadratic cost function for tracking. Besides being of interest in its own right, this objective alleviates the need to specify a desired trajectory that can actually be performed by the system. The approach used here is to adapt appropriate methods from numerical optimization theory in order to produce learning control algorithms that adjust the system command from repetition to repetition in order to converge to the quadratic cost optimal trajectory.

  16. Linear force device

    NASA Technical Reports Server (NTRS)

    Clancy, John P.

    1988-01-01

    The object of the invention is to provide a mechanical force actuator which is lightweight and manipulatable and utilizes linear motion for push or pull forces while maintaining a constant overall length. The mechanical force producing mechanism comprises a linear actuator mechanism and a linear motion shaft mounted parallel to one another. The linear motion shaft is connected to a stationary or fixed housing and to a movable housing where the movable housing is mechanically actuated through actuator mechanism by either manual means or motor means. The housings are adapted to releasably receive a variety of jaw or pulling elements adapted for clamping or prying action. The stationary housing is adapted to be pivotally mounted to permit an angular position of the housing to allow the tool to adapt to skewed interfaces. The actuator mechanisms is operated by a gear train to obtain linear motion of the actuator mechanism.

  17. Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

    NASA Astrophysics Data System (ADS)

    Du, Liang; Zhou, Xiaoting; Fiete, Gregory A.

    2017-01-01

    In this paper we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three-band model, while leaving the flat band dispersionless. We find a small gap is also opened at the quadratic band touching point by two-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this three-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems.

  18. A search-free method for calculating the tunings of PID controllers for the minimum of a quadratic criterion

    NASA Astrophysics Data System (ADS)

    Pikina, G. A.; Meshcheryakova, Yu. S.

    2012-10-01

    A new method for calculating the tunings of PID controllers for linear plants with a time delay minimizing the quadratic criterion I 2 is considered. The idea of the proposed method consists in obtaining the complex frequency response of the optimal linear controller followed by approaching to it the complex frequency response of a PID controller in the essential frequency band using the least squares method.

  19. Geometric quadratic stochastic operator on countable infinite set

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-02-03

    In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

  20. Tangent Lines without Derivatives for Quadratic and Cubic Equations

    ERIC Educational Resources Information Center

    Carroll, William J.

    2009-01-01

    In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

  1. Some Paradoxical Results for the Quadratically Weighted Kappa

    ERIC Educational Resources Information Center

    Warrens, Matthijs J.

    2012-01-01

    The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories "n" it is shown that if one of the raters uses the same…

  2. Visualising the Roots of Quadratic Equations with Complex Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2014-01-01

    This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

  3. Convexity preserving C2 rational quadratic trigonometric spline

    NASA Astrophysics Data System (ADS)

    Dube, Mridula; Tiwari, Preeti

    2012-09-01

    A C2 rational quadratic trigonometric spline interpolation has been studied using two kind of rational quadratic trigonometric splines. It is shown that under some natural conditions the solution of the problem exits and is unique. The necessary and sufficient condition that constrain the interpolation curves to be convex in the interpolating interval or subinterval are derived.

  4. Sketching the General Quadratic Equation Using Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Stols, G. H.

    2005-01-01

    This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

  5. Analysis of Students' Error in Learning of Quadratic Equations

    ERIC Educational Resources Information Center

    Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

    2010-01-01

    The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

  6. An Authentic Task That Models Quadratics

    ERIC Educational Resources Information Center

    Baron, Lorraine M.

    2015-01-01

    As students develop algebraic reasoning in grades 5 to 9, they learn to recognize patterns and understand expressions, equations, and variables. Linear functions are a focus in eighth-grade mathematics, and by algebra 1, students must make sense of functions that are not linear. This article describes how students worked through a classroom task…

  7. Simple quadratic magneto-optic Kerr effect measurement system using permanent magnets.

    PubMed

    Pradeep, A V; Ghosh, Sayak; Anil Kumar, P S

    2017-01-01

    In recent times, quadratic magneto-optic Kerr effect (QMOKE) is emerging as an important experimental tool to investigate higher-order spin-orbit interactions in magnetic thin films and heterostructures. We have designed and constructed a simple, cost-effective QMOKE measurement system using permanent magnets. The permanent magnets are mounted on the inner surface of a cylindrical ferromagnetic yoke which can be rotated about its axis. Our system is sensitive to both the quadratic and linear MOKE signals. We use rotating field method to extract the QMOKE components in saturation. This system is capable of extracting the QMOKE signal from single crystals and thin film samples. Here we present the construction and working of the QMOKE measurement system using permanent magnets and report, for the first time, the QMOKE signal from Fe3O4 single crystal.

  8. Magneto-optical conductivity of Weyl semimetals with quadratic term in momentum

    NASA Astrophysics Data System (ADS)

    Shao, J. M.; Yang, G. W.

    2016-02-01

    Weyl semimetal is a three-dimensional Dirac material whose low energy dispersion is linear in momentum. Adding a quadratic (Schrödinger) term to the Weyl node breaks the original particle-hole symmetry and also breaks the mirror symmetry between the positive and negative Landau levels in present of magnetic field. This asymmetry splits the absorption line of the longitudinal magneto-optical conductivity into a two peaks structure. It also results in an oscillation pattern in the absorption part of the Hall conductivity. The two split peaks in Reσxx (or the positive and negative oscillation in Imσxy) just correspond to the absorptions of left-handed (σ-) and right-handed (σ+) polarization light, respectively. The split in Reσxx and the displacement between the absorption of σ+ and σ- are decided by the magnitude of the quadratic term and the magnetic field.

  9. The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

    NASA Technical Reports Server (NTRS)

    Townsend, Barbara K.

    1986-01-01

    A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

  10. The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

    NASA Technical Reports Server (NTRS)

    Townsend, Barbara K.

    1987-01-01

    A control-system design method, quadratic optimal cooperative control synthesis (CCS), is applied to the design of a stability and control augmentation system (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design method, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and linear quadratic regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

  11. Stochastic resonance in a fractional oscillator driven by multiplicative quadratic noise

    NASA Astrophysics Data System (ADS)

    Ren, Ruibin; Luo, Maokang; Deng, Ke

    2017-02-01

    Stochastic resonance of a fractional oscillator subject to an external periodic field as well as to multiplicative and additive noise is investigated. The fluctuations of the eigenfrequency are modeled as the quadratic function of the trichotomous noise. Applying the moment equation method and Shapiro–Loginov formula, we obtain the exact expression of the complex susceptibility and related stability criteria. Theoretical analysis and numerical simulations indicate that the spectral amplification (SPA) depends non-monotonicly both on the external driving frequency and the parameters of the quadratic noise. In addition, the investigations into fractional stochastic systems have suggested that both the noise parameters and the memory effect can induce the phenomenon of stochastic multi-resonance (SMR), which is previously reported and believed to be absent in the case of the multiplicative noise with only a linear term.

  12. A Neurodynamic Optimization Approach to Bilevel Quadratic Programming.

    PubMed

    Qin, Sitian; Le, Xinyi; Wang, Jun

    2016-08-19

    This paper presents a neurodynamic optimization approach to bilevel quadratic programming (BQP). Based on the Karush-Kuhn-Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). It is proved that the global solution of the MPCC is the minimal one of the optimal solutions to multiple convex optimization subproblems. A recurrent neural network is developed for solving these convex optimization subproblems. From any initial state, the state of the proposed neural network is convergent to an equilibrium point of the neural network, which is just the optimal solution of the convex optimization subproblem. Compared with existing recurrent neural networks for BQP, the proposed neural network is guaranteed for delivering the exact optimal solutions to any convex BQP problems. Moreover, it is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time. Finally, three numerical examples are elaborated to substantiate the efficacy of the proposed approach.

  13. Approximate Graph Edit Distance in Quadratic Time.

    PubMed

    Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst

    2015-09-14

    Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

  14. Extremal Optimization for Quadratic Unconstrained Binary Problems

    NASA Astrophysics Data System (ADS)

    Boettcher, S.

    We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.

  15. Estimability and Regulability of Linear Systems

    NASA Technical Reports Server (NTRS)

    Baram, Yoram; Kailath, Thomas

    1988-01-01

    A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feedback is used. Estimability and regulability are shown to be dual properties, equivalent to the nonreducibility of the Kalman filter and of the optimal linear quadratic regulator, respectively.

  16. Adaptive control of Space Station with control moment gyros

    NASA Technical Reports Server (NTRS)

    Bishop, Robert H.; Paynter, Scott J.; Sunkel, John W.

    1992-01-01

    An adaptive approach to Space Station attitude control is investigated. The main components of the controller are the parameter identification scheme, the control gain calculation, and the control law. The control law is a full-state feedback space station baseline control law. The control gain calculation is based on linear-quadratic regulator theory with eigenvalues placement in a vertical strip. The parameter identification scheme is a recursive extended Kalman filter that estimates the inertias and also provides an estimate of the unmodeled disturbances due to the aerodynamic torques and to the nonlinear effects. An analysis of the inertia estimation problem suggests that it is possible to estimate Space Station inertias accurately during nominal control moment gyro operations. The closed-loop adaptive control law is shown to be capable of stabilizing the Space Station after large inertia changes. Results are presented for the pitch axis.

  17. Adaptive control of large space structures using recursive lattice filters

    NASA Technical Reports Server (NTRS)

    Sundararajan, N.; Goglia, G. L.

    1985-01-01

    The use of recursive lattice filters for identification and adaptive control of large space structures is studied. Lattice filters were used to identify the structural dynamics model of the flexible structures. This identification model is then used for adaptive control. Before the identified model and control laws are integrated, the identified model is passed through a series of validation procedures and only when the model passes these validation procedures is control engaged. This type of validation scheme prevents instability when the overall loop is closed. Another important area of research, namely that of robust controller synthesis, was investigated using frequency domain multivariable controller synthesis methods. The method uses the Linear Quadratic Guassian/Loop Transfer Recovery (LQG/LTR) approach to ensure stability against unmodeled higher frequency modes and achieves the desired performance.

  18. Wavelet domain image restoration with adaptive edge-preserving regularization.

    PubMed

    Belge, M; Kilmer, M E; Miller, E L

    2000-01-01

    In this paper, we consider a wavelet based edge-preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e., edges in two dimensions or jumps in one dimension). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image. In particular, we are able to adapt quite easily to scale-varying and orientation-varying features in the image while simultaneously retaining the edge preservation properties of the regularizer. We demonstrate a half-quadratic algorithm for obtaining the restorations from observed data.

  19. Emotion suppression moderates the quadratic association between RSA and executive function.

    PubMed

    Spangler, Derek P; Bell, Martha Ann; Deater-Deckard, Kirby

    2015-09-01

    There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated (a) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (b) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a 2-min resting period during which electrocardiogram (ECG) was continually assessed. In the next phase, the women completed an array of executive function and nonexecutive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance.

  20. Emotion suppression moderates the quadratic association between RSA and executive function

    PubMed Central

    Spangler, Derek P.; Bell, Martha Ann; Deater-Deckard, Kirby

    2016-01-01

    There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated: (1) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (2) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a two-minute resting period during which ECG was continually assessed. In the next phase, the women completed an array of executive function and non-executive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. PMID:26018941

  1. Zeta-determinants of Sturm-Liouville operators with quadratic potentials at infinity

    NASA Astrophysics Data System (ADS)

    Hartmann, Luiz; Lesch, Matthias; Vertman, Boris

    2017-03-01

    We consider Sturm-Liouville operators on a half line [ a , ∞) , a > 0, with potentials that are growing at most quadratically at infinity. Such operators arise naturally in the analysis of hyperbolic manifolds, or more generally manifolds with cusps. We establish existence and a formula for the associated zeta-determinant in terms of the Wronski-determinant of a fundamental system of solutions adapted to the boundary conditions. Despite being the natural objects in the context of hyperbolic geometry, spectral geometry of such operators has only recently been studied in the context of analytic torsion.

  2. Finite-element analysis of earing using non-quadratic yield surfaces

    SciTech Connect

    Logan, R.W.

    1995-06-18

    During deep draw cupping, the phenomenon known as earing may occur as the cup wall is formed, resulting in a periodic variation of cup wall height around the perimeter of the finished cup. This is generally due to planar anisotropy of flow in rolled sheet product. It is generally observed that the anisotropy parameter R will vary in the plane of the sheet when ears are observed in cupping, with a parameter {Delta}R describing the variation of R in the plane of the sheet. For many common textures in face-centered and body-centered materials, the ears form relative to the sheet rolling direction at 0{degrees} and 90{degrees} around the perimeter if {Delta}R>0, and at -45{degrees} and +45{degrees} if {Delta}R<0. There is extensive experimental evidence that ear height shows a linear correlation with {Delta}R/R, but attempts to duplicate this using the finite-element method are highly dependent on both the methodology and yield surface used. It was shown previously that using a coarse mesh and the quadratic Hill yield surface tends to greatly under predict earing. In this study, we have used two different finite-element codes developed at LLNL to examine the predicted earing using both quadratic Hill and alternative non-quadratic yield surfaces. These results are compared to experimental data and conclusions drawn about the most desirable closed-form yield surfaces to duplicate the observed earing phenomena.

  3. Chaos synchronization based on quadratic optimum regulation and control

    NASA Astrophysics Data System (ADS)

    Gong, Lihua

    2005-03-01

    Based on the method of the quadratic optimum control, a quadratic optimal regulator used for synchronizing chaotic systems is constructed to realize chaos synchronization. The synchronization method can maintain the least error with less control energy, and then realize the optimization on both sides of energy and error synthetically. In addition, the control cost can also be reduced by using this method intermittently. The simulation results of the chaotic Chua's circuit and the Rossler chaos system prove that the method is effective.

  4. Quadratic bulk viscosity and the topology of space time.

    NASA Astrophysics Data System (ADS)

    Wolf, C.

    1997-12-01

    By considering a homogeneous isotropic universe admitting quadratic bulk viscosity the author shows that if the bulk viscosity coefficient is large the effective topology of space time attains an antiintuitive interpretation in the sense that a positive curvature space time is ever-expanding. This is true for all cosmologies studied except in the case of small quadratic bulk viscosity (3γ+1-kβ ≥ 0, 3γ+1 > 0).

  5. The dynamics of a symmetric coupling of three modified quadratic maps

    NASA Astrophysics Data System (ADS)

    Paulo, C. Rech

    2013-08-01

    We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark—Sacker bifurcations of stable period-1, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.

  6. MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements

    NASA Technical Reports Server (NTRS)

    Mitchell, William F.

    1993-01-01

    MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.

  7. Gravity waves from non-minimal quadratic inflation

    SciTech Connect

    Pallis, Constantinos; Shafi, Qaisar

    2015-03-12

    We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio r≃(2−4)⋅10{sup −3}, and an inflaton mass close to 3⋅10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kähler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s}≃0.963 and r≃0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kähler potential, and the prefactor encountered in it. Increasing slightly the latter above (−3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5−9)⋅10{sup 13} GeV.

  8. Linear stochastic optimal control and estimation

    NASA Technical Reports Server (NTRS)

    Geyser, L. C.; Lehtinen, F. K. B.

    1976-01-01

    Digital program has been written to solve the LSOCE problem by using a time-domain formulation. LSOCE problem is defined as that of designing controls for linear time-invariant system which is disturbed by white noise in such a way as to minimize quadratic performance index.

  9. On the linear and non-linear electronic spectroscopy of chlorophylls: a computational study.

    PubMed

    Graczyk, Alicja; Żurek, Justyna M; Paterson, Martin J

    2014-01-01

    A theoretical analysis of linear and non-linear (two-photon absorption) electronic spectroscopy of all known porphyrinic pigments has been performed using linear and quadratic density functional response theory, with the long-range corrected CAM-B3LYP functional. We found that higher Soret transitions often contain non-Gouterman contributions and that each chlorophyll has the possibility for resonance enhanced TPA in the Soret region, although there is also significant TPA in the Q region.

  10. Adaptive control of Space Station during nominal operations with CMGs. [Control Moment Gyroscopes

    NASA Technical Reports Server (NTRS)

    Bishop, R. H.; Paynter, S. J.; Sunkel, J. W.

    1991-01-01

    An adaptive control approach is investigated for the Space Station. The main components of the adaptive controller are the parameter identification scheme, the control gain calculation, and the control law. The control law is the Space Station baseline control law. The control gain calculation is based on linear quadratic regulator theory with eigenvalue placement in a vertical strip. The parameter identification scheme is a real-time recursive extended Kalman filter which estimates the inertias and also provides an estimate of the unmodeled disturbances due to the aerodynamic torques and to the nonlinear effects. An analysis of the inertia estimation problem suggests that it is possible to compute accurate estimates of the Space Station inertias during nominal CMG (control moment gyro) operations. The closed-loop adaptive control law is shown to be capable of stabilizing the Space Station after large inertia changes. Results are presented for the pitch axis.

  11. An adaptive guidance law for single stage to low earth orbit

    NASA Technical Reports Server (NTRS)

    Pamadi, Bandu N.

    1989-01-01

    An adaptive guidance algorithm based on a cubic spline representation of the ascent profile and imposition of a dynamic pressure constraint is studied for a single stage to low earth orbit. The flight path is divided into initial and terminal phases. In the initial phase, fully adaptive, and in the terminal phase, semi-adaptive, guidance schemes are used. The cubic spline paqrameters are determined by gradient optimization for maximum payload to orbit. In the terminal phase, a linear quadratic regulator is used to derive the optimal feedback gains to keep the vehicle close to the nominal path. The computational aspects of the guidance algorithm are examined and criteria are developed to ensure stability and convergence.

  12. An Adaptive Control Technology for Safety of a GTM-like Aircraft

    NASA Technical Reports Server (NTRS)

    Matsutani, Megumi; Crespo, Luis G.; Annaswamy, Anuradha; Jang, Jinho

    2010-01-01

    An adaptive control architecture for safe performance of a transport aircraft subject to various adverse conditions is proposed and verified in this report. This architecture combines a nominal controller based on a Linear Quadratic Regulator with integral action, and an adaptive controller that accommodates actuator saturation and bounded disturbances. The effectiveness of the baseline controller and its adaptive augmentation are evaluated using a stand-alone control veri fication methodology. Case studies that pair individual parameter uncertainties with critical flight maneuvers are studied. The resilience of the controllers is determined by evaluating the degradation in closed-loop performance resulting from increasingly larger deviations in the uncertain parameters from their nominal values. Symmetric and asymmetric actuator failures, flight upsets, and center of gravity displacements, are some of the uncertainties considered.

  13. Robust and reliable control via quadratic Lyapunov functions

    NASA Astrophysics Data System (ADS)

    Alt, Terry Robert

    In this dissertation we present a new approach to design robust and reliable controllers. Our results are used to find control laws for systems that are subject to (1) real polytopic and norm bounded uncertainties, (2) actuator and sensor variations and (3) actuator and sensor failure. In addition, we present conditions that can be added to the control design problem to constrain the controller to be stable or strictly positive real, further strengthening the robustness and reliability of the control design. The basic framework relies on the use of quadratic Lyapunov functions to accommodate potentially time varying uncertainty. Conditions are derived that, when satisfied, allow a robust control design to be obtained by performing two convex optimizations. These controllers recover the performance robustness of either state feedback or full information controllers. Sufficient conditions are presented that remove the non-convexity in terms of the control design variables. This allows a robust control design to be obtained by solving a set of linear matrix inequalities. These general robustness results are then applied to the reliability problem. Actuator and sensor variations are modeled using real polytopic uncertainties. It is shown that under some simplifying assumptions the state feedback problem reduces to a single linear matrix inequality. It also shows that the Riccati equations for standard LQR and Hsb{infty} need only a slight modification to obtain a control law that is reliable with respect to actuator variability. For the output feedback case, convex conditions are presented that yield controllers which are reliable to actuator and sensor variations. Utilizing the simultaneous Lyapunov function approach, we further extend these results to include actuator or sensor failure. Additionally, when applicable, stronger reliability guaranties may be obtained by constraining the controller to be strictly positive real. This guarantees stability for positive real

  14. Effects of classroom instruction on students' understanding of quadratic equations

    NASA Astrophysics Data System (ADS)

    Vaiyavutjamai, Pongchawee; Clements, M. A. (Ken)

    2006-05-01

    Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of transcripts of 36 interviews with 18 interviewees (a high performer, a medium performer, and a low performer from each of the six classes), were analysed. Using a rubric for assessing students' understanding, the analysis revealed that at the post-teaching stage students improved their performance on quadratic equations and had a better understanding of associated concepts than they had at the pre-teaching stage. However, many were still confused about the concepts of a variable and of a "solution" to a quadratic equation. After the lessons, most students had acquired neither an instrumental nor a relational understanding of the mathematics associated with solving elementary quadratic equations.

  15. Fast source optimization involving quadratic line-contour objectives for the resist image.

    PubMed

    Yu, Jue-Chin; Yu, Peichen; Chao, Hsueh-Yung

    2012-03-26

    In Abbe's formulation, source optimization (SO) is often formulated into a linear or quadratic problem, depending on the choice of objective functions. However, the conventional approach for the resist image, involving a sigmoid transformation of the aerial image, results in an objective with a functional form. The applicability of the resist-image objective to SO or simultaneous source and mask optimization (SMO) is therefore limited. In this paper, we present a linear combination of two quadratic line-contour objectives to approximate the resist image effect for fast convergence. The line-contour objectives are based on the aerial image on drawn edges using a constant threshold resist model and that of pixels associated with an intensity minimum for side-lobe suppression. A conjugate gradient method is employed to assure the convergence to the global minimum within the number of iterations less than that of source variables. We further compare the optimized illumination with the proposed line-contour objectives to that with a sigmoid resist-image using a steepest decent method. The results show a 100x speedup with comparable image fidelity and a slightly improved process window for the two cases studied.

  16. On the prediction of free turbulent jets with swirl using a quadratic pressure-strain model

    NASA Technical Reports Server (NTRS)

    Younis, Bassam A.; Gatski, Thomas B.; Speziale, Charles G.

    1994-01-01

    Data from free turbulent jets both with and without swirl are used to assess the performance of the pressure-strain model of Speziale, Sarkar and Gatski which is quadratic in the Reynolds stresses. Comparative predictions are also obtained with the two versions of the Launder, Reece and Rodi model which are linear in the same terms. All models are used as part of a complete second-order closure based on the solution of differential transport equations for each non-zero component of the Reynolds stress tensor together with an equation for the scalar energy dissipation rate. For non-swirling jets, the quadratic model underestimates the measured spreading rate of the plane jet but yields a better prediction for the axisymmetric case without resolving the plane jet/round jet anomaly. For the swirling axisymmetric jet, the same model accurately reproduces the effects of swirl on both the mean flow and the turbulence structure in sharp contrast with the linear models which yield results that are in serious error. The reasons for these differences are discussed.

  17. On Volterra quadratic stochastic operators with continual state space

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-05-15

    Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

  18. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

    SciTech Connect

    Fernández, Francisco M.

    2016-06-15

    We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.

  19. The linear separability problem: some testing methods.

    PubMed

    Elizondo, D

    2006-03-01

    The notion of linear separability is used widely in machine learning research. Learning algorithms that use this concept to learn include neural networks (single layer perceptron and recursive deterministic perceptron), and kernel machines (support vector machines). This paper presents an overview of several of the methods for testing linear separability between two classes. The methods are divided into four groups: Those based on linear programming, those based on computational geometry, one based on neural networks, and one based on quadratic programming. The Fisher linear discriminant method is also presented. A section on the quantification of the complexity of classification problems is included.

  20. Simple robust control laws for robot manipulators. Part 2: Adaptive case

    NASA Technical Reports Server (NTRS)

    Bayard, D. S.; Wen, J. T.

    1987-01-01

    A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations.

  1. A piecewise linear approximation scheme for hereditary optimal control problems

    NASA Technical Reports Server (NTRS)

    Cliff, E. M.; Burns, J. A.

    1977-01-01

    An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.

  2. Convergence properties of the softassign quadratic assignment algorithm.

    PubMed

    Rangarajan, A; Vuille, A; Mjolsness, E

    1999-08-15

    The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.

  3. Construction of the wave operator for non-linear dispersive equations

    NASA Astrophysics Data System (ADS)

    Tsuruta, Kai Erik

    In this thesis, we will study non-linear dispersive equations. The primary focus will be on the construction of the positive-time wave operator for such equations. The positive-time wave operator problem arises in the study of the asymptotics of a partial differential equation. It is a map from a space of initial data X into itself, and is loosely defined as follows: Suppose that for a solution ψlin to the dispersive equation with no non-linearity and initial data ψ +, there exists a unique solution ψ to the non-linear equation with initial data ψ0 such that ψ behaves as ψ lin as t → infinity. Then the wave operator is the map W+ that takes ψ + to ψ0. By its definition, W+ is injective. An important additional question is whether or not the map is also surjective. If so, then every non-linear solution emanating from X behaves, in some sense, linearly as it evolves (this is known as asymptotic completeness). Thus, there is some justification for treating these solutions as their much simpler linear counterparts. The main results presented in this thesis revolve around the construction of the wave operator(s) at critical non-linearities. We will study the "semi-relativistic" Schrodinger equation as well as the Klein-Gordon-Schrodinger system on R2 . In both cases, we will impose fairly general quadratic non-linearities for which conservation laws cannot be relied upon. These non-linearities fall below the scaling required to employ such tools as the Strichartz estimates. We instead adapt the "first iteration method" of Jang, Li, and Zhang to our setting which depends crucially on the critical decay of the non-linear interaction of the linear evolution. To see the critical decay in our problem, careful analysis is needed to treat the regime where one has spatial and/or time resonance.

  4. A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints

    SciTech Connect

    Orsi, R. J.; Mahony, R. E.; Moore, J. B.

    1999-09-15

    This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.

  5. On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with a Quadratic Trap

    NASA Astrophysics Data System (ADS)

    Chen, Xuwen

    2013-11-01

    We consider the dynamics of the three-dimensional N-body Schrödinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N 3 β-1 V( N β x). We justify the mean-field approximation and offer a rigorous derivation of the three-dimensional cubic nonlinear Schrödinger equation (NLS) with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon (Commun Math Phys 279:169-185, 2008) for by adapting and simplifying an argument in Chen and Pavlović (Annales Henri Poincaré, 2013) which solves the problem for in the absence of a trap.

  6. Solving quadratic programming problems by delayed projection neural network.

    PubMed

    Yang, Yongqing; Cao, Jinde

    2006-11-01

    In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.

  7. Unravelling Student Challenges with Quadratics: A Cognitive Approach

    ERIC Educational Resources Information Center

    Kotsopoulos, Donna

    2007-01-01

    The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

  8. Solving the Quadratic Capacitated Facilities Location Problem by Computer.

    ERIC Educational Resources Information Center

    Cote, Leon C.; Smith, Wayland P.

    Several computer programs were developed to solve various versions of the quadratic capacitated facilities location problem. Matrices, which represent various business costs, are defined for the factors of sites, facilities, customers, commodities, and production units. The objective of the program is to find an optimization matrix for the lowest…

  9. Tuning a fuzzy controller using quadratic response surfaces

    NASA Technical Reports Server (NTRS)

    Schott, Brian; Whalen, Thomas

    1992-01-01

    Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

  10. Confidence set interference with a prior quadratic bound. [in geophysics

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

  11. Entanglement entropy of fermionic quadratic band touching model

    NASA Astrophysics Data System (ADS)

    Chen, Xiao; Cho, Gil Young; Fradkin, Eduardo

    2014-03-01

    The entanglement entropy has been proven to be a useful tool to diagnose and characterize strongly correlated systems such as topologically ordered phases and some critical points. Motivated by the successes, we study the entanglement entropy (EE) of a fermionic quadratic band touching model in (2 + 1) dimension. This is a fermionic ``spinor'' model with a finite DOS at k=0 and infinitesimal instabilities. The calculation on two-point correlation functions shows that a Dirac fermion model and the quadratic band touching model both have the asymptotically identical behavior in the long distance limit. This implies that EE for the quadratic band touching model also has an area law as the Dirac fermion. This is in contradiction with the expectation that dense fermi systems with a finite DOS should exhibit LlogL violations to the area law of entanglement entropy (L is the length of the boundary of the sub-region) by analogy with the Fermi surface. We performed numerical calculations of entanglement entropies on a torus of the lattice models for the quadratic band touching point and the Dirac fermion to confirm this. The numerical calculation shows that EE for both cases satisfy the area law. We further verify this result by the analytic calculation on the torus geometry. This work was supported in part by the NSF grant DMR-1064319.

  12. Clustered Self Organising Migrating Algorithm for the Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Davendra, Donald; Zelinka, Ivan; Senkerik, Roman

    2009-08-01

    An approach of population dynamics and clustering for permutative problems is presented in this paper. Diversity indicators are created from solution ordering and its mapping is shown as an advantage for population control in metaheuristics. Self Organising Migrating Algorithm (SOMA) is modified using this approach and vetted with the Quadratic Assignment Problem (QAP). Extensive experimentation is conducted on benchmark problems in this area.

  13. Visualising the Complex Roots of Quadratic Equations with Real Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2012-01-01

    The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

  14. Radar Rainfall Estimation using a Quadratic Z-R equation

    NASA Astrophysics Data System (ADS)

    Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan

    2016-04-01

    The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.

  15. Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions

    ERIC Educational Resources Information Center

    Leyendekkers, J. V.; Shannon, A. G.

    2004-01-01

    An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

  16. Beam steering and routing in quadratic nonlinear media

    SciTech Connect

    Aceves, A.B.; Santos, M.C.; Torner, L.

    1997-04-01

    We show how the spatial phase modulation of weak second-harmonic signals controls the overall direction of propagation of spatial solitons in quadratic nonlinear media. We investigate numerically such a process and discuss its applications to all-optical beam routing. 5 refs., 3 figs.

  17. Finding the Best Quadratic Approximation of a Function

    ERIC Educational Resources Information Center

    Yang, Yajun; Gordon, Sheldon P.

    2011-01-01

    This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

  18. The influence of a prediction display on the quasi-linear describing function and remnant measured with an adaptive analog-pilot in a closed loop

    NASA Technical Reports Server (NTRS)

    Dey, D.

    1972-01-01

    The effect of a prediction display on the human transfer characteristics is explained with the aid of a quasi-linear model. The prediction display causes an increase of the gain factor and the lead factor, a diminishing of the lag factor and a decrease of the remnant. Altogether, these factors yield a smaller mean square value of the control deviation and a simultaneous decrease of the mean square value of the stick signal.

  19. Algebraic linearization of dynamics of Calogero type for any Coxeter group

    NASA Astrophysics Data System (ADS)

    Caseiro, R.; Françoise, J.-P.; Sasaki, R.

    2000-07-01

    Calogero-Moser systems can be generalized for any root system (including the noncrystallographic cases). The algebraic linearization of the generalized Calogero-Moser systems and of their quadratic (respectively quartic) perturbations are discussed.

  20. Effect of SLM pixelation on two-photon fluorescence by applying an off-centered quadratic spectral phase mask

    NASA Astrophysics Data System (ADS)

    Martins, R. J.; Siqueira, J. P.; Mendonça, C. R.

    2016-12-01

    Spatial light modulators (SLMs) have become a valuable tool to shape ultrashort laser pulses, which have found innumerous applications in different areas of ultrafast science. Despite the fact that this family of devices can be used to produce almost any arbitrary pulse shape, as long as enough bandwidth is available, there are limitations related to their discrete nature that may lead to distortions in the expected pulse shape. Here we investigate such collateral temporal distortions by quantifying the effect imposed by the discrete nature (pixelation) of liquid-crystal-based SLMs on the two-photon excited fluorescence signal of a conjugated polymer, when the central position of a quadratic spectral phase mask is scanned across the laser bandwidth. We conclude that the observed temporal distortions are related to replica pulses generated by an interplay between the additional linear phase resultant of an off-centered quadratic phase mask and pixelation of the applied phase mask.

  1. Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

    NASA Astrophysics Data System (ADS)

    Landsman, Zinoviy

    2008-10-01

    We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see , articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.

  2. Adaptive linear predictor FIR filter based on the Cyclone V FPGA with HPS to reduce narrow band RFI in AERA radio detection of cosmic rays

    SciTech Connect

    Szadkowski, Zbigniew

    2015-07-01

    We present the new approach to a filtering of radio frequency interferences (RFI) in the Auger Engineering Radio Array (AERA) which study the electromagnetic part of the Extensive Air Showers. The radio stations can observe radio signals caused by coherent emissions due to geomagnetic radiation and charge excess processes. AERA observes frequency band from 30 to 80 MHz. This range is highly contaminated by human-made RFI. In order to improve the signal to noise ratio RFI filters are used in AERA to suppress this contamination. The first kind of filter used by AERA was the Median one, based on the Fast Fourier Transform (FFT) technique. The second one, which is currently in use, is the infinite impulse response (IIR) notch filter. The proposed new filter is a finite impulse response (FIR) filter based on a linear prediction (LP). A periodic contamination hidden in a registered signal (digitized in the ADC) can be extracted and next subtracted to make signal cleaner. The FIR filter requires a calculation of n=32, 64 or even 128 coefficients (dependent on a required speed or accuracy) by solving of n linear equations with coefficients built from the covariance Toeplitz matrix. This matrix can be solved by the Levinson recursion, which is much faster than the Gauss procedure. The filter has been already tested in the real AERA radio stations on Argentinean pampas with a very successful results. The linear equations were solved either in the virtual soft-core NIOSR processor (implemented in the FPGA chip as a net of logic elements) or in the external Voipac PXA270M ARM processor. The NIOS processor is relatively slow (50 MHz internal clock), calculations performed in an external processor consume a significant amount of time for data exchange between the FPGA and the processor. Test showed a very good efficiency of the RFI suppression for stationary (long-term) contaminations. However, we observed a short-time contaminations, which could not be suppressed either by the

  3. An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems

    SciTech Connect

    Zhang Jianzhong; Zhang Liwei

    2010-02-15

    We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC{sup 1}) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/{radical}r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC{sup 1} function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.

  4. Quadratic Herman-Wallis contributions associated with vibration-rotation resonances

    NASA Astrophysics Data System (ADS)

    Watson, James K. G.

    1988-12-01

    The quadratic terms A2PRm2 and A2QJ( J + 1) in the Herman-Wallis correction factors for infrared line intensities in linear molecules are normally small for transitions between nonresonant states, but significant values are obtained for transitions involving states perturbed by Fermi or l-type resonance. Detailed equations are given for these quadratic Herman-Wallis terms in transitions from a nonresonant state to the Fermi dyad [(1, 0 0, V' 3), (0, 2 0, V' 3)] together with its l-resonance partner (0, 2 2 e, V' 3). Applications to the parallel bands [(1, 0 0, 1), (0, 2 0, 1)] ← (0, 0 0, 0) and the perpendicular bands [(1, 0 0, 0), (0, 2 0, 0), (0, 2 2, 0)] ← (0, 1 1, 0) of CO 2 and to the parallel bands [(1, 0 0, 0), (0, 2 0, 0)] ← (0, 0 0, 0) of N 2O give good agreement with recent measurements. In particular, the pattern of A2 coefficients in the three perpendicular bands of CO 2, in which the A2 coefficients have been found by Johns to be small for all three pairs of P and R branches and for the Q branch to the l = 2 component, but not for the Q branches to the l = 0 components, is shown to be due to cancellations between contributions in all branches except these two Q branches.

  5. Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Jeon, G. J.

    1983-01-01

    Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

  6. A multi-loop guidance scheme using singular perturbation and linear quadratic regulator techniques simultaneously

    NASA Astrophysics Data System (ADS)

    Bushong, Philip M.; Lutze, Frederick H.

    1992-08-01

    A design method for a multi-loop mixed discrete/continuous trajectory following pitch control algorithm for a generic aerospace vehicle is presented. This design methodology is facilitated by a time scale separation observed in the dynamical system. Results are presented for a single-stage-to-orbit hypersonic vehicle with both elevator and thrust-vector control. It is shown that the control algorithm results in a pitch loop feedback controller that is robust and very stable, and is at least near optimal for the class of trajectories considered. No claims of optimality are made for the outer loop, but it is shown in the simulations that the outer loop tracker can do a reasonable job of following the prescribed trajectory.

  7. Unified development of multiplicative algorithms for linear and quadratic nonnegative matrix factorization.

    PubMed

    Yang, Zhirong; Oja, Erkki

    2011-12-01

    Multiplicative updates have been widely used in approximative nonnegative matrix factorization (NMF) optimization because they are convenient to deploy. Their convergence proof is usually based on the minimization of an auxiliary upper-bounding function, the construction of which however remains specific and only available for limited types of dissimilarity measures. Here we make significant progress in developing convergent multiplicative algorithms for NMF. First, we propose a general approach to derive the auxiliary function for a wide variety of NMF problems, as long as the approximation objective can be expressed as a finite sum of monomials with real exponents. Multiplicative algorithms with theoretical guarantee of monotonically decreasing objective function sequence can thus be obtained. The solutions of NMF based on most commonly used dissimilarity measures such as α- and β-divergence as well as many other more comprehensive divergences can be derived by the new unified principle. Second, our method is extended to a nonseparable case that includes e.g., γ-divergence and Rényi divergence. Third, we develop multiplicative algorithms for NMF using second-order approximative factorizations, in which each factorizing matrix may appear twice. Preliminary numerical experiments demonstrate that the multiplicative algorithms developed using the proposed procedure can achieve satisfactory Karush-Kuhn-Tucker optimality. We also demonstrate NMF problems where algorithms by the conventional method fail to guarantee descent at each iteration but those by our principle are immune to such violation.

  8. Cost Cumulant-Based Control for a Class of Linear Quadratic Tracking Problems

    DTIC Science & Technology

    2006-08-04

    with the initial condition (t0, x0; u) ∈ [t0, tf ] × Rn × L2Ft(Ω; C([t0, tf ];Rm)) is a traditional finite-horizon IQF random cost J : [t0, tf ] × Rn...x0 , (5) y(t) = C(t)x(t) , (6) and the IQF random cost J(t0, x0; K, uext) = [z(tf )− y(tf )]T Qf [z(tf )− y(tf )] + ∫ tf t0 { [z(τ)− y(τ)]T Q(τ) [z(τ...track the prescribed signal z(t) with the finite-horizon IQF cost (7). For k ∈ Z+ fixed, the kth cost cumulant in the tracking problem is given κk(t0

  9. Cost Cumulant-Based Control for a Class of Linear Quadratic Tracking Problems

    DTIC Science & Technology

    2007-01-01

    t0, x0; u) ∈ [t0, tf ] × Rn × L2Ft(Ω; C([t0, tf ];Rm)) is a traditional finite-horizon IQF random cost J : [t0, tf ] × Rn × L2Ft(Ω; C([t0, tf ];Rm...C(t)x(t) , (6) and the IQF random cost J(t0, x0; K, uz) = [z(tf )− y(tf )]T Qf [z(tf )− y(tf )] + ∫ tf t0 { [z(τ)− y(τ)]T Q(τ) [z(τ)− y(τ)] + [K(τ)x(τ... IQF cost (7). For k ∈ Z+ fixed, the kth-cost cumulant of the Chi-square type random cost (7) is given by κk(t0, x0;K, uz) = xT0 H(t0, k)x0 + 2xT0 D̆

  10. Output Feedback Pole-Placement in the Design of Compensators for Suboptimal Linear Quadratic Regulators.

    DTIC Science & Technology

    1979-06-01

    summation indices to k i-J, I -i the equation becomes PCW ( Po (X) -gCQRs(%) (1.8) where I a 1 ...... a1 1. . n-1 Q [b:Ab:. . A b], R= . ,s(X)= % 1 a 1-1...remaining min(n-r+1,m) eigenvalues. With A, b, c, [ai f ai = ’W), p (X) to be defined below let: nl .T ATT" . ^n-lTTT Q [b :Ab :...:A b] Q .[ :Ac...adj(7I-A)B = C( a .Ai’ n’il)B i j=0 n-j n-i n-k-I (1.23) a .CA (n-k-)-JB)% k k0 (.j-o Q n-j n-k-i -1j Defining a .CAn-k-l- B equation (1.22) becomes

  11. Quadratic free energy for the linearized gyrokinetic Vlasov-Maxwell equations

    NASA Astrophysics Data System (ADS)

    Brizard, Alain

    1994-08-01

    The motivation for the present work resides in the search for a new formalism for investigating the stability of plasma equilibria perturbed by low-frequency electromagnetic field fluctuations. In this context, the free-energy method of Morrison and Pfirsch [Phys. Fluids B 2, 1105 (1990)] has been extended by deriving an expression for the gyrokinetic free energy. As a check on the gyrokinetic free-energy method, known formulas previously obtained in the electrostatic limit are recovered, while recent (drift-kinetic) formulas obtained by Betti and Freidberg [Phys. Fluids B 4, 1465 (1992)] in the electromagnetic limit are generalized.

  12. A Linear Quadratic Regulator Weight Selection Algorithm for Robust Pole Assignment

    DTIC Science & Technology

    1990-12-01

    MATLAB . Five test cases are run with the algorithm. First and second order systems that can be solved in closed form are compared with the algorithm poles...The MATLAB "m"-file used to solve the second order SISO system is included in appendix A. Run time on the Compaq 286 was 4 minutes. Table I! Second...poles but it should get close. When this system 3 was run on MATLAB with the algorithm m-files, the achievable poles were found to be -2.096 z 2.389j

  13. Approximation Schemes for the Linear-Quadratic Optimal Control Problem Associated with Delay-Equations.

    DTIC Science & Technology

    1980-03-01

    dt over u E L 2(to,t*’ R) subject to (.2,9) zN’p(t) - TN4 (t,t 0 )PN+ z + -ftTN41(t, n)_N(Tn)u(n)dnto0 for t o 5 t < t*. For v = N - 0 and by Lenla 2.2...t) * 9S t*t)z - - TNtirt-t*NIS~~*tZ4,Y +t + ft(nt)*(n)S(nt)z - <YIS(t*,t)z, T(t*,t )y _ TN4 (t,Oy + <-FS(t*,t)z- -t <,~I t t) ZN41 , l,",(t* ,t) Y

  14. Antenna Linear-Quadratic-Gaussian (LQG) Ccontrollers: Properties, Limits of Performance, and Tuning

    NASA Technical Reports Server (NTRS)

    Gawronski, Wodek K.

    2004-01-01

    The LQG controllers significantly improve antenna tracking precision, but their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller, and the selection of weights of the LQG performance index. The paper selects the coordinates of the open-loop model that simplify the shaping of the closed-loop performance. and analyzes the impact of thc weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. Finally, it presents the LQG controller tuning procedure that rationally shapes the closed-loop performance.

  15. On the cost of approximating and recognizing a noise perturbed straight line or a quadratic curve segment in the plane. [central processing units

    NASA Technical Reports Server (NTRS)

    Cooper, D. B.; Yalabik, N.

    1975-01-01

    Approximation of noisy data in the plane by straight lines or elliptic or single-branch hyperbolic curve segments arises in pattern recognition, data compaction, and other problems. The efficient search for and approximation of data by such curves were examined. Recursive least-squares linear curve-fitting was used, and ellipses and hyperbolas are parameterized as quadratic functions in x and y. The error minimized by the algorithm is interpreted, and central processing unit (CPU) times for estimating parameters for fitting straight lines and quadratic curves were determined and compared. CPU time for data search was also determined for the case of straight line fitting. Quadratic curve fitting is shown to require about six times as much CPU time as does straight line fitting, and curves relating CPU time and fitting error were determined for straight line fitting. Results are derived on early sequential determination of whether or not the underlying curve is a straight line.

  16. Phase and speed synchronization control of four eccentric rotors driven by induction motors in a linear vibratory feeder with unknown time-varying load torques using adaptive sliding mode control algorithm

    NASA Astrophysics Data System (ADS)

    Kong, Xiangxi; Zhang, Xueliang; Chen, Xiaozhe; Wen, Bangchun; Wang, Bo

    2016-05-01

    In this paper, phase and speed synchronization control of four eccentric rotors (ERs) driven by induction motors in a linear vibratory feeder with unknown time-varying load torques is studied. Firstly, the electromechanical coupling model of the linear vibratory feeder is established by associating induction motor's model with the dynamic model of the system, which is a typical under actuated model. According to the characteristics of the linear vibratory feeder, the complex control problem of the under actuated electromechanical coupling model converts to phase and speed synchronization control of four ERs. In order to keep the four ERs operating synchronously with zero phase differences, phase and speed synchronization controllers are designed by employing adaptive sliding mode control (ASMC) algorithm via a modified master-slave structure. The stability of the controllers is proved by Lyapunov stability theorem. The proposed controllers are verified by simulation via Matlab/Simulink program and compared with the conventional sliding mode control (SMC) algorithm. The results show the proposed controllers can reject the time-varying load torques effectively and four ERs can operate synchronously with zero phase differences. Moreover, the control performance is better than the conventional SMC algorithm and the chattering phenomenon is attenuated. Furthermore, the effects of reference speed and parametric perturbations are discussed to show the strong robustness of the proposed controllers. Finally, experiments on a simple vibratory test bench are operated by using the proposed controllers and without control, respectively, to validate the effectiveness of the proposed controllers further.

  17. Total and local (atom and atom type) molecular quadratic indices: significance interpretation, comparison to other molecular descriptors, and QSPR/QSAR applications.

    PubMed

    Ponce, Yovani Marrero

    2004-12-15

    This paper describes the significance interpretation, comparison to other molecular descriptors, and QSPR/QSAR applications of a new set of molecular descriptors: atom, atom type, and total molecular quadratic indices. The features of the kth total and local quadratic indices are illustrated by examples of various types of molecular structures, including chain lengthening, branching, heteroatoms content, and multiple bonds. The linear independence of the local (atom type) quadratic indices to others 0D, 1D, 2D, and 3D molecular descriptors is demonstrated by using principal component analysis for 42 heterogeneous molecules. It is concluded that the local quadratic indices are independent indices containing important structural information to be used in QSPR/QSAR and drug design studies. In this sense, molecular quadratic indices were used to the description and prediction of the boiling point of 28 alkyl alcohols and to the modeling of the partition coefficient (logP), specific rate constant (logk), and antibacterial activity of 2-furylethylene derivatives. These models were statistically significant and showed very good stability to data variation in leave-one-out (LOO) cross-validation experiment. The comparison with the other approaches also revealed good behaviors of our method in this QSAR study.

  18. Quarter-sweep Gauss-Seidel method with quadratic spline scheme applied to fourth order two-point boundary value problems

    NASA Astrophysics Data System (ADS)

    Mohd Fauzi, Norizyan Izzati; Sulaiman, Jumat

    2013-04-01

    The aim of this paper is to describe the application of Quarter-Sweep Gauss-Seidel (QSGS) iterative method using quadratic spline scheme for solving fourth order two-point linear boundary value problems. In the line to derive approximation equations, firstly the fourth order problems need to be reduced onto a system of second-order two-point boundary value problems. Then two linear systems have been constructed via discretization process by using the corresponding quarter-sweep quadratic spline approximation equations. The generated linear systems have been solved using the proposed QSGS iterative method to show the superiority over Full-Sweep Gauss-Seidel (FSGS) and Half-Sweep Gauss-Seidel (HSGS) methods. Computational results are provided to illustrate that the effectiveness of the proposed QSGS method is more superior in terms of computational time and number of iterations as compared to other tested methods.

  19. Gravitomagnetic effects in quadratic gravity with a scalar field

    NASA Astrophysics Data System (ADS)

    Finch, Andrew; Said, Jackson Levi

    2016-10-01

    The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.

  20. Quadratic nonlinear Klein-Gordon equation in one dimension

    NASA Astrophysics Data System (ADS)

    Hayashi, Nakao; Naumkin, Pavel I.

    2012-10-01

    We study the initial value problem for the quadratic nonlinear Klein-Gordon equation vtt + v - vxx = λv2, t ∈ R, x ∈ R, with initial conditions v(0, x) = v0(x), vt(0, x) = v1(x), x ∈ R, where v0 and v1 are real-valued functions, λ ∈ R. Using the method of normal forms of Shatah ["Normal forms and quadratic nonlinear Klein-Gordon equations," Commun. Pure Appl. Math. 38, 685-696 (1985)], we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data, which was assumed in the previous work of J.-M. Delort ["Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi-linéaire á données petites en dimension 1," Ann. Sci. Ec. Normale Super. 34(4), 1-61 (2001)].

  1. Robust reinforcement learning control using integral quadratic constraints for recurrent neural networks.

    PubMed

    Anderson, Charles W; Young, Peter Michael; Buehner, Michael R; Knight, James N; Bush, Keith A; Hittle, Douglas C

    2007-07-01

    The applicability of machine learning techniques for feedback control systems is limited by a lack of stability guarantees. Robust control theory offers a framework for analyzing the stability of feedback control loops, but for the integral quadratic constraint (IQC) framework used here, all components are required to be represented as linear, time-invariant systems plus uncertainties with, for IQCs used here, bounded gain. In this paper, the stability of a control loop including a recurrent neural network (NN) is analyzed by replacing the nonlinear and time-varying components of the NN with IQCs on their gain. As a result, a range of the NN's weights is found within which stability is guaranteed. An algorithm is demonstrated for training the recurrent NN using reinforcement learning and guaranteeing stability while learning.

  2. Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

    NASA Technical Reports Server (NTRS)

    Badavi, F. F.; Everhart, Joel L.

    1987-01-01

    This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

  3. A generalized quadratic flow law for sheet metals

    NASA Astrophysics Data System (ADS)

    Jones, S. E.; Gillis, P. P.

    1984-01-01

    A planar quadratic flow law is proposed for anisotropic sheet materials. This law is similar to the anisotropic strength criterion of Tsai and Wu. It has six experimentally determinable coefficients as compared to four in Hill’s flow law and, thus, allows more experimental information to be accommodated. However, the resulting strain increment vector, while unique, is not necessarily normal to the flow surface.

  4. Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications

    NASA Astrophysics Data System (ADS)

    Li, Jibin; Feng, Zhaosheng

    We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.

  5. Quantum integrals of motion for variable quadratic Hamiltonians

    SciTech Connect

    Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.

    2010-09-15

    We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

  6. Linear Accelerators

    NASA Astrophysics Data System (ADS)

    Sidorin, Anatoly

    2010-01-01

    In linear accelerators the particles are accelerated by either electrostatic fields or oscillating Radio Frequency (RF) fields. Accordingly the linear accelerators are divided in three large groups: electrostatic, induction and RF accelerators. Overview of the different types of accelerators is given. Stability of longitudinal and transverse motion in the RF linear accelerators is briefly discussed. The methods of beam focusing in linacs are described.

  7. Nonhydrostatic correction for shallow water equations with quadratic vertical pressure distribution: A Boussinesq-type equation

    NASA Astrophysics Data System (ADS)

    Jeschke, Anja; Behrens, Jörn

    2015-04-01

    In tsunami modeling, two different systems of dispersive long wave equations are common: The nonhydrostatic pressure correction for the shallow water equations derived out of the depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of Boussinesq-type equations obtained by an expansion in the nondimensional parameters for nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a linear vertical interpolation of the nonhydrostatic pressure, whereas the second system's derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure. In this case the analytical dispersion relations do not coincide. We show that the nonhydrostatic correction with a quadratic vertical interpolation yields an equation set equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case of a horizontal bottom. Now, both systems yield the same analytical dispersion relation according up to the first order with the reference dispersion relation of the linear wave theory. The adjusted model is also compared to other Boussinesq-type equations. The numerical model with the nonhydrostatic correction for the shallow water equations uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element space discretization. The numerical dispersion relations are computed and compared by employing a testcase of a standing wave in a closed basin. All numerical values match their theoretical expectations. This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support given by Geir K. Petersen from the University of Oslo.

  8. Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

    NASA Astrophysics Data System (ADS)

    Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.

    2016-03-01

    To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.

  9. Evolving evolutionary algorithms using linear genetic programming.

    PubMed

    Oltean, Mihai

    2005-01-01

    A new model for evolving Evolutionary Algorithms is proposed in this paper. The model is based on the Linear Genetic Programming (LGP) technique. Every LGP chromosome encodes an EA which is used for solving a particular problem. Several Evolutionary Algorithms for function optimization, the Traveling Salesman Problem and the Quadratic Assignment Problem are evolved by using the considered model. Numerical experiments show that the evolved Evolutionary Algorithms perform similarly and sometimes even better than standard approaches for several well-known benchmarking problems.

  10. Electric current effect on the energy barrier of magnetic domain wall depinning: origin of the quadratic contribution.

    PubMed

    Kim, Kab-Jin; Ryu, Jisu; Gim, Gi-Hong; Lee, Jae-Chul; Shin, Kyung-Ho; Lee, Hyun-Woo; Choe, Sug-Bong

    2011-11-18

    The energy barrier of a magnetic domain wall trapped at a defect is measured experimentally. When the domain wall is pushed by an electric current and/or a magnetic field, the depinning time from the barrier exhibits perfect exponential distribution, indicating that a single energy barrier governs the depinning. The electric current is found to generate linear and quadratic contributions to the energy barrier, which are attributed to the nonadiabatic and adiabatic spin-transfer torques, respectively. The adiabatic spin-transfer torque reduces the energy barrier and, consequently, causes depinning at lower current densities, promising a way toward low-power current-controlled magnetic applications.

  11. An optimization of the FPGA/NIOS adaptive FIR filter using linear prediction to reduce narrow band RFI for the next generation ground-based ultra-high energy cosmic-ray experiment

    NASA Astrophysics Data System (ADS)

    Szadkowski, Zbigniew; Fraenkel, E. D.; Glas, Dariusz; Legumina, Remigiusz

    2013-12-01

    The electromagnetic part of an extensive air shower developing in the atmosphere provides significant information complementary to that obtained by water Cherenkov detectors which are predominantly sensitive to the muonic content of an air shower at ground. The emissions can be observed in the frequency band between 10 and 100 MHz. However, this frequency range is significantly contaminated by narrow-band RFI and other human-made distortions. The Auger Engineering Radio Array currently suppresses the RFI by multiple time-to-frequency domain conversions using an FFT procedure as well as by a set of manually chosen IIR notch filters in the time-domain. An alternative approach developed in this paper is an adaptive FIR filter based on linear prediction (LP). The coefficients for the linear predictor are dynamically refreshed and calculated in the virtual NIOS processor. The radio detector is an autonomous system installed on the Argentinean pampas and supplied from a solar panel. Powerful calculation capacity inside the FPGA is a factor. Power consumption versus the degree of effectiveness of the calculation inside the FPGA is a figure of merit to be minimized. Results show that the RFI contamination can be significantly suppressed by the LP FIR filter for 64 or less stages.

  12. Linear inflation from quartic potential

    NASA Astrophysics Data System (ADS)

    Kannike, Kristjan; Racioppi, Antonio; Raidal, Martti

    2016-01-01

    We show that if the inflaton has a non-minimal coupling to gravity and the Planck scale is dynamically generated, the results of Coleman-Weinberg inflation are confined in between two attractor solutions: quadratic inflation, which is ruled out by the recent measurements, and linear inflation which, instead, is in the experimental allowed region. The minimal scenario has only one free parameter — the inflaton's non-minimal coupling to gravity — that determines all physical parameters such as the tensor-to-scalar ratio and the reheating temperature of the Universe. Should the more precise future measurements of inflationary parameters point towards linear inflation, further interest in scale-invariant scenarios would be motivated.

  13. Energy dependent mesh adaptivity of discontinuous isogeometric discrete ordinate methods with dual weighted residual error estimators

    NASA Astrophysics Data System (ADS)

    Owens, A. R.; Kópházi, J.; Welch, J. A.; Eaton, M. D.

    2017-04-01

    In this paper a hanging-node, discontinuous Galerkin, isogeometric discretisation of the multigroup, discrete ordinates (SN) equations is presented in which each energy group has its own mesh. The equations are discretised using Non-Uniform Rational B-Splines (NURBS), which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest; this would not be the case using straight-sided finite elements. Information is transferred between meshes via the construction of a supermesh. This is a non-trivial task for two arbitrary meshes, but is significantly simplified here by deriving every mesh from a common coarsest initial mesh. In order to take full advantage of this flexible discretisation, goal-based error estimators are derived for the multigroup, discrete ordinates equations with both fixed (extraneous) and fission sources, and these estimators are used to drive an adaptive mesh refinement (AMR) procedure. The method is applied to a variety of test cases for both fixed and fission source problems. The error estimators are found to be extremely accurate for linear NURBS discretisations, with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the ;exact; adjoint solution required to calculate the estimators. Nevertheless, the method seems to produce optimal meshes in the AMR process for both linear and quadratic discretisations, and is ≈×100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem.

  14. Asymmetric Simple Exclusion Process with Open Boundaries and Quadratic Harnesses

    NASA Astrophysics Data System (ADS)

    Bryc, Włodek; Wesołowski, Jacek

    2017-02-01

    We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.

  15. Neural network for solving convex quadratic bilevel programming problems.

    PubMed

    He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

    2014-03-01

    In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.

  16. Solving the quadratic assignment problem with clues from nature.

    PubMed

    Nissen, V

    1994-01-01

    This paper describes a new evolutionary approach to solving quadratic assignment problems. The proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies (ES). These methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems, particularly in continuous optimization. The combinatorial variant of ES presented here performs very well on the given test problems as compared with the standard 2-Opt heuristic and results with simulated annealing and tabu search. Extensions for practical applications in factory layout are described.

  17. Rigorous performance bounds for quadratic and nested dynamical decoupling

    SciTech Connect

    Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A.

    2011-12-15

    We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.

  18. Restart-Based Genetic Algorithm for the Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Misevicius, Alfonsas

    The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.

  19. On a quadratic transformation due to Kummer and its generalizations

    NASA Astrophysics Data System (ADS)

    Shekhawat, Nidhi; Rathie, Arjun K.; Prakash, Om

    2016-05-01

    The aim of this paper is to obtain explicit expressions of (1-x ) -a2F1[a ,b 2 b +j ; -2/x 1 -x ] for j = 0, ±1,…, ±9. For j = 0, we have a well-known quadratic transformations formula of Kummer. The results are obtained by using the known hypergeometric identities available in the literature. Several known results obtained earlier by Kim, et al. follow special cases of our main findings. The results derived in this paper are simple, interesting and potentially useful in the applicable sciences.

  20. On stability of the Kasner solution in quadratic gravity

    NASA Astrophysics Data System (ADS)

    Toporensky, A.; Müller, D.

    2017-01-01

    We consider the dynamics of a flat anisotropic Universe filled by a perfect fluid near a cosmological singularity in quadratic gravity. Two possible regimes are described—the Kasner anisotropic solution and an isotropic "vacuum radiation" solution which has three sub cases depending on whether the equation of state parameter w is bigger, smaller or equals to 1 / 3. Initial conditions for numerical integrations have been chosen near a General Relativity anisotropic solution with matter (Jacobs solution). We have found that for such initial conditions there is a range of values of the coupling constants so that the resulting cosmological singularity is isotropic.

  1. Compact stellar models obeying quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Bhar, Piyali; Singh, Ksh. Newton; Pant, Neeraj

    2016-10-01

    In present paper we obtain a new model of compact star by considering quadratic equation of state for the matter distribution and assuming a physically reasonable choice for metric coefficient g_{rr}. The solution is singularity free and well behaved inside the stellar interior. Several features are described analytically as well as graphically. From our analysis we have shown that our model is compatible with the observational data of the compact stars. We have discussed a detail analysis of neutron star PSR J1614-2230 via different graphs after determining all the constant parameters from boundary conditions.

  2. Linear ubiquitination in immunity.

    PubMed

    Shimizu, Yutaka; Taraborrelli, Lucia; Walczak, Henning

    2015-07-01

    Linear ubiquitination is a post-translational protein modification recently discovered to be crucial for innate and adaptive immune signaling. The function of linear ubiquitin chains is regulated at multiple levels: generation, recognition, and removal. These chains are generated by the linear ubiquitin chain assembly complex (LUBAC), the only known ubiquitin E3 capable of forming the linear ubiquitin linkage de novo. LUBAC is not only relevant for activation of nuclear factor-κB (NF-κB) and mitogen-activated protein kinases (MAPKs) in various signaling pathways, but importantly, it also regulates cell death downstream of immune receptors capable of inducing this response. Recognition of the linear ubiquitin linkage is specifically mediated by certain ubiquitin receptors, which is crucial for translation into the intended signaling outputs. LUBAC deficiency results in attenuated gene activation and increased cell death, causing pathologic conditions in both, mice, and humans. Removal of ubiquitin chains is mediated by deubiquitinases (DUBs). Two of them, OTULIN and CYLD, are constitutively associated with LUBAC. Here, we review the current knowledge on linear ubiquitination in immune signaling pathways and the biochemical mechanisms as to how linear polyubiquitin exerts its functions distinctly from those of other ubiquitin linkage types.

  3. Gain optimization with non-linear controls

    NASA Technical Reports Server (NTRS)

    Slater, G. L.; Kandadai, R. D.

    1984-01-01

    An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

  4. Optimal Regulator Algorithms For The Control Of Linear Systems (ORACLS)

    NASA Technical Reports Server (NTRS)

    Frisch, Harold P.

    1990-01-01

    Control theory design package offers engineer full range of subroutines to manipulate and solve Linear-Quadratic-Gaussian types of problems. ORACLS is rigorous tool, intended for multi-input and multi-output dynamic systems in both continuous and discrete form. Written in FORTRAN.

  5. Estimability and regulability of linear systems

    NASA Technical Reports Server (NTRS)

    Baram, Yoram; Kailath, Thomas

    1987-01-01

    A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feedback is used. These properties, which are are shown to be dual, are different from the well known observability and controllability properties of linear systems. Necessary and sufficient conditions for estimability and regulability are derived for time variant and time invariant systems, in discrete and continuous time.

  6. Portfolio optimization using fuzzy linear programming

    NASA Astrophysics Data System (ADS)

    Pandit, Purnima K.

    2013-09-01

    Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.

  7. Controller design approach based on linear programming.

    PubMed

    Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa

    2013-11-01

    This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor.

  8. Estimability and regulability of linear systems

    NASA Technical Reports Server (NTRS)

    Baram, Yoram; Kailath, Thomas

    1987-01-01

    A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feedback is used. These properties, which are shown to be dual, are different from the well known observability and controllability properties of linear systems. Necessary and sufficient conditions for estimability and regulability are derived for time variant and time invariant systems, in discrete and continuous time.

  9. A theoretical stochastic control framework for adapting radiotherapy to hypoxia.

    PubMed

    Saberian, Fatemeh; Ghate, Archis; Kim, Minsun

    2016-10-07

    Hypoxia, that is, insufficient oxygen partial pressure, is a known cause of reduced radiosensitivity in solid tumors, and especially in head-and-neck tumors. It is thus believed to adversely affect the outcome of fractionated radiotherapy. Oxygen partial pressure varies spatially and temporally over the treatment course and exhibits inter-patient and intra-tumor variation. Emerging advances in non-invasive functional imaging offer the future possibility of adapting radiotherapy plans to this uncertain spatiotemporal evolution of hypoxia over the treatment course. We study the potential benefits of such adaptive planning via a theoretical stochastic control framework using computer-simulated evolution of hypoxia on computer-generated test cases in head-and-neck cancer. The exact solution of the resulting control problem is computationally intractable. We develop an approximation algorithm, called certainty equivalent control, that calls for the solution of a sequence of convex programs over the treatment course; dose-volume constraints are handled using a simple constraint generation method. These convex programs are solved using an interior point algorithm with a logarithmic barrier via Newton's method and backtracking line search. Convexity of various formulations in this paper is guaranteed by a sufficient condition on radiobiological tumor-response parameters. This condition is expected to hold for head-and-neck tumors and for other similarly responding tumors where the linear dose-response parameter is larger than the quadratic dose-response parameter. We perform numerical experiments on four test cases by using a first-order vector autoregressive process with exponential and rational-quadratic covariance functions from the spatiotemporal statistics literature to simulate the evolution of hypoxia. Our results suggest that dynamic planning could lead to a considerable improvement in the number of tumor cells remaining at the end of the treatment course. Through

  10. A theoretical stochastic control framework for adapting radiotherapy to hypoxia

    NASA Astrophysics Data System (ADS)

    Saberian, Fatemeh; Ghate, Archis; Kim, Minsun

    2016-10-01

    Hypoxia, that is, insufficient oxygen partial pressure, is a known cause of reduced radiosensitivity in solid tumors, and especially in head-and-neck tumors. It is thus believed to adversely affect the outcome of fractionated radiotherapy. Oxygen partial pressure varies spatially and temporally over the treatment course and exhibits inter-patient and intra-tumor variation. Emerging advances in non-invasive functional imaging offer the future possibility of adapting radiotherapy plans to this uncertain spatiotemporal evolution of hypoxia over the treatment course. We study the potential benefits of such adaptive planning via a theoretical stochastic control framework using computer-simulated evolution of hypoxia on computer-generated test cases in head-and-neck cancer. The exact solution of the resulting control problem is computationally intractable. We develop an approximation algorithm, called certainty equivalent control, that calls for the solution of a sequence of convex programs over the treatment course; dose-volume constraints are handled using a simple constraint generation method. These convex programs are solved using an interior point algorithm with a logarithmic barrier via Newton’s method and backtracking line search. Convexity of various formulations in this paper is guaranteed by a sufficient condition on radiobiological tumor-response parameters. This condition is expected to hold for head-and-neck tumors and for other similarly responding tumors where the linear dose-response parameter is larger than the quadratic dose-response parameter. We perform numerical experiments on four test cases by using a first-order vector autoregressive process with exponential and rational-quadratic covariance functions from the spatiotemporal statistics literature to simulate the evolution of hypoxia. Our results suggest that dynamic planning could lead to a considerable improvement in the number of tumor cells remaining at the end of the treatment course

  11. Quadratic coupling between a classical nanomechanical oscillator and a single spin

    NASA Astrophysics Data System (ADS)

    Dhingra, Shonali

    Though the motions of macroscopic objects must ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden or washed out by thermal excitations and coupling to the environment. For the work of this thesis, we tried to develop a hybrid system consisting a classical and a quantum component, which can be used to probe the quantum nature of both these components. This hybrid system quadratically coupled a nanomechanical oscillator (NMO) with a single spin in presence of a uniform external magnetic field. The NMO was fabricated out of single-layer graphene, grown using Chemical Vapor Deposition (CVD) and patterned using various lithography and etching techniques. The NMO was driven electrically and detected optically. The NMO's resonant frequencies, and their stabilities were studied. The spin originated from a nitrogen vacancy (NV) center in a diamond nanocrystal which is positioned on the NMO. In presence of an external magnetic field, we show that the NV centers are excellen theta2 sensors. Their sensitivity is shown to increase much faster than linearly with the external magnetic field and diverges as the external field approaches an internally-defined limit. Both these components of the hybrid system get coupled by physical placement of NVcontaining diamond nanocrystals on top of NMO undergoing torsional mode of oscillation, in presence of an external magnetic field. The capability of the NV centers to detect the quadratic behavior of the oscillation angle of the NMO with excellent sensitivity, ensures quantum non-demolition (QND) measurement of both components of the hybrid system. This enables a bridge between the quantum and classical worlds for a simple readout of the NV center spin and observation of the discrete states of the NMO. This system could become the building block for a wide range of quantum nanomechanical devices.

  12. A Hybrid Evolutionary Algorithm to Quadratic Three-Dimensional Assignment Problem with Local Search for Many-Core Graphics Processors

    NASA Astrophysics Data System (ADS)

    Lipinski, Piotr

    This paper concerns the quadratic three-dimensional assignment problem (Q3AP), an extension of the quadratic assignment problem (QAP), and proposes an efficient hybrid evolutionary algorithm combining stochastic optimization and local search with a number of crossover operators, a number of mutation operators and an auto-adaptation mechanism. Auto-adaptation manages the pool of evolutionary operators applying different operators in different computation phases to better explore the search space and to avoid premature convergence. Local search additionally optimizes populations of candidate solutions and accelerates evolutionary search. It uses a many-core graphics processor to optimize a number of solutions in parallel, which enables its incorporation into the evolutionary algorithm without excessive increases in the computation time. Experiments performed on benchmark Q3AP instances derived from the classic QAP instances proposed by Nugent et al. confirmed that the proposed algorithm is able to find optimal solutions to Q3AP in a reasonable time and outperforms best known results found in the literature.

  13. Hidden and Nonstandard Bifurcation Diagram of an Alternate Quadratic System

    NASA Astrophysics Data System (ADS)

    Pastor, G.; Romera, M.; Danca, M.-F.; Martin, A.; Orue, A. B.; Montoya, F.; Encinas, L. Hernández

    Alternate quadratic systems A : xn+1 = 1 - axn2,if n is even 1 - a∗xn2,if n is odd andB : xn+1 = 1 - a∗xn2,if n is even 1 - axn2, if n is odd, where a and a∗ are different parameters, seem to be interval maps in a range of the parameter values. However, after a careful graphical analysis of their bifurcation diagrams we conclude that this is true only for system B, but not for system A. In system A we find a hidden and nonstandard bifurcation diagram (“hidden” because it is not visible at normal resolution and “nonstandard” because the bifurcation diagram is empty for some ranges of the parameter values). The different behavior of the underlying critical polynomial in the range of parameter values in both alternate quadratic systems explains why the hidden and nonstandard bifurcation diagram is present in system A and not in system B. The analysis of the Lyapunov exponent also shows both the existence and the different behavior of the hidden bifurcation diagram of system A.

  14. Quadratic Reciprocity and the Group Orders of Particle States

    SciTech Connect

    DAI,YANG; BORISOV,ALEXEY B.; LONGWORTH,JAMES W.; BOYER,KEITH; RHODES,CHARLES K.

    2001-06-01

    The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.

  15. Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

    NASA Astrophysics Data System (ADS)

    Yang, Xiaofeng; Zhao, Jia; Wang, Qi

    2017-03-01

    The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg-Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the "Invariant Energy Quadratization" (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.

  16. Complex complete quadratic combination method for damped system with repeated eigenvalues

    NASA Astrophysics Data System (ADS)

    Yu, Ruifang; Zhou, Xiyuan; Abduwaris, Abduwahit

    2016-09-01

    A new response-spectrum mode superposition method, entirely in real value form, is developed to analyze the maximum structural response under earthquake ground motion for generally damped linear systems with repeated eigenvalues and defective eigenvectors. This algorithm has clear physical concepts and is similar to the complex complete quadratic combination (CCQC) method previously established. Since it can consider the effect of repeated eigenvalues, it is called the CCQC-R method, in which the correlation coefficients of high-order modal responses are enclosed in addition to the correlation coefficients in the normal CCQC method. As a result, the formulas for calculating the correlation coefficients of high-order modal responses are deduced in this study, including displacement, velocity and velocity-displacement correlation coefficients. Furthermore, the relationship between high-order displacement and velocity covariance is derived to make the CCQC-R algorithm only relevant to the high-order displacement response spectrum. Finally, a practical step-by-step integration procedure for calculating high-order displacement response spectrum is obtained by changing the earthquake ground motion input, which is evaluated by comparing it to the theory solution under the sine-wave input. The method derived here is suitable for generally linear systems with classical or non-classical damping.

  17. Adaptive Optimal Control Using Frequency Selective Information of the System Uncertainty With Application to Unmanned Aircraft.

    PubMed

    Maity, Arnab; Hocht, Leonhard; Heise, Christian; Holzapfel, Florian

    2016-11-28

    A new efficient adaptive optimal control approach is presented in this paper based on the indirect model reference adaptive control (MRAC) architecture for improvement of adaptation and tracking performance of the uncertain system. The system accounts here for both matched and unmatched unknown uncertainties that can act as plant as well as input effectiveness failures or damages. For adaptation of the unknown parameters of these uncertainties, the frequency selective learning approach is used. Its idea is to compute a filtered expression of the system uncertainty using multiple filters based on online instantaneous information, which is used for augmentation of the update law. It is capable of adjusting a sudden change in system dynamics without depending on high adaptation gains and can satisfy exponential parameter error convergence under certain conditions in the presence of structured matched and unmatched uncertainties as well. Additionally, the controller of the MRAC system is designed using a new optimal control method. This method is a new linear quadratic regulator-based optimal control formulation for both output regulation and command tracking problems. It provides a closed-form control solution. The proposed overall approach is applied in a control of lateral dynamics of an unmanned aircraft problem to show its effectiveness.

  18. Linear Time Vertex Partitioning on Massive Graphs.

    PubMed

    Mell, Peter; Harang, Richard; Gueye, Assane

    The problem of optimally removing a set of vertices from a graph to minimize the size of the largest resultant component is known to be NP-complete. Prior work has provided near optimal heuristics with a high time complexity that function on up to hundreds of nodes and less optimal but faster techniques that function on up to thousands of nodes. In this work, we analyze how to perform vertex partitioning on massive graphs of tens of millions of nodes. We use a previously known and very simple heuristic technique: iteratively removing the node of largest degree and all of its edges. This approach has an apparent quadratic complexity since, upon removal of a node and adjoining set of edges, the node degree calculations must be updated prior to choosing the next node. However, we describe a linear time complexity solution using an array whose indices map to node degree and whose values are hash tables indicating the presence or absence of a node at that degree value. This approach also has a linear growth with respect to memory usage which is surprising since we lowered the time complexity from quadratic to linear. We empirically demonstrate linear scalability and linear memory usage on random graphs of up to 15000 nodes. We then demonstrate tractability on massive graphs through execution on a graph with 34 million nodes representing Internet wide router connectivity.

  19. Linear Time Vertex Partitioning on Massive Graphs

    PubMed Central

    Mell, Peter; Harang, Richard; Gueye, Assane

    2016-01-01

    The problem of optimally removing a set of vertices from a graph to minimize the size of the largest resultant component is known to be NP-complete. Prior work has provided near optimal heuristics with a high time complexity that function on up to hundreds of nodes and less optimal but faster techniques that function on up to thousands of nodes. In this work, we analyze how to perform vertex partitioning on massive graphs of tens of millions of nodes. We use a previously known and very simple heuristic technique: iteratively removing the node of largest degree and all of its edges. This approach has an apparent quadratic complexity since, upon removal of a node and adjoining set of edges, the node degree calculations must be updated prior to choosing the next node. However, we describe a linear time complexity solution using an array whose indices map to node degree and whose values are hash tables indicating the presence or absence of a node at that degree value. This approach also has a linear growth with respect to memory usage which is surprising since we lowered the time complexity from quadratic to linear. We empirically demonstrate linear scalability and linear memory usage on random graphs of up to 15000 nodes. We then demonstrate tractability on massive graphs through execution on a graph with 34 million nodes representing Internet wide router connectivity. PMID:27336059

  20. Adaptive equalization

    NASA Astrophysics Data System (ADS)

    Qureshi, S. U. H.

    1985-09-01

    Theoretical work which has been effective in improving data transmission by telephone and radio links using adaptive equalization (AE) techniques is reviewed. AE has been applied to reducing the temporal dispersion effects, such as intersymbol interference, caused by the channel accessed. Attention is given to the Nyquist telegraph transmission theory, least mean square error adaptive filtering and the theory and structure of linear receive and transmit filters for reducing error. Optimum nonlinear receiver structures are discussed in terms of optimality criteria as a function of error probability. A suboptimum receiver structure is explored in the form of a decision-feedback equalizer. Consideration is also given to quadrature amplitude modulation and transversal equalization for receivers.

  1. LINEAR ACCELERATOR

    DOEpatents

    Christofilos, N.C.; Polk, I.J.

    1959-02-17

    Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.

  2. Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

    NASA Astrophysics Data System (ADS)

    Neumeyer, S.; Sorokin, V. S.; Thomsen, J. J.

    2017-01-01

    We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing-Mathieu equation with appended quadratic nonlinearity is considered as the model system, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic nonlinearities may generate additional amplitude-frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi-stability in the amplitude-phase characteristics are predicted, supporting previously reported experimental observations.

  3. Stable adaptive control using new critic designs

    NASA Astrophysics Data System (ADS)

    Werbos, Paul J.

    1999-03-01

    Classical adaptive control proves total-system stability for control of linear plants, but only for plants meeting very restrictive assumptions. Approximate Dynamic Programming (ADP) has the potential, in principle, to ensure stability without such tight restrictions. It also offers nonlinear and neural extensions for optimal control, with empirically supported links to what is seen in the brain. However, the relevant ADP methods in use today--TD, HDP, DHP, GDHP--and the Galerkin-based versions of these all have serious limitations when used here as parallel distributed real-time learning systems; either they do not possess quadratic unconditional stability (to be defined) or they lead to incorrect results in the stochastic case. (ADAC or Q- learning designs do not help.) After explaining these conclusions, this paper describes new ADP designs which overcome these limitations. It also addresses the Generalized Moving Target problem, a common family of static optimization problems, and describes a way to stabilize large-scale economic equilibrium models, such as the old long-term energy mode of DOE.

  4. SUBOPT: A CAD program for suboptimal linear regulators

    NASA Technical Reports Server (NTRS)

    Fleming, P. J.

    1985-01-01

    An interactive software package which provides design solutions for both standard linear quadratic regulator (LQR) and suboptimal linear regulator problems is described. Intended for time-invariant continuous systems, the package is easily modified to include sampled-data systems. LQR designs are obtained by established techniques while the large class of suboptimal problems containing controller and/or performance index options is solved using a robust gradient minimization technique. Numerical examples demonstrate features of the package and recent developments are described.

  5. More Results on the Convergence of Iterative Methods for the Symmetric Linear Complementarity Problem.

    DTIC Science & Technology

    1983-08-01

    earlier paper, our present analysis applies only to the symmetric linear complementarity problem . Various applications to a strictly convex quadratic...characterization requires no such constraint qualification as (F). There is yet another approach to apply an iterative method for solving the strictly convex ...described a Lagrangian relaxation algorithm for a constrained matrix problem which is formulated as a strictly convex separable quadratic program. They

  6. Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

    NASA Astrophysics Data System (ADS)

    Leonenko, N. N.; Ruiz-Medina, M. D.

    2006-07-01

    The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

  7. Consultant-Guided Search Algorithms for the Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Iordache, Serban

    Consultant-Guided Search (CGS) is a recent swarm intelligence metaheuristic for combinatorial optimization problems, inspired by the way real people make decisions based on advice received from consultants. Until now, CGS has been successfully applied to the Traveling Salesman Problem. Because a good metaheuristic should be able to tackle efficiently a large variety of problems, it is important to see how CGS behaves when applied to other classes of problems. In this paper, we propose an algorithm for the Quadratic Assignment Problem (QAP), which hybridizes CGS with a local search procedure. Our experimental results show that CGS is able to compete in terms of solution quality with one of the best Ant Colony Optimization algorithms, the MAX-MIN Ant System.

  8. Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories

    NASA Astrophysics Data System (ADS)

    Adamson, L. N. C.; Osbaldestin, A. H.

    2014-03-01

    We present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisation approach for quadratic irrational trajectories. Depending on the nature of the barrier, this leads to either self-similar or chaotic behaviour. In the self-similar case we give an analysis of the half barrier and present a detailed calculation of the locations, asymptotic heights and signs of the main peaks in the autocorrelation function. Then we consider arbitrary barriers, illustrating that typically these give rise to chaotic correlations of the autocorrelation function which we further represent by showing the invariant sets associated with these correlations. Our main ingredient here is a functional recurrence which has been previously derived and used in work on the Harper equation, strange non-chaotic attractors and a quasi-periodically forced two-level system.

  9. Absence of the Gribov ambiguity in a quadratic gauge

    NASA Astrophysics Data System (ADS)

    Raval, Haresh

    2016-05-01

    The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold {S}^3, when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge.

  10. Nonlinear equality constraints in feasible sequential quadratic programming

    SciTech Connect

    Lawrence, C.; Tits, A.

    1994-12-31

    In this talk we show that convergence of a feasible sequential quadratic programming algorithm modified to handle smooth nonlinear equality constraints. The modification of the algorithm to incorporate equality constraints is based on a scheme proposed by Mayne and Polak and is implemented in fsqp/cfsqp, an optimization package that generates feasible iterates. Nonlinear equality constraints are treated as {open_quotes}{<=}-type constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function which penalizes negative values. For example, the problem minimize f(x) s.t. h(x) = 0, with h(x) a scalar, is replaced by minimize f(x) - ch(x) s.t. h(x) {<=} 0. The modified problem is equivalent to the original problem when c is large enough (but finite). Such a value is determined automatically via iterative adjustments.

  11. Adiabatic theory, Liapunov exponents, and rotation number for quadratic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Delyon, François; Foulon, Patrick

    1987-11-01

    We consider the adiabatic problem for general time-dependent quadratic Hamiltonians and develop a method quite different from WKB. In particular, we apply our results to the Schrödinger equation in a strip. We show that there exists a first regular step (avoiding resonance problems) providing one adiabatic invariant, bounds on the Liapunov exponents, and estimates on the rotation number at any order of the perturbation theory. The further step is shown to be equivalent to a quantum adiabatic problem, which, by the usual adiabatic techniques, provides the other possible adiabatic invariants. In the special case of the Schrödinger equation our method is simpler and more powerful than the WKB techniques.

  12. A linear discretization of the volume conductor boundary integral equation using analytically integrated elements.

    PubMed

    de Munck, J C

    1992-09-01

    A method is presented to compute the potential distribution on the surface of a homogeneous isolated conductor of arbitrary shape. The method is based on an approximation of a boundary integral equation as a set linear algebraic equations. The potential is described as a piecewise linear or quadratic function. The matrix elements of the discretized equation are expressed as analytical formulas.

  13. Does Dirac-Born-Infeld modification of quadratic theories really matter?

    SciTech Connect

    Quiros, Israel; Urena-Lopez, L. Arturo

    2010-08-15

    We study the consequences of further modification of f(R,R{sub {mu}{nu}R}{sup {mu}{nu}},R{sub {mu}{nu}{sigma}{rho}R}{sup {mu}{nu}{sigma}{rho}})/f(R) theories by means of the Dirac-Born-Infeld procedure, which is the replacement of f by {lambda}({radical}(1+2f/{lambda})-1) (the free parameter {lambda} fixes an additional energy scale). We pay special attention to the definition of masses of the linearized propagating degrees of freedom because they are important to judge the stability of the linearization around vacuum background spaces. In this context we discuss the subtleties associated with expanding f(R,R{sub {mu}{nu}R}{sup {mu}{nu}},R{sub {mu}{nu}{sigma}{rho}R}{sup {mu}{nu}{sigma}{rho}}) Lagrangians around maximally symmetric spaces of constant curvature, as well as with equivalence of the linearized Lagrangian to a scalar-tensor theory. Investigation of the consequences of applying the Dirac-Born-Infeld (DBI) strategy to further modify quadratic theories on the stability of de Sitter vacuum, as well as its impact on the cosmological dynamics, are the main concern of this paper. We show that (i) although the DBI deformation does not affect the Ostrogradski stability, other important instabilities such as the Ricci and scalar-tachyon ones, may be indeed surmounted (sometimes at the cost of renouncing to the original motivation of the DBI strategy, to avoid singularities), and (ii) DBI transforming the original theory broadens its possibilities to do cosmology since the asymptotic structure of the DBI-dual theory is richer than in the standard case. In particular, either the dimension of the phase space is increased, or there appear bifurcations in the control-parameter space.

  14. Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

    NASA Astrophysics Data System (ADS)

    Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

    2014-11-01

    By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.

  15. Quantifying the Effects of Higher Order Jahn-Teller Coupling Terms on a Quadratic Jahn-Teller Hamiltonian in the Case of NO_3 and Li_3.

    NASA Astrophysics Data System (ADS)

    Tran, Henry; Stanton, John F.; Miller, Terry A.

    2016-06-01

    The Jahn-Teller (JT) effect represents an enormous complication in the understanding of many molecules. We have been able to assign ˜20 vibronic bands in the tilde{A}^2E'' ← tilde{X}^2A_2' transition of NO_3 and determine the linear and quadratic JT coupling terms for ν_3 and ν_4, indicating strong and weak JT coupling along these modes respectively. It was found that the experimental results quantitatively disagree with ones determined from a vibronic Hamiltonian based on high-level ab-initio theory. Typical analyses of experimental data use the quadratic JT Hamiltonian because limited measured levels tend to allow fitting only to coupling terms up to quadratic JT coupling. Hence, these analyses may neglect key contributions from cubic and quartic terms. To quantify this limitation, we have fit artificial spectra calculated with up to fourth order terms in the potential using a quadratic JT Hamiltonian and analyzed the results. The parameters chosen for this analysis are determined from ab-initio potentials for the tilde{A} state of NO_3 and tilde{X} state of Li_3 to gain further insight on these molecules. Our initial results concerning the limitations of the quadratic JT Hamiltonian will be presented. T. Codd, M.-W. Chen, M. Roudjane, J. F. Stanton, and T. A. Miller. Jet cooled cavity ringdown spectroscopy of the tilde{A}^2E'' ← tilde{X}^2A'_2 Transition of the NO_3 Radical. J. Chem. Phys., 142:184305, 2015

  16. Quadratic coupling treatment of the Jahn-Teller effect in the triply-degenerate electronic state of CH4(+): can one account for floppiness?

    PubMed

    Mondal, T; Varandas, A J C

    2012-12-07

    The Jahn-Teller (JT) coupling effects in the triply degenerate ground electronic state of methane radical cation are investigated theoretically within a quadratic vibronic coupling approach. The underlying potential energy surfaces over the two-dimensional space of nuclear coordinates, subject to the T(2) ⊗ (e + t(2) + t(2)) Jahn-Teller effect, are established from extensive ab initio calculations using the multi-reference configuration interaction method and then employed to determine the various parameters of a diabatic Hamiltonian of this system. Our previous investigation [T. Mondal and A. J. C. Varandas, J. Chem. Phys. 135, 174304 (2011)], relying on the linear vibronic coupling approach augmented by only a diagonal second-order term of the totally symmetric mode, are extended here by including all possible quadratic coupling constants of JT active e and t(2) modes. Inclusion of these quadratic couplings is found to be important to reproduce correctly the broad vibrational structure and for a better description of dynamical JT effect in the first vibronic band of this radical cation. The impact of large amplitude motions (which are responsible for floppiness of the molecule) on the vibronic structure and dynamics of the first photoelectron band have been examined via readjustment of their linear coupling parameters up to ±10%.

  17. Revealing Ozgur's Thoughts of a Quadratic Function with a Clinical Interview: Concepts and Their Underlying Reasons

    ERIC Educational Resources Information Center

    Ozaltun Celik, Aytug; Bukova Guzel, Esra

    2017-01-01

    The quadratic function is an important concept for calculus but the students at high school have many difficulties related to this concept. It is important that the teaching of the quadratic function is realized considering the students' thinking. In this context, the aim of this study conducted through a qualitative case study is to reveal the…

  18. Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

    ERIC Educational Resources Information Center

    Man, Yiu-Kwong

    2012-01-01

    In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

  19. Hidden Lessons: How a Focus on Slope-Like Properties of Quadratic Functions Encouraged Unexpected Generalizations

    ERIC Educational Resources Information Center

    Ellis, Amy B.; Grinstead, Paul

    2008-01-01

    This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…

  20. Exploration of Quadratic Expressions through Multiple Representations for Students with Mathematics Difficulties

    ERIC Educational Resources Information Center

    Strickland, Tricia K.; Maccini, Paula

    2013-01-01

    The current study focuses on the effects of incorporating multiple visual representations on students' conceptual understanding of quadratic expressions embedded within area word problems and students' procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the…

  1. Bogoliubov theory and Lee-Huang-Yang corrections in spin-1 and spin-2 Bose-Einstein condensates in the presence of the quadratic Zeeman effect

    SciTech Connect

    Uchino, Shun; Kobayashi, Michikazu; Ueda, Masahito

    2010-06-15

    We develop Bogoliubov theory of spin-1 and spin-2 Bose-Einstein condensates (BECs) in the presence of a quadratic Zeeman effect, and derive the Lee-Huang-Yang (LHY) corrections to the ground-state energy, pressure, sound velocity, and quantum depletion. We investigate all the phases of spin-1 and spin-2 BECs that can be realized experimentally. We also examine the stability of each phase against quantum fluctuations and the quadratic Zeeman effect. Furthermore, we discuss a relationship between the number of symmetry generators that are spontaneously broken and that of Nambu-Goldstone (NG) modes. It is found that in the spin-2 nematic phase there are special Bogoliubov modes that have gapless linear dispersion relations but do not belong to the NG modes.

  2. Phosphorescence lifetime analysis with a quadratic programming algorithm for determining quencher distributions in heterogeneous systems.

    PubMed Central

    Vinogradov, S A; Wilson, D F

    1994-01-01

    A new method for analysis of phosphorescence lifetime distributions in heterogeneous systems has been developed. This method is based on decomposition of the data vector to a linearly independent set of exponentials and uses quadratic programming principles for x2 minimization. Solution of the resulting algorithm requires a finite number of calculations (it is not iterative) and is computationally fast and robust. The algorithm has been tested on various simulated decays and for analysis of phosphorescence measurements of experimental systems with descrete distributions of lifetimes. Critical analysis of the effect of signal-to-noise on the resolving capability of the algorithm is presented. This technique is recommended for resolution of the distributions of quencher concentration in heterogeneous samples, of which oxygen distributions in tissue is an important example. Phosphors of practical importance for biological oxygen measurements: Pd-meso-tetra (4-carboxyphenyl) porphyrin (PdTCPP) and Pd-meso-porphyrin (PdMP) have been used to provide experimental test of the algorithm. PMID:7858142

  3. Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene

    NASA Astrophysics Data System (ADS)

    Pujari, Sumiran; Lang, Thomas C.; Murthy, Ganpathy; Kaul, Ribhu K.

    2016-08-01

    We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U /t despite the U =0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2 +1 )D Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.

  4. Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

    NASA Technical Reports Server (NTRS)

    Kottapalli, Sesi; Leyland, Jane

    2014-01-01

    In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

  5. Universality of Effective Medium and Random Resistor Network models for disorder-induced linear unsaturating magnetoresistance

    NASA Astrophysics Data System (ADS)

    Lara, Silvia; Lai, Ying Tong; Love, Cameron; Ramakrishnan, Navneeth; Adam, Shaffique

    In recent years, the Effective Medium Theory (EMT) and the Random Resistor Network (RRN) have been separately used to explain disorder induced magnetoresistance that is quadratic at low fields and linear at high fields. We demonstrate that the quadratic and linear coefficients of the magnetoresistance and the transition point from the quadratic to the linear regime depend only on the inhomogeneous carrier density profile. We use this to find a mapping between the two models using dimensionless parameters that determine the magnetoresistance and show numerically that they belong to the same universality class. This work is supported by the Singapore National Research Foundation (NRF-NRFF2012-01) and the Singapore Ministry of Education and Yale-NUS College through Grant Number R-607-265-01312.

  6. An optimized index of human cardiovascular adaptation to simulated weightlessness

    NASA Technical Reports Server (NTRS)

    Wang, M.; Hassebrook, L.; Evans, J.; Varghese, T.; Knapp, C.

    1996-01-01

    Prolonged exposure to weightlessness is known to produce a variety of cardiovascular changes, some of which may influence the astronaut's performance during a mission. In order to find a reliable indicator of cardiovascular adaptation to weightlessness, we analyzed data from nine male subjects after a 24-hour period of normal activity and after a period of simulated weightlessness produced by two hours in a launch position followed by 20 hours of 6 degrees head-down tilt plus pharmacologically induced diuresis (furosemide). Heart rate, arterial pressure, thoracic fluid index, and radial flow were analyzed. Autoregressive spectral estimation and decomposition were used to obtain the spectral components of each variable from the subjects in the supine position during pre- and post-simulated weightlessness. We found a significant decrease in heart rate power and an increase in thoracic fluid index power in the high frequency region (0.2-0.45 Hz) and significant increases in radial flow and arterial pressure powers in the low frequency region (<0.2 Hz) in response to simulated weightlessness. However, due to the variability among subjects, any single variable appeared limited as a dependable index of cardiovascular adaptation to weightlessness. The backward elimination algorithm was then used to select the best discriminatory features from these spectral components. Fisher's linear discriminant and Bayes' quadratic discriminant were used to combine the selected features to obtain an optimal index of adaptation to simulated weightlessness. Results showed that both techniques provided improved discriminant performance over any single variable and thus have the potential for use as an index to track adaptation and prescribe countermeasures to the effects of weightlessness.

  7. Memetic algorithms for the unconstrained binary quadratic programming problem.

    PubMed

    Merz, Peter; Katayama, Kengo

    2004-12-01

    This paper presents a memetic algorithm, a highly effective evolutionary algorithm incorporating local search for solving the unconstrained binary quadratic programming problem (BQP). To justify the approach, a fitness landscape analysis is conducted experimentally for several instances of the BQP. The results of the analysis show that recombination-based variation operators are well suited for the evolutionary algorithms with local search. Therefore, the proposed approach includes--besides a highly effective randomized k-opt local search--a new variation operator that has been tailored specially for the application in the hybrid evolutionary framework. The operator is called innovative variation and is fundamentally different from traditional crossover operators, since new genetic material is included in the offspring which is not contained in one of the parents. The evolutionary heuristic is tested on 35 publicly available BQP instances, and it is shown experimentally that the algorithm is capable of finding best-known solutions to large BQPs in a short time and with a high frequency. In comparison to other approaches for the BQP, the approach appears to be much more effective, particularly for large instances of 1000 or 2500 binary variables.

  8. Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

    NASA Technical Reports Server (NTRS)

    Orr, Jeb S.

    2012-01-01

    A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

  9. Quadratic Fermi node in a 3D strongly correlated semimetal

    DOE PAGES

    Kondo, Takeshi; Nakayama, M.; Chen, R.; ...

    2015-12-07

    We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour ismore » predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.« less

  10. Quadratic Optimization in the Problems of Active Control of Sound

    NASA Technical Reports Server (NTRS)

    Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

  11. Two simple approximations to the distributions of quadratic forms.

    PubMed

    Yuan, Ke-Hai; Bentler, Peter M

    2010-05-01

    Many test statistics are asymptotically equivalent to quadratic forms of normal variables, which are further equivalent to T = sigma(d)(i=1) lambda(i)z(i)(2) with z(i) being independent and following N(0,1). Two approximations to the distribution of T have been implemented in popular software and are widely used in evaluating various models. It is important to know how accurate these approximations are when compared to each other and to the exact distribution of T. The paper systematically studies the quality of the two approximations and examines the effect of the lambda(i) and the degrees of freedom d by analysis and Monte Carlo. The results imply that the adjusted distribution for T can be as good as knowing its exact distribution. When the coefficient of variation of the lambda(i) is small, the rescaled statistic T(R) = dT/(sigma(d)(i=1) lambda(i)) is also adequate for practical model inference. But comparing T(R) against chi2(d) will inflate type I errors when substantial differences exist among the lambda(i), especially, when d is also large.

  12. The Quadratic Spinor Lagrangian, Axial Torsion Current and Generalizations

    NASA Astrophysics Data System (ADS)

    Da Rocha, R.; Pereira, J. G.

    We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field — Weyl, Majorana, flagpole, or flag-dipole spinor fields — yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.

  13. Bright nonlocal quadratic solitons induced by boundary confinement

    NASA Astrophysics Data System (ADS)

    Zheng, Yizhou; Gao, Yan; Wang, Jing; Lv, Fang; Lu, Daquan; Hu, Wei

    2017-01-01

    Under the Dirichlet boundary conditions, a family of bright quadratic solitons exists in the regime where the second harmonic can be regarded as the refractive index of the fundamental wave with an oscillatory nonlocal response. By simplifying the governing equations into the Snyder-Mitchell mode, the approximate analytical solutions are obtained. Taking them as the initial guess and using a numerical code, we found two branches of bright solitons, of which the beam width increases (branch I) and decreases (branch II) with the increase of the sample size, respectively. If the nonlocality is fixed and the sample size is varied, the soliton width varies piecewise and approximately periodically. In each period, solitons only exist in a small range of sample size. Single-hump fundamental wave solitons with the same beam width in narrower samples can be, if the second harmonics are connected smoothly, jointed to be a multihump soliton in a wider sample whose size is the sum of those for the narrower ones. The dynamical simulation shows that the found solitons are unstable.

  14. Monitoring bioeroding sponges: using rubble, Quadrat, or intercept surveys?

    PubMed

    Schönberg, C H L

    2015-04-01

    Relating to recent environmental changes, bioerosion rates of calcium carbonate materials appear to be increasing worldwide, often driven by sponges that cause bioerosion and are recognized bioindicators for coral reef health. Various field methods were compared to encourage more vigorous research on bioeroding sponges and their inclusion in major monitoring projects. The rubble technique developed by Holmes et al. (2000) had drawbacks often due to small specimen sizes: it was time-costly, generated large variation, and created a biased impression about dominant species. Quadrat surveys were most rapid but overestimated cover of small specimens. Line intercepts are recommended as easiest, least spatially biased, and most accurate, especially when comparing results from different observers. Intercepts required fewer samples and provided the best statistical efficiency, evidenced by better significances and test power. Bioeroding sponge abundances and biodiversities are influenced by water depth, sediment quality, and most importantly by availability of suitable attached substrate. Any related data should thus be standardized to amount of suitable substrate to allow comparison between different environments, concentrating on dominant, easily recognized species to avoid bias due to experience of observers.

  15. GR angular momentum in the quadratic spinor Lagrangian formulation

    NASA Astrophysics Data System (ADS)

    Li, Siao-Jing

    2016-08-01

    We inquire into the question of whether the quadratic spinor Lagrangian (QSL) formulation can describe the angular momentum for a general-relativistic system. The QSL Hamiltonian has previously been shown to be able to yield an energy-momentum quasilocalization which brings a proof of the positive gravitational energy when the spinor satisfies the conformal Witten equation. After inspection, we find that, under the constraint that the spinor on the asymptotic boundary is a constant, the QSL Hamiltonian is successful in giving an angular momentum quasilocalization. We also make certain the spinor in the Hamiltonian plays the role of a gauge field, a warrant of our permission to impose constraints on the spinor. Then, by some adjustment of the QSL Hamiltonian, we gain a covariant center-of-mass moment quasilocalization only under the condition that the displacement on the asymptotic boundary is a Killing boost vector. We expect the spinor expression will bring a proof of some connection between the gravitational energy and angular momentum.

  16. Quadratic Fermi node in a 3D strongly correlated semimetal

    SciTech Connect

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

    2015-12-07

    We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

  17. Junction conditions in quadratic gravity: thin shells and double layers

    NASA Astrophysics Data System (ADS)

    Reina, Borja; Senovilla, José M. M.; Vera, Raül

    2016-05-01

    The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface—termed as thin shells, domain walls or braneworlds in the literature—as well as the proper matching conditions where only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in general relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The consequences of all these results are briefly analyzed.

  18. Quadratic Fermi node in a 3D strongly correlated semimetal

    PubMed Central

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

    2015-01-01

    Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114

  19. Sequential Quadratic Programming (SQP) for optimal control in direct numerical simulation of turbulent flow

    NASA Astrophysics Data System (ADS)

    Badreddine, Hassan; Vandewalle, Stefan; Meyers, Johan

    2014-01-01

    The current work focuses on the development and application of an efficient algorithm for optimization of three-dimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or Large-Eddy Simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a damped formulation of the limited-memory BFGS method. The latter is suitable for solving large-scale constrained optimization problems whose Hessian matrices cannot be computed and stored at a reasonable cost. We combine the algorithm with a line-search merit function based on an L1-norm to enforce the convergence from any remote point. It is first shown that the proposed form of the damped L-BFGS algorithm is suitable for solving equality constrained Rosenbrock type functions. Then, we apply the algorithm to an optimal-control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon T. The controls are further subject to a non-linear equality constraint on the total control energy. DNSs are used to resolve all turbulent scales of motion, and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals. We compare the convergence speed of the SQP L-BFGS algorithm to a conventional non-linear conjugate-gradient method (i.e. the current standard in DNS-based optimal control), and find that the SQP algorithm is more than an order of magnitude faster than the conjugate-gradient method.

  20. Optimized Large-scale CMB Likelihood and Quadratic Maximum Likelihood Power Spectrum Estimation

    NASA Astrophysics Data System (ADS)

    Gjerløw, E.; Colombo, L. P. L.; Eriksen, H. K.; Górski, K. M.; Gruppuso, A.; Jewell, J. B.; Plaszczynski, S.; Wehus, I. K.

    2015-11-01

    We revisit the problem of exact cosmic microwave background (CMB) likelihood and power spectrum estimation with the goal of minimizing computational costs through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al., and here we develop it into a fully functioning computational framework for large-scale polarization analysis, adopting WMAP as a working example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors, and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked WMAP sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8% at ℓ ≤ 32 and a maximum shift in the mean values of a joint distribution of an amplitude-tilt model of 0.006σ. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation, which requires less than 3 GB of memory and 2 CPU minutes per iteration for ℓ ≤ 32, rendering low-ℓ QML CMB power spectrum analysis fully tractable on a standard laptop.