Attitude and Configuration Control of Flexible Multi-Body Spacecraft

NASA Astrophysics Data System (ADS)

Cho, Sung-Ki; Cochran, John E., Jr.

2002-06-01

Multi-body spacecraft attitude and configuration control formulations based on the use of collaborative control theory are considered. The control formulations are based on two-player, nonzero-sum, differential game theory applied using a Nash strategy. It is desired that the control laws allow different components of the multi-body system to perform different tasks. For example, it may be desired that one body points toward a fixed star while another body in the system slews to track another satellite. Although similar to the linear quadratic regulator formulation, the collaborative control formulation contains a number of additional design parameters because the problem is formulated as two control problems coupled together. The use of the freedom of the partitioning of the total problem into two coupled control problems and the selection of the elements of the cross-coupling matrices are specific problems addressed in this paper. Examples are used to show that significant improvement in performance, as measured by realistic criteria, of collaborative control over conventional linear quadratic regulator control can be achieved by using proposed design guidelines.

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

NASA Astrophysics Data System (ADS)

Lu, Yanrong; Liao, Fucheng; Deng, Jiamei; Liu, Huiyang

2017-09-01

This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS

NASA Technical Reports Server (NTRS)

Lehtinen, B.

1994-01-01

AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user with open-loop system information including stability, controllability, and observability. The AESOP program is written in FORTRAN IV for interactive execution and has been implemented on an IBM 3033 computer using TSS 370. As currently configured, AESOP has a central memory requirement of approximately 2 Megs of 8 bit bytes. Memory requirements can be reduced by redimensioning arrays in the AESOP program. Graphical output requires adaptation of the AESOP plot routines to whatever device is available. The AESOP program was developed in 1984.

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.

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.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Is greater improvement in early self-regulation associated with fewer behavioral problems later in childhood?

PubMed

Sawyer, Alyssa C P; Miller-Lewis, Lauren R; Searle, Amelia K; Sawyer, Michael G; Lynch, John W

2015-12-01

The aim of this study was to determine whether the extent of improvement in self-regulation achieved between ages 4 and 6 years is associated with the level of behavioral problems later in childhood. Participants were 4-year-old children (n = 510) attending preschools in South Australia. Children's level of self-regulation was assessed using the parent-completed Devereux Early Childhood Assessment when children were aged 4, 5, and 6. Children's level of behavioral problems was assessed using total, internalizing, and externalizing scores on parent- and teacher-rated Strengths and Difficulties Questionnaires (SDQs) when children were 6 years old. Random effects regression was used to describe the changes to children's self-regulation between 4 and 6 years. Linear regression models were then used to determine the strength of the association between the extent of self-regulation improvement and level of behavioral problems. Greater improvement in self-regulation, adjusted for family characteristics and baseline self-regulation scores, was associated with lower levels of parent- (B = -3.57, 95% confidence interval [CI] [-4.49, -2.65]) and teacher-rated SDQ total difficulties scores at 6 years (B = -2.42, 95% CI [-3.50, -1.34]). These effects remained after adjustment for level of parent-rated behavioral problems at 4 years. Similar effects were found for internalizing and externalizing scores at age 6 years. The results highlight the importance of improvements in self-regulation from 4-6 years for childhood behavioral problems during the early school years. Children with lower levels of improvement in self-regulation early in life are at risk for higher levels of behavioral problems both at home and at school. (c) 2015 APA, all rights reserved).

Randomly Sampled-Data Control Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Han, Kuoruey

1990-01-01

The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions.

An FPGA Testbed for Characterizing and Mapping DOD Applications

DTIC Science & Technology

2017-12-27

series expansion helps to linearize pitch control design for wind turbine using linear quadratic regulator (LQR) [15]. In multi-static radar system...A. Mahmud, M. A. Chowdhury, and J. Zhang, “Stability enhancement of dfig wind turbine using lqr pitch control over rated wind speed,” in 2016 IEEE...the problem of meeting payload design specifications is exacerbated by the need to identify manufacturers with interfaces that match the sensors

An efficient method for model refinement in diffuse optical tomography

NASA Astrophysics Data System (ADS)

Zirak, A. R.; Khademi, M.

2007-11-01

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.

State-Dependent Riccati Equation Regulation of Systems with State and Control Nonlinearities

NASA Technical Reports Server (NTRS)

Beeler, Scott C.; Cox, David E. (Technical Monitor)

2004-01-01

The state-dependent Riccati equations (SDRE) is the basis of a technique for suboptimal feedback control of a nonlinear quadratic regulator (NQR) problem. It is an extension of the Riccati equation used for feedback control of linear problems, with the addition of nonlinearities in the state dynamics of the system resulting in a state-dependent gain matrix as the solution of the equation. In this paper several variations on the SDRE-based method will be considered for the feedback control problem with control nonlinearities. The control nonlinearities may result in complications in the numerical implementation of the control, which the different versions of the SDRE method must try to overcome. The control methods will be applied to three test problems and their resulting performance analyzed.

Low-rank regularization for learning gene expression programs.

PubMed

Ye, Guibo; Tang, Mengfan; Cai, Jian-Feng; Nie, Qing; Xie, Xiaohui

2013-01-01

Learning gene expression programs directly from a set of observations is challenging due to the complexity of gene regulation, high noise of experimental measurements, and insufficient number of experimental measurements. Imposing additional constraints with strong and biologically motivated regularizations is critical in developing reliable and effective algorithms for inferring gene expression programs. Here we propose a new form of regulation that constrains the number of independent connectivity patterns between regulators and targets, motivated by the modular design of gene regulatory programs and the belief that the total number of independent regulatory modules should be small. We formulate a multi-target linear regression framework to incorporate this type of regulation, in which the number of independent connectivity patterns is expressed as the rank of the connectivity matrix between regulators and targets. We then generalize the linear framework to nonlinear cases, and prove that the generalized low-rank regularization model is still convex. Efficient algorithms are derived to solve both the linear and nonlinear low-rank regularized problems. Finally, we test the algorithms on three gene expression datasets, and show that the low-rank regularization improves the accuracy of gene expression prediction in these three datasets.

Adaptive Failure Compensation for Aircraft Flight Control Using Engine Differentials: Regulation

NASA Technical Reports Server (NTRS)

Yu, Liu; Xidong, Tang; Gang, Tao; Joshi, Suresh M.

2005-01-01

The problem of using engine thrust differentials to compensate for rudder and aileron failures in aircraft flight control is addressed in this paper in a new framework. A nonlinear aircraft model that incorporates engine di erentials in the dynamic equations is employed and linearized to describe the aircraft s longitudinal and lateral motion. In this model two engine thrusts of an aircraft can be adjusted independently so as to provide the control flexibility for rudder or aileron failure compensation. A direct adaptive compensation scheme for asymptotic regulation is developed to handle uncertain actuator failures in the linearized system. A design condition is specified to characterize the system redundancy needed for failure compensation. The adaptive regulation control scheme is applied to the linearized model of a large transport aircraft in which the longitudinal and lateral motions are coupled as the result of using engine thrust differentials. Simulation results are presented to demonstrate the effectiveness of the adaptive compensation scheme.

Pregaming and Emotion Regulation's Relationship to Alcohol Problems in College Students: A Cross-Sectional Study.

PubMed

Norberg, Melissa M; Ham, Lindsay S; Olivier, Jake; Zamboanga, Byron L; Melkonian, Alexander; Fugitt, Jessica L

2016-07-02

Pregaming is a high-risk drinking behavior associated with increased alcohol consumption and alcohol-related problems. Quantity of alcohol consumed does not fully explain the level of problems associated with pregaming; yet, limited research has examined factors that may interact with pregaming behavior to contribute to the experience of alcohol-related problems. The current study examined whether use of two emotion regulation strategies influence pregaming's contribution to alcohol-related problems. Undergraduates (N = 1857) aged 18-25 years attending 19 different colleges completed an online survey in 2008-2009. Linear mixed models were used to test whether emotion regulation strategies moderate the association between pregaming status (pregamers vs. non/infrequent pregamers) and alcohol-related problems, when controlling for alcohol consumption, demographic covariates, and site as a random effect. Greater use of cognitive reappraisal was associated with decreased alcohol problems. Expressive suppression interacted with pregaming status. There was no relationship between pregaming status and alcohol problems for students who rarely used expression suppression; however, the relationship between pregaming status and alcohol problems was statistically significant for students who occasionally to frequently used expression suppression. Findings suggest that the relationship between pregaming and alcohol-related problems is complex. Accordingly, future studies should utilize event-level methodology to understand how emotion regulation strategies influence alcohol-related problems. Further, clinicians should tailor alcohol treatments to help students increase their use of cognitive reappraisal and decrease their use of suppression.

Decentralized regulation of dynamic systems. [for controlling large scale linear systems

NASA Technical Reports Server (NTRS)

Chu, K. C.

1975-01-01

A special class of decentralized control problem is discussed in which the objectives of the control agents are to steer the state of the system to desired levels. Each agent is concerned about certain aspects of the state of the entire system. The state and control equations are given for linear time-invariant systems. Stability and coordination, and the optimization of decentralized control are analyzed, and the information structure design is presented.

Improving stability margins in discrete-time LQG controllers

NASA Technical Reports Server (NTRS)

Oranc, B. Tarik; Phillips, Charles L.

1987-01-01

Some of the problems are discussed which are encountered in the design of discrete-time stochastic controllers for problems that may adequately be described by the Linear Quadratic Gaussian (LQG) assumptions; namely, the problems of obtaining acceptable relative stability, robustness, and disturbance rejection properties. A dynamic compensator is proposed to replace the optimal full state feedback regulator gains at steady state, provided that all states are measurable. The compensator increases the stability margins at the plant input, which may possibly be inadequate in practical applications. Though the optimal regulator has desirable properties the observer based controller as implemented with a Kalman filter, in a noisy environment, has inadequate stability margins. The proposed compensator is designed to match the return difference matrix at the plant input to that of the optimal regulator while maintaining the optimality of the state estimates as directed by the measurement noise characteristics.

Incremental passivity and output regulation for switched nonlinear systems

NASA Astrophysics Data System (ADS)

Pang, Hongbo; Zhao, Jun

2017-10-01

This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.

Active control of panel vibrations induced by boundary-layer flow

NASA Technical Reports Server (NTRS)

Chow, Pao-Liu

1991-01-01

Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.

A parametric LQ approach to multiobjective control system design

NASA Technical Reports Server (NTRS)

Kyr, Douglas E.; Buchner, Marc

1988-01-01

The synthesis of a constant parameter output feedback control law of constrained structure is set in a multiple objective linear quadratic regulator (MOLQR) framework. The use of intuitive objective functions such as model-following ability and closed-loop trajectory sensitivity, allow multiple objective decision making techniques, such as the surrogate worth tradeoff method, to be applied. For the continuous-time deterministic problem with an infinite time horizon, dynamic compensators as well as static output feedback controllers can be synthesized using a descent Anderson-Moore algorithm modified to impose linear equality constraints on the feedback gains by moving in feasible directions. Results of three different examples are presented, including a unique reformulation of the sensitivity reduction problem.

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.

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.

Trends in modern system theory

NASA Technical Reports Server (NTRS)

Athans, M.

1976-01-01

The topics considered are related to linear control system design, adaptive control, failure detection, control under failure, system reliability, and large-scale systems and decentralized control. It is pointed out that the design of a linear feedback control system which regulates a process about a desirable set point or steady-state condition in the presence of disturbances is a very important problem. The linearized dynamics of the process are used for design purposes. The typical linear-quadratic design involving the solution of the optimal control problem of a linear time-invariant system with respect to a quadratic performance criterion is considered along with gain reduction theorems and the multivariable phase margin theorem. The stumbling block in many adaptive design methodologies is associated with the amount of real time computation which is necessary. Attention is also given to the desperate need to develop good theories for large-scale systems, the beginning of a microprocessor revolution, the translation of the Wiener-Hopf theory into the time domain, and advances made in dynamic team theory, dynamic stochastic games, and finite memory stochastic control.

Design a software real-time operation platform for wave piercing catamarans motion control using linear quadratic regulator based genetic algorithm.

PubMed

Liang, Lihua; Yuan, Jia; Zhang, Songtao; Zhao, Peng

2018-01-01

This work presents optimal linear quadratic regulator (LQR) based on genetic algorithm (GA) to solve the two degrees of freedom (2 DoF) motion control problem in head seas for wave piercing catamarans (WPC). The proposed LQR based GA control strategy is to select optimal weighting matrices (Q and R). The seakeeping performance of WPC based on proposed algorithm is challenged because of multi-input multi-output (MIMO) system of uncertain coefficient problems. Besides the kinematical constraint problems of WPC, the external conditions must be considered, like the sea disturbance and the actuators (a T-foil and two flaps) control. Moreover, this paper describes the MATLAB and LabVIEW software plats to simulate the reduction effects of WPC. Finally, the real-time (RT) NI CompactRIO embedded controller is selected to test the effectiveness of the actuators based on proposed techniques. In conclusion, simulation and experimental results prove the correctness of the proposed algorithm. The percentage of heave and pitch reductions are more than 18% in different high speeds and bad sea conditions. And the results also verify the feasibility of NI CompactRIO embedded controller.

Design a software real-time operation platform for wave piercing catamarans motion control using linear quadratic regulator based genetic algorithm

PubMed Central

Liang, Lihua; Zhang, Songtao; Zhao, Peng

2018-01-01

This work presents optimal linear quadratic regulator (LQR) based on genetic algorithm (GA) to solve the two degrees of freedom (2 DoF) motion control problem in head seas for wave piercing catamarans (WPC). The proposed LQR based GA control strategy is to select optimal weighting matrices (Q and R). The seakeeping performance of WPC based on proposed algorithm is challenged because of multi-input multi-output (MIMO) system of uncertain coefficient problems. Besides the kinematical constraint problems of WPC, the external conditions must be considered, like the sea disturbance and the actuators (a T-foil and two flaps) control. Moreover, this paper describes the MATLAB and LabVIEW software plats to simulate the reduction effects of WPC. Finally, the real-time (RT) NI CompactRIO embedded controller is selected to test the effectiveness of the actuators based on proposed techniques. In conclusion, simulation and experimental results prove the correctness of the proposed algorithm. The percentage of heave and pitch reductions are more than 18% in different high speeds and bad sea conditions. And the results also verify the feasibility of NI CompactRIO embedded controller. PMID:29709008

Self-tuning regulators for multicyclic control of helicopter vibration

NASA Technical Reports Server (NTRS)

Johnson, W.

1982-01-01

A class of algorithms for the multicyclic control of helicopter vibration and loads is derived and discussed. This class is characterized by a linear, quasi-static, frequency-domain model of the helicopter response to control; identification of the helicopter model by least-squared-error or Kalman filter methods; and a minimum variance or quadratic performance function controller. Previous research on such controllers is reviewed. The derivations and discussions cover the helicopter model; the identification problem, including both off-line and on-line (recursive) algorithms; the control problem, including both open-loop and closed-loop feedback; and the various regulator configurations possible within this class. Conclusions from analysis and numerical simulations of the regulators provide guidance in the design and selection of algorithms for further development, including wind tunnel and flight tests.

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach is presented for deriving approximations to the optimal feedback gain 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 feedback kernels.

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.

Optimal control of LQR for discrete time-varying systems with input delays

NASA Astrophysics Data System (ADS)

Yin, Yue-Zhu; Yang, Zhong-Lian; Yin, Zhi-Xiang; Xu, Feng

2018-04-01

In this work, we consider the optimal control problem of linear quadratic regulation for discrete time-variant systems with single input and multiple input delays. An innovative and simple method to derive the optimal controller is given. The studied problem is first equivalently converted into a problem subject to a constraint condition. Last, with the established duality, the problem is transformed into a static mathematical optimisation problem without input delays. The optimal control input solution to minimise performance index function is derived by solving this optimisation problem with two methods. A numerical simulation example is carried out and its results show that our two approaches are both feasible and very effective.

Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

NASA Technical Reports Server (NTRS)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

Genetics-based control of a mimo boiler-turbine plant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimeo, R.M.; Lee, K.Y.

1994-12-31

A genetic algorithm is used to develop an optimal controller for a non-linear, multi-input/multi-output boiler-turbine plant. The algorithm is used to train a control system for the plant over a wide operating range in an effort to obtain better performance. The results of the genetic algorithm`s controller designed from the linearized plant model at a nominal operating point. Because the genetic algorithm is well-suited to solving traditionally difficult optimization problems it is found that the algorithm is capable of developing the controller based on input/output information only. This controller achieves a performance comparable to the standard linear quadratic regulator.

Application of modern control theory to the design of optimum aircraft controllers

NASA Technical Reports Server (NTRS)

Power, L. J.

1973-01-01

The synthesis procedure presented is based on the solution of the output regulator problem of linear optimal control theory for time-invariant systems. By this technique, solution of the matrix Riccati equation leads to a constant linear feedback control law for an output regulator which will maintain a plant in a particular equilibrium condition in the presence of impulse disturbances. Two simple algorithms are presented that can be used in an automatic synthesis procedure for the design of maneuverable output regulators requiring only selected state variables for feedback. The first algorithm is for the construction of optimal feedforward control laws that can be superimposed upon a Kalman output regulator and that will drive the output of a plant to a desired constant value on command. The second algorithm is for the construction of optimal Luenberger observers that can be used to obtain feedback control laws for the output regulator requiring measurement of only part of the state vector. This algorithm constructs observers which have minimum response time under the constraint that the magnitude of the gains in the observer filter be less than some arbitrary limit.

Robust set-point regulation for ecological models with multiple management goals.

PubMed

Guiver, Chris; Mueller, Markus; Hodgson, Dave; Townley, Stuart

2016-05-01

Population managers will often have to deal with problems of meeting multiple goals, for example, keeping at specific levels both the total population and population abundances in given stage-classes of a stratified population. In control engineering, such set-point regulation problems are commonly tackled using multi-input, multi-output proportional and integral (PI) feedback controllers. Building on our recent results for population management with single goals, we develop a PI control approach in a context of multi-objective population management. We show that robust set-point regulation is achieved by using a modified PI controller with saturation and anti-windup elements, both described in the paper, and illustrate the theory with examples. Our results apply more generally to linear control systems with positive state variables, including a class of infinite-dimensional systems, and thus have broader appeal.

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

NASA Technical Reports Server (NTRS)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

Mixed Integer Linear Programming based machine learning approach identifies regulators of telomerase in yeast.

PubMed

Poos, Alexandra M; Maicher, André; Dieckmann, Anna K; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer

2016-06-02

Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments. © The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.

Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task.

PubMed

Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

2013-01-01

Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.

The application of LQR synthesis techniques to the turboshaft engine control problem. [Linear Quadratic Regulator

NASA Technical Reports Server (NTRS)

Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.

1985-01-01

A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

Fuzzy Model-based Pitch Stabilization and Wing Vibration Suppression of Flexible Wing Aircraft.

NASA Technical Reports Server (NTRS)

Ayoubi, Mohammad A.; Swei, Sean Shan-Min; Nguyen, Nhan T.

2014-01-01

This paper presents a fuzzy nonlinear controller to regulate the longitudinal dynamics of an aircraft and suppress the bending and torsional vibrations of its flexible wings. The fuzzy controller utilizes full-state feedback with input constraint. First, the Takagi-Sugeno fuzzy linear model is developed which approximates the coupled aeroelastic aircraft model. Then, based on the fuzzy linear model, a fuzzy controller is developed to utilize a full-state feedback and stabilize the system while it satisfies the control input constraint. Linear matrix inequality (LMI) techniques are employed to solve the fuzzy control problem. Finally, the performance of the proposed controller is demonstrated on the NASA Generic Transport Model (GTM).

Cognitive problems, self-rated changes in driving skills, driving-related discomfort and self-regulation of driving in old drivers.

PubMed

Meng, Annette; Siren, Anu

2012-11-01

Ageing in general is associated with functional decline that may have an adverse effect on driving. Nevertheless, older drivers have been found to show good judgement and to self-regulate their driving, which may enable them to continue driving safely despite functional decline. The process of the self-monitoring of driving ability and the awareness of functional decline, and its association with the self-regulation of driving is, however, not fully understood. The aim of the present study was to examine the perceived changes in driving skills, the discomfort experienced in driving, and the self-regulation of driving as measured by the avoidance of certain driving situations by older drivers with different levels of self-rated cognitive problems. Eight hundred and forty Danish drivers aged 75-95 completed a structured telephone interview. The results showed that the recognition of cognitive problems was associated with an experience of improvement in higher level driving skills but also of a decline in lower level driving skills. Moreover, cognitive problems recognised by drivers were associated with discomfort in, and avoidance of, driving situations. Finally, a linear relationship between discomfort in driving and avoidance was found and this tended to be stronger for drivers recognising cognitive problems. The results indicate that older drivers who recognise problems with cognitive functions display good self-assessment of changes in their driving skills. In addition, the results suggest that driving-related discomfort is an important factor affecting the self-regulation of driving. Finally, the findings indicate that driving-related discomfort functions as an indirect self-monitoring of driving ability and may contribute to the safe driving performance of Danish older drivers. Copyright © 2012 Elsevier Ltd. All rights reserved.

Aerospace plane guidance using geometric control theory

NASA Technical Reports Server (NTRS)

Van Buren, Mark A.; Mease, Kenneth D.

1990-01-01

A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.

Distribution-Agnostic Stochastic Optimal Power Flow for Distribution Grids: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

2016-09-01

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-04-15

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilizemore » the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-01-28

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modi ed Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in ow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then a modelbased feedback controller is designed for the reduced order model using linear quadratic regulators (LQR). Finally, a linear quadratic gaussian (LQG) controller, which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHWmore » equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Computational methods of robust controller design for aerodynamic flutter suppression

NASA Technical Reports Server (NTRS)

Anderson, L. R.

1981-01-01

The development of Riccati iteration, a tool for the design and analysis of linear control systems is examined. First, Riccati iteration is applied to the problem of pole placement and order reduction in two-time scale control systems. Order reduction, yielding a good approximation to the original system, is demonstrated using a 16th order linear model of a turbofan engine. Next, a numerical method for solving the Riccati equation is presented and demonstrated for a set of eighth order random examples. A literature review of robust controller design methods follows which includes a number of methods for reducing the trajectory and performance index sensitivity in linear regulators. Lastly, robust controller design for large parameter variations is discussed.

Expendable launch vehicle studies

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reiss, Robert

1995-01-01

Analytical support studies of expendable launch vehicles concentrate on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed and linearized. The information from LeRC about the grids, masses, and modes is incorporated into the model. The eigenvalues of the plant are analyzed for several modeling factors: utilizing diagonal mass matrix, uniform beam assumption, inclusion of aerodynamics, and the interaction between the aerodynamics and the flexible bending motion. Preliminary PID, LQR, and LQG control designs with sensor and actuator dynamics for this system and simulations are also conducted. The initial analysis for comparison of PD (proportional-derivative) and full state feedback LQR Linear quadratic regulator) shows that the split weighted LQR controller has better performance than that of the PD. In order to meet both the performance and robustness requirements, the H(sub infinity) robust controller for the expendable launch vehicle is developed. The simulation indicates that both the performance and robustness of the H(sub infinity) controller are better than that for the PID and LQG controllers. The modelling and analysis support studies team has continued development of methodology, using eigensensitivity analysis, to solve three classes of discrete eigenvalue equations. In the first class, the matrix elements are non-linear functions of the eigenvector. All non-linear periodic motion can be cast in this form. Here the eigenvector is comprised of the coefficients of complete basis functions spanning the response space and the eigenvalue is the frequency. The second class of eigenvalue problems studied is the quadratic eigenvalue problem. Solutions for linear viscously damped structures or viscoelastic structures can be reduced to this form. Particular attention is paid to Maxwell and Kelvin models. The third class of problems consists of linear eigenvalue problems in which the elements of the mass and stiffness matrices are stochastic. dynamic structural response for which the parameters are given by probabilistic distribution functions, rather than deterministic values, can be cast in this form. Solutions for several problems in each class will be presented.

The optimal location of piezoelectric actuators and sensors for vibration control of plates

NASA Astrophysics Data System (ADS)

Kumar, K. Ramesh; Narayanan, S.

2007-12-01

This paper considers the optimal placement of collocated piezoelectric actuator-sensor pairs on a thin plate using a model-based linear quadratic regulator (LQR) controller. LQR performance is taken as objective for finding the optimal location of sensor-actuator pairs. The problem is formulated using the finite element method (FEM) as multi-input-multi-output (MIMO) model control. The discrete optimal sensor and actuator location problem is formulated in the framework of a zero-one optimization problem. A genetic algorithm (GA) is used to solve the zero-one optimization problem. Different classical control strategies like direct proportional feedback, constant-gain negative velocity feedback and the LQR optimal control scheme are applied to study the control effectiveness.

On the modelling of linear-assisted DC-DC voltage regulators for photovoltaic solar energy systems

NASA Astrophysics Data System (ADS)

Martínez-García, Herminio; García-Vílchez, Encarna

2017-11-01

This paper shows the modelling of linear-assisted or hybrid (linear & switching) DC/DC voltage regulators. In this kind of regulators, an auxiliary linear regulator is used, which objective is to cancel the ripple at the output voltage and provide fast responses for load variations. On the other hand, a switching DC/DC converter, connected in parallel with the linear regulator, allows to supply almost the whole output current demanded by the load. The objective of this topology is to take advantage of the suitable regulation characteristics that series linear voltage regulators have, but almost achieving the high efficiency that switching DC/DC converters provide. Linear-assisted DC/DC regulators are feedback systems with potential instability. Therefore, their modelling is mandatory in order to obtain design guidelines and assure stability of the implemented power supply system.

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.

Pupils' over-reliance on linearity: a scholastic effect?

PubMed

Van Dooren, Wim; De Bock, Dirk; Janssens, Dirk; Verschaffel, Lieven

2007-06-01

From upper elementary education on, children develop a tendency to over-use linearity. Particularly, it is found that many pupils assume that if a figure enlarges k times, the area enlarges k times too. However, most research was conducted with traditional, school-like word problems. This study examines whether pupils also over-use linearity if non-linear problems are embedded in meaningful, authentic performance tasks instead of traditional, school-like word problems, and whether this experience influences later behaviour. Ninety-three sixth graders from two primary schools in Flanders, Belgium. Pupils received a pre-test with traditional word problems. Those who made a linear error on the non-linear area problem were subjected to individual interviews. They received one new non-linear problem, in the S-condition (again a traditional, scholastic word problem), D-condition (the same word problem with a drawing) or P-condition (a meaningful performance-based task). Shortly afterwards, pupils received a post-test, containing again a non-linear word problem. Most pupils from the S-condition displayed linear reasoning during the interview. Offering drawings (D-condition) had a positive effect, but presenting the problem as a performance task (P-condition) was more beneficial. Linear reasoning was nearly absent in the P-condition. Remarkably, at the post-test, most pupils from all three groups again applied linear strategies. Pupils' over-reliance on linearity seems partly elicited by the school-like word problem format of test items. Pupils perform much better if non-linear problems are offered as performance tasks. However, a single experience does not change performances on a comparable word problem test afterwards.

Exact-Output Tracking Theory for Systems with Parameter Jumps

NASA Technical Reports Server (NTRS)

Devasia, Santosh; Paden, Brad; Rossi, Carlo

1996-01-01

In this paper we consider the exact output tracking problem for systems with parameter jumps. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches). Such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is applicable to nonminimum-phase systems and obtains bounded but possibly non-causal solutions. If the reference trajectories are generated by an exo-system, then we develop an exact-tracking controller in a feedback form. As in standard regulator theory, we obtain a linear map from the states of the exo-system to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.

Exact-Output Tracking Theory for Systems with Parameter Jumps

NASA Technical Reports Server (NTRS)

Devasia, Santosh; Paden, Brad; Rossi, Carlo

1997-01-01

We consider the exact output tracking problem for systems with parameter jumps. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches). Such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is applicable to non-minimum-phase systems and it obtains bounded but possibly non-causal solutions. If the reference trajectories are generated by an exosystem, then we develop an exact-tracking controller in a feed-back form. As in standard regulator theory, we obtain a linear map from the states of the exosystem to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.

Optimal Regulation of Virtual Power Plants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall Anese, Emiliano; Guggilam, Swaroop S.; Simonetto, Andrea

This paper develops a real-time algorithmic framework for aggregations of distributed energy resources (DERs) in distribution networks to provide regulation services in response to transmission-level requests. Leveraging online primal-dual-type methods for time-varying optimization problems and suitable linearizations of the nonlinear AC power-flow equations, we believe this work establishes the system-theoretic foundation to realize the vision of distribution-level virtual power plants. The optimization framework controls the output powers of dispatchable DERs such that, in aggregate, they respond to automatic-generation-control and/or regulation-services commands. This is achieved while concurrently regulating voltages within the feeder and maximizing customers' and utility's performance objectives. Convergence andmore » tracking capabilities are analytically established under suitable modeling assumptions. Simulations are provided to validate the proposed approach.« less

A linear-encoding model explains the variability of the target morphology in regeneration

PubMed Central

Lobo, Daniel; Solano, Mauricio; Bubenik, George A.; Levin, Michael

2014-01-01

A fundamental assumption of today's molecular genetics paradigm is that complex morphology emerges from the combined activity of low-level processes involving proteins and nucleic acids. An inherent characteristic of such nonlinear encodings is the difficulty of creating the genetic and epigenetic information that will produce a given self-assembling complex morphology. This ‘inverse problem’ is vital not only for understanding the evolution, development and regeneration of bodyplans, but also for synthetic biology efforts that seek to engineer biological shapes. Importantly, the regenerative mechanisms in deer antlers, planarian worms and fiddler crabs can solve an inverse problem: their target morphology can be altered specifically and stably by injuries in particular locations. Here, we discuss the class of models that use pre-specified morphological goal states and propose the existence of a linear encoding of the target morphology, making the inverse problem easy for these organisms to solve. Indeed, many model organisms such as Drosophila, hydra and Xenopus also develop according to nonlinear encodings producing linear encodings of their final morphologies. We propose the development of testable models of regeneration regulation that combine emergence with a top-down specification of shape by linear encodings of target morphology, driving transformative applications in biomedicine and synthetic bioengineering. PMID:24402915

Research in Applied Mathematics Related to Nonlinear System Theory.

DTIC Science & Technology

1985-08-01

This list includes A. OZGULER, P. KHARGONEKAR, J. RIBERA , and T. GEORGIOU. Also supported was the Principal Investigator (partial summer support only...regulator problem with internal stability", Ph.D. dissertation, University of Florida, 63 pages. J. RIBERA [1982] "Identification of linear relations... Ribera , doctoral student (now on faculty of I. E. S. E., Barcelona, SPAIN) Dr. A. Tannenbaum, Visiting Professor (partial summer support only, now

Regulation of Renewable Energy Sources to Optimal Power Flow Solutions Using ADMM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhang, Yijian; Hong, Mingyi

This paper considers power distribution systems featuring renewable energy sources (RESs), and develops a distributed optimization method to steer the RES output powers to solutions of AC optimal power flow (OPF) problems. The design of the proposed method leverages suitable linear approximations of the AC-power flow equations, and is based on the Alternating Direction Method of Multipliers (ADMM). Convergence of the RES-inverter output powers to solutions of the OPF problem is established under suitable conditions on the stepsize as well as mismatches between the commanded setpoints and actual RES output powers. In a broad sense, the methods and results proposedmore » here are also applicable to other distributed optimization problem setups with ADMM and inexact dual updates.« less

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

Approximations of thermoelastic and viscoelastic control systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Liu, Z. Y.; Miller, R. E.

1990-01-01

Well-posed models and computational algorithms are developed and analyzed for control of a class of partial differential equations that describe the motions of thermo-viscoelastic structures. An abstract (state space) framework and a general well-posedness result are presented that can be applied to a large class of thermo-elastic and thermo-viscoelastic models. This state space framework is used in the development of a computational scheme to be used in the solution of a linear quadratic regulator (LQR) control problem. A detailed convergence proof is provided for the viscoelastic model and several numerical results are presented to illustrate the theory and to analyze problems for which the theory is incomplete.

Mechanisms of Behavioral and Affective Treatment Outcomes in a Cognitive Behavioral Intervention for Boys.

PubMed

Burke, Jeffrey D; Loeber, Rolf

2016-01-01

Evidence for effective treatment for behavioral problems continues to grow, yet evidence about the effective mechanisms underlying those interventions has lagged behind. The Stop Now and Plan (SNAP) program is a multicomponent intervention for boys between 6 and 11. This study tested putative treatment mechanisms using data from 252 boys in a randomized controlled trial of SNAP versus treatment as usual. SNAP includes a 3 month group treatment period followed by individualized intervention, which persisted through the 15 month study period. Measures were administered in four waves: at baseline and at 3, 9 and 15 months after baseline. A hierarchical linear modeling strategy was used. SNAP was associated with improved problem-solving skills, prosocial behavior, emotion regulation skills, and reduced parental stress. Prosocial behavior, emotion regulation skills and reduced parental stress partially mediated improvements in child aggression. Improved emotion regulation skills partially mediated treatment-related child anxious-depressed outcomes. Improvements in parenting behaviors did not differ between treatment conditions. The results suggest that independent processes may drive affective and behavioral outcomes, with some specificity regarding the mechanisms related to differing treatment outcomes.

Multiphysics analysis of liquid metal annular linear induction pumps: A project overview

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maidana, Carlos Omar; Nieminen, Juha E.

Liquid metal-cooled fission reactors are both moderated and cooled by a liquid metal solution. These reactors are typically very compact and they can be used in regular electric power production, for naval and space propulsion systems or in fission surface power systems for planetary exploration. The coupling between the electromagnetics and thermo-fluid mechanical phenomena observed in liquid metal thermo-magnetic systems for nuclear and space applications gives rise to complex engineering magnetohydrodynamics and numerical problems. It is known that electromagnetic pumps have a number of advantages over rotating mechanisms: absence of moving parts, low noise and vibration level, simplicity of flowmore » rate regulation, easy maintenance and so on. However, while developing annular linear induction pumps, we are faced with a significant problem of magnetohydrodynamic instability arising in the device. The complex flow behavior in this type of devices includes a time-varying Lorentz force and pressure pulsation due to the time-varying electromagnetic fields and the induced convective currents that originates from the liquid metal flow, leading to instability problems along the device geometry. The determinations of the geometry and electrical configuration of liquid metal thermo-magnetic devices give rise to a complex inverse magnetohydrodynamic field problem were techniques for global optimization should be used, magnetohydrodynamics instabilities understood –or quantified- and multiphysics models developed and analyzed. Lastly, we present a project overview as well as a few computational models developed to study liquid metal annular linear induction pumps using first principles and the a few results of our multi-physics analysis.« less

Multiphysics analysis of liquid metal annular linear induction pumps: A project overview

DOE PAGES

Maidana, Carlos Omar; Nieminen, Juha E.

2016-03-14

Liquid metal-cooled fission reactors are both moderated and cooled by a liquid metal solution. These reactors are typically very compact and they can be used in regular electric power production, for naval and space propulsion systems or in fission surface power systems for planetary exploration. The coupling between the electromagnetics and thermo-fluid mechanical phenomena observed in liquid metal thermo-magnetic systems for nuclear and space applications gives rise to complex engineering magnetohydrodynamics and numerical problems. It is known that electromagnetic pumps have a number of advantages over rotating mechanisms: absence of moving parts, low noise and vibration level, simplicity of flowmore » rate regulation, easy maintenance and so on. However, while developing annular linear induction pumps, we are faced with a significant problem of magnetohydrodynamic instability arising in the device. The complex flow behavior in this type of devices includes a time-varying Lorentz force and pressure pulsation due to the time-varying electromagnetic fields and the induced convective currents that originates from the liquid metal flow, leading to instability problems along the device geometry. The determinations of the geometry and electrical configuration of liquid metal thermo-magnetic devices give rise to a complex inverse magnetohydrodynamic field problem were techniques for global optimization should be used, magnetohydrodynamics instabilities understood –or quantified- and multiphysics models developed and analyzed. Lastly, we present a project overview as well as a few computational models developed to study liquid metal annular linear induction pumps using first principles and the a few results of our multi-physics analysis.« less

Menu-Driven Solver Of Linear-Programming Problems

NASA Technical Reports Server (NTRS)

Viterna, L. A.; Ferencz, D.

1992-01-01

Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).

The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem.

PubMed

Narayanamoorthy, S; Kalyani, S

2015-01-01

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

Ultra-Low-Dropout Linear Regulator

NASA Technical Reports Server (NTRS)

Thornton, Trevor; Lepkowski, William; Wilk, Seth

2011-01-01

A radiation-tolerant, ultra-low-dropout linear regulator can operate between -150 and 150 C. Prototype components were demonstrated to be performing well after a total ionizing dose of 1 Mrad (Si). Unlike existing components, the linear regulator developed during this activity is unconditionally stable over all operating regimes without the need for an external compensation capacitor. The absence of an external capacitor reduces overall system mass/volume, increases reliability, and lowers cost. Linear regulators generate a precisely controlled voltage for electronic circuits regardless of fluctuations in the load current that the circuit draws from the regulator.

On regulators with a prescribed degree of stability. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ng, P. T. P.

1981-01-01

Several important aspects of the Regulator with a Prescribed Degree of Stability (RPDS) methodology and its applications are considered. The solution of the time varying RPDS problem as well as the characterization of RPDS closed loop eigenstructure properties are obtained. Based on the asymptotic behavior of RPDS root loci, a one step algorithm for designing Regulators with Prescribed Damping Ratio (RPDR) is developed. The robustness properties of RPDS are characterized in terms of the properties of the return difference and the inverse return difference matrices for the RPDS state feedback loop. This class of regulators is found to possess excellent multiloop margins with respect to stability and degree of stability properties. The ability of RPDS design to tolerate changing operating conditions and unmodelled dynamics are illustrated with a multiterminal dc/ac power system example. The output feedback realization of RPDS requires the use of Linear Quadratic Gaussian (LQG) methodology.

Stimulation of a turbofan engine for evaluation of multivariable optimal control concepts. [(computerized simulation)

NASA Technical Reports Server (NTRS)

Seldner, K.

1976-01-01

The development of control systems for jet engines requires a real-time computer simulation. The simulation provides an effective tool for evaluating control concepts and problem areas prior to actual engine testing. The development and use of a real-time simulation of the Pratt and Whitney F100-PW100 turbofan engine is described. The simulation was used in a multi-variable optimal controls research program using linear quadratic regulator theory. The simulation is used to generate linear engine models at selected operating points and evaluate the control algorithm. To reduce the complexity of the design, it is desirable to reduce the order of the linear model. A technique to reduce the order of the model; is discussed. Selected results between high and low order models are compared. The LQR control algorithms can be programmed on digital computer. This computer will control the engine simulation over the desired flight envelope.

The Intelligence of Dual Simplex Method to Solve Linear Fractional Fuzzy Transportation Problem

PubMed Central

Narayanamoorthy, S.; Kalyani, S.

2015-01-01

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example. PMID:25810713

Comparative study of flare control laws. [optimal control of b-737 aircraft approach and landing

NASA Technical Reports Server (NTRS)

Nadkarni, A. A.; Breedlove, W. J., Jr.

1979-01-01

A digital 3-D automatic control law was developed to achieve an optimal transition of a B-737 aircraft between various initial glid slope conditions and the desired final touchdown condition. A discrete, time-invariant, optimal, closed-loop control law presented for a linear regulator problem, was extended to include a system being acted upon by a constant disturbance. Two forms of control laws were derived to solve this problem. One method utilized the feedback of integral states defined appropriately and augmented with the original system equations. The second method formulated the problem as a control variable constraint, and the control variables were augmented with the original system. The control variable constraint control law yielded a better performance compared to feedback control law for the integral states chosen.

Robust Stability and Control of Multi-Body Ground Vehicles with Uncertain Dynamics and Failures

DTIC Science & Technology

2010-01-01

and N. Zhang, 2008. “Robust stability control of vehicle rollover subject to actuator time delay”. Proc. IMechE Part I: J. of systems and control ...Dynamic Systems and Control Conference, Boston, MA, Sept 2010 R.K. Yedavalli,”Robust Stability of Linear Interval Parameter Matrix Family Problem...for control coupled output regulation for a class of systems is presented. In section 2.1.7, the control design algorithm developed in section

Boredom proneness and emotion regulation predict emotional eating.

PubMed

Crockett, Amanda C; Myhre, Samantha K; Rokke, Paul D

2015-05-01

Emotional eating is considered a risk factor for eating disorders and an important contributor to obesity and its associated health problems. It has been suggested that boredom may be an important contributor to overeating, but has received relatively little attention. A sample of 552 college students was surveyed. Linear regression analyses found that proneness to boredom and difficulties in emotion regulation simultaneously predicted inappropriate eating behavior, including eating in response to boredom, other negative emotions, and external cues. The unique contributions of these variables to emotional eating were discussed. These findings help to further identify which individuals could be at risk for emotional eating and potentially for unhealthy weight gain. © The Author(s) 2015.

An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

PubMed

Zhao, Yingfeng; Liu, Sanyang

2016-01-01

We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.

Hybrid Solution of Stochastic Optimal Control Problems Using Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithms

DTIC Science & Technology

2012-03-01

0-486-41183-4. 15. Brown , Robert G. and Patrick Y. C. Hwang . Introduction to Random Signals and Applied Kalman Filtering. Wiley, New York, 1996. ISBN...stability and perfor- mance criteria. In the 1960’s, Kalman introduced the Linear Quadratic Regulator (LQR) method using an integral performance index...feedback of the state variables and was able to apply this method to time-varying and Multi-Input Multi-Output (MIMO) systems. Kalman further showed

Confining potential in momentum space

NASA Technical Reports Server (NTRS)

Norbury, John W.; Kahana, David E.; Maung, Khin Maung

1992-01-01

A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations.

Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration.

PubMed

Xia, Youshen; Sun, Changyin; Zheng, Wei Xing

2012-05-01

There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L1 estimation problems but also needs much less computational time than the related algorithms in solving both linear L1 estimation and image restoration problems.

Can Linear Superiorization Be Useful for Linear Optimization Problems?

PubMed Central

Censor, Yair

2017-01-01

Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? and (ii) How does linear superiorization fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: “yes” and “very well”, respectively. PMID:29335660

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1996-01-01

The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.

Longitudinal effects of prenatal exposure to air pollutants on self-regulatory capacities and social competence.

PubMed

Margolis, Amy E; Herbstman, Julie B; Davis, Katie S; Thomas, Valerie K; Tang, Deliang; Wang, Ya; Wang, Shuang; Perera, Frederica P; Peterson, Bradley S; Rauh, Virginia A

2016-07-01

We evaluated the influence of prenatal exposure to widespread urban air pollutants on the development of self-regulation and social competence in a longitudinal prospective cohort of children born to nonsmoking minority women in New York City. Air pollutant exposure was estimated categorically by level of polycyclic aromatic hydrocarbon (PAH)-DNA adducts in maternal blood collected at delivery, providing a biomarker of maternal exposure to PAH over a 2- to 3-month period. Deficient emotional self-regulation (DESR) was defined as moderate elevations on three specific scales of the child behavior checklist (anxious/depressed, aggressive behavior, and attention problems). We used generalized estimating equations to assess the influence of prenatal exposure to PAH on DESR in children at 3-5, 7, 9, and 11 years of age, adjusted for gender and race/ethnicity. Next, we assessed the association of prenatal exposure to PAH with social competence, as measured by the social responsiveness scale (SRS), the association of impaired self-regulation with social competence, and whether impairment in self-regulation mediated the association of prenatal exposure to PAH with social competence. We detected a significant interaction (at p = .05) of exposure with time, in which the developmental trajectory of self-regulatory capacity was delayed in the exposed children. Multiple linear regression revealed a positive association between presence of PAH-DNA adducts and problems with social competence (p < .04), level of dysregulation and problems with social competence (p < .0001), and evidence that self-regulation mediates the association of prenatal exposure to PAH with social competence (p < .0007). These data suggest that prenatal exposure to PAH produces long-lasting effects on self-regulatory capacities across early and middle childhood, and that these deficits point to emerging social problems with real-world consequences for high-risk adolescent behaviors in this minority urban cohort. © 2016 Association for Child and Adolescent Mental Health.

The dynamics and optimal control of spinning spacecraft and movable telescoping appendages, part A. [two axis control with single offset boom

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Sellappan, R.

1977-01-01

The problem of optimal control with a minimum time criterion as applied to a single boom system for achieving two axis control is discussed. The special case where the initial conditions are such that the system can be driven to the equilibrium state with only a single switching maneuver in the bang-bang optimal sequence is analyzed. The system responses are presented. Application of the linear regulator problem for the optimal control of the telescoping system is extended to consider the effects of measurement and plant noises. The noise uncertainties are included with an application of the estimator - Kalman filter problem. Different schemes for measuring the components of the angular velocity are considered. Analytical results are obtained for special cases, and numerical results are presented for the general case.

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

A sequential linear optimization approach for controller design

NASA Technical Reports Server (NTRS)

Horta, L. G.; Juang, J.-N.; Junkins, J. L.

1985-01-01

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

NASA Astrophysics Data System (ADS)

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

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

On the linear programming bound for linear Lee codes.

PubMed

Astola, Helena; Tabus, Ioan

2016-01-01

Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field [Formula: see text] on the set of Lee-compositions. We show some useful properties of certain sums of Lee-numbers, which are the eigenvalues of the Lee association scheme, appearing in the linear programming problem of linear Lee codes. Using the additional equality constraints, we formulate the linear programming problem of linear Lee codes in a very compact form, leading to a fast execution, which allows to efficiently compute the bounds for large parameter values of the linear codes.

Chameleon-like elastomers with molecularly encoded strain-adaptive stiffening and coloration

NASA Astrophysics Data System (ADS)

Vatankhah-Varnosfaderani, Mohammad; Keith, Andrew N.; Cong, Yidan; Liang, Heyi; Rosenthal, Martin; Sztucki, Michael; Clair, Charles; Magonov, Sergei; Ivanov, Dimitri A.; Dobrynin, Andrey V.; Sheiko, Sergei S.

2018-03-01

Active camouflage is widely recognized as a soft-tissue feature, and yet the ability to integrate adaptive coloration and tissuelike mechanical properties into synthetic materials remains elusive. We provide a solution to this problem by uniting these functions in moldable elastomers through the self-assembly of linear-bottlebrush-linear triblock copolymers. Microphase separation of the architecturally distinct blocks results in physically cross-linked networks that display vibrant color, extreme softness, and intense strain stiffening on par with that of skin tissue. Each of these functional properties is regulated by the structure of one macromolecule, without the need for chemical cross-linking or additives. These materials remain stable under conditions characteristic of internal bodily environments and under ambient conditions, neither swelling in bodily fluids nor drying when exposed to air.

Fundamental solution of the problem of linear programming and method of its determination

NASA Technical Reports Server (NTRS)

Petrunin, S. V.

1978-01-01

The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

An historical survey of computational methods in optimal control.

NASA Technical Reports Server (NTRS)

Polak, E.

1973-01-01

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1986-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

Can linear superiorization be useful for linear optimization problems?

NASA Astrophysics Data System (ADS)

Censor, Yair

2017-04-01

Linear superiorization (LinSup) considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are: (i) does LinSup provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? (ii) How does LinSup fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: ‘yes’ and ‘very well’, respectively.

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.

Review of Chinese Environmental Risk Assessment Regulations and Case Studies

PubMed Central

Meng, Xiaojie; Zhang, Yan; Zhao, Yuchao; Lou, In Chio; Gao, Jixi

2012-01-01

Environmental risk assessment is an essential step in the development of solutions for pollution problems and new environmental regulations. An assessment system for environmental risks has been developed in China in recent decades. However, many of the Chinese technical guidelines, standards, and regulations were directly adapted from those of developed countries, and were not based on the Chinese environmental and socioeconomic context. Although existing environmental regulations for pollutants are usually obtained by extrapolations from high-dose toxicological data to low-dose scenarios using linear-non-threshold (LNT) models, toxicologists have argued that J-shaped or inverse J-shaped curves may dominate the dose–response relationships for environmental pollutants at low doses because low exposures stimulate biological protective mechanisms that are ineffective at higher doses. The costs of regulations based on LNT and J-shaped models could therefore be dramatically different. Since economic factors strongly affect the decision-making process, particularly for developing countries, it is time to strengthen basic research to provide more scientific support for Chinese environmental regulations. In this paper, we summarize current Chinese environmental policies and standards and the application of environmental risk assessment in China, and recommend a more scientific approach to the development of Chinese regulations. PMID:22740787

A linear programming manual

NASA Technical Reports Server (NTRS)

Tuey, R. C.

1972-01-01

Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

Exploiting Bounded Signal Flow for Graph Orientation Based on Cause-Effect Pairs

NASA Astrophysics Data System (ADS)

Dorn, Britta; Hüffner, Falk; Krüger, Dominikus; Niedermeier, Rolf; Uhlmann, Johannes

We consider the following problem: Given an undirected network and a set of sender-receiver pairs, direct all edges such that the maximum number of "signal flows" defined by the pairs can be routed respecting edge directions. This problem has applications in communication networks and in understanding protein interaction based cell regulation mechanisms. Since this problem is NP-hard, research so far concentrated on polynomial-time approximation algorithms and tractable special cases. We take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixed-parameter tractability results, and in one case a sharp complexity dichotomy between a linear-time solvable case and a slightly more general NP-hard case. We examine the value of these parameters for several real-world network instances. For many relevant cases, the NP-hard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies.

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.

Local Approximation and Hierarchical Methods for Stochastic Optimization

NASA Astrophysics Data System (ADS)

Cheng, Bolong

In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the PJM Interconnect and show that it outperforms the baseline approach used in the industry.

Electrical Characterization and Specification of Special Purpose Linear Microcircuits.

DTIC Science & Technology

1981-06-01

was therefore deleted from the slash sheet. Testing of these devices at 125 0C did not uncover any additional failures and/or test problems. However...Whereas, the 4- terminal adjustable regulators are evolved from their fixed voltage counterparts by deleting the two internal resistors used to set the...current 1-55 0 C-TA 0.001 3.00 uA _ _125C Output short LOS1 VIN = -10V Figure 12 0.002 2.0 A circuit cur- [OS2 VIN=-30V kaveforms 𔃺.002 1.0 rent

Digital adaptive flight controller development

NASA Technical Reports Server (NTRS)

Kaufman, H.; Alag, G.; Berry, P.; Kotob, S.

1974-01-01

A design study of adaptive control logic suitable for implementation in modern airborne digital flight computers was conducted. Two designs are described for an example aircraft. Each of these designs uses a weighted least squares procedure to identify parameters defining the dynamics of the aircraft. The two designs differ in the way in which control law parameters are determined. One uses the solution of an optimal linear regulator problem to determine these parameters while the other uses a procedure called single stage optimization. Extensive simulation results and analysis leading to the designs are presented.

The median problems on linear multichromosomal genomes: graph representation and fast exact solutions.

PubMed

Xu, Andrew Wei

2010-09-01

In genome rearrangement, given a set of genomes G and a distance measure d, the median problem asks for another genome q that minimizes the total distance [Formula: see text]. This is a key problem in genome rearrangement based phylogenetic analysis. Although this problem is known to be NP-hard, we have shown in a previous article, on circular genomes and under the DCJ distance measure, that a family of patterns in the given genomes--represented by adequate subgraphs--allow us to rapidly find exact solutions to the median problem in a decomposition approach. In this article, we extend this result to the case of linear multichromosomal genomes, in order to solve more interesting problems on eukaryotic nuclear genomes. A multi-way capping problem in the linear multichromosomal case imposes an extra computational challenge on top of the difficulty in the circular case, and this difficulty has been underestimated in our previous study and is addressed in this article. We represent the median problem by the capped multiple breakpoint graph, extend the adequate subgraphs into the capped adequate subgraphs, and prove optimality-preserving decomposition theorems, which give us the tools to solve the median problem and the multi-way capping optimization problem together. We also develop an exact algorithm ASMedian-linear, which iteratively detects instances of (capped) adequate subgraphs and decomposes problems into subproblems. Tested on simulated data, ASMedian-linear can rapidly solve most problems with up to several thousand genes, and it also can provide optimal or near-optimal solutions to the median problem under the reversal/HP distance measures. ASMedian-linear is available at http://sites.google.com/site/andrewweixu .

Prospective Middle School Mathematics Teachers' Knowledge of Linear Graphs in Context of Problem-Posing

ERIC Educational Resources Information Center

Kar, Tugrul

2016-01-01

This study examined prospective middle school mathematics teachers' problem-posing skills by investigating their ability to associate linear graphs with daily life situations. Prospective teachers were given linear graphs and asked to pose problems that could potentially be represented by the graphs. Their answers were analyzed in two stages. In…

Analyzing Multilevel Data: An Empirical Comparison of Parameter Estimates of Hierarchical Linear Modeling and Ordinary Least Squares Regression

ERIC Educational Resources Information Center

Rocconi, Louis M.

2011-01-01

Hierarchical linear models (HLM) solve the problems associated with the unit of analysis problem such as misestimated standard errors, heterogeneity of regression and aggregation bias by modeling all levels of interest simultaneously. Hierarchical linear modeling resolves the problem of misestimated standard errors by incorporating a unique random…

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre

2014-07-01

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

Inference of Vohradský's Models of Genetic Networks by Solving Two-Dimensional Function Optimization Problems

PubMed Central

Kimura, Shuhei; Sato, Masanao; Okada-Hatakeyama, Mariko

2013-01-01

The inference of a genetic network is a problem in which mutual interactions among genes are inferred from time-series of gene expression levels. While a number of models have been proposed to describe genetic networks, this study focuses on a mathematical model proposed by Vohradský. Because of its advantageous features, several researchers have proposed the inference methods based on Vohradský's model. When trying to analyze large-scale networks consisting of dozens of genes, however, these methods must solve high-dimensional non-linear function optimization problems. In order to resolve the difficulty of estimating the parameters of the Vohradský's model, this study proposes a new method that defines the problem as several two-dimensional function optimization problems. Through numerical experiments on artificial genetic network inference problems, we showed that, although the computation time of the proposed method is not the shortest, the method has the ability to estimate parameters of Vohradský's models more effectively with sufficiently short computation times. This study then applied the proposed method to an actual inference problem of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. PMID:24386175

Linear solver performance in elastoplastic problem solution on GPU cluster

NASA Astrophysics Data System (ADS)

Khalevitsky, Yu. V.; Konovalov, A. V.; Burmasheva, N. V.; Partin, A. S.

2017-12-01

Applying the finite element method to severe plastic deformation problems involves solving linear equation systems. While the solution procedure is relatively hard to parallelize and computationally intensive by itself, a long series of large scale systems need to be solved for each problem. When dealing with fine computational meshes, such as in the simulations of three-dimensional metal matrix composite microvolume deformation, tens and hundreds of hours may be needed to complete the whole solution procedure, even using modern supercomputers. In general, one of the preconditioned Krylov subspace methods is used in a linear solver for such problems. The method convergence highly depends on the operator spectrum of a problem stiffness matrix. In order to choose the appropriate method, a series of computational experiments is used. Different methods may be preferable for different computational systems for the same problem. In this paper we present experimental data obtained by solving linear equation systems from an elastoplastic problem on a GPU cluster. The data can be used to substantiate the choice of the appropriate method for a linear solver to use in severe plastic deformation simulations.

Design of Linear-Quadratic-Regulator for a CSTR process

NASA Astrophysics Data System (ADS)

Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.

2017-11-01

This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.

Differential-Drive Mobile Robot Control Design based-on Linear Feedback Control Law

NASA Astrophysics Data System (ADS)

Nurmaini, Siti; Dewi, Kemala; Tutuko, Bambang

2017-04-01

This paper deals with the problem of how to control differential driven mobile robot with simple control law. When mobile robot moves from one position to another to achieve a position destination, it always produce some errors. Therefore, a mobile robot requires a certain control law to drive the robot’s movement to the position destination with a smallest possible error. In this paper, in order to reduce position error, a linear feedback control is proposed with pole placement approach to regulate the polynoms desired. The presented work leads to an improved understanding of differential-drive mobile robot (DDMR)-based kinematics equation, which will assist to design of suitable controllers for DDMR movement. The result show by using the linier feedback control method with pole placement approach the position error is reduced and fast convergence is achieved.

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.

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.

Parameterized LMI Based Diagonal Dominance Compensator Study for Polynomial Linear Parameter Varying System

NASA Astrophysics Data System (ADS)

Han, Xiaobao; Li, Huacong; Jia, Qiusheng

2017-12-01

For dynamic decoupling of polynomial linear parameter varying(PLPV) system, a robust dominance pre-compensator design method is given. The parameterized precompensator design problem is converted into an optimal problem constrained with parameterized linear matrix inequalities(PLMI) by using the conception of parameterized Lyapunov function(PLF). To solve the PLMI constrained optimal problem, the precompensator design problem is reduced into a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a new constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator is achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation on a turbofan engine PLPV model.

Students’ difficulties in solving linear equation problems

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Assessing non-uniqueness: An algebraic approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

ALPS: A Linear Program Solver

NASA Technical Reports Server (NTRS)

Ferencz, Donald C.; Viterna, Larry A.

1991-01-01

ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.

Genetic programming over context-free languages with linear constraints for the knapsack problem: first results.

PubMed

Bruhn, Peter; Geyer-Schulz, Andreas

2002-01-01

In this paper, we introduce genetic programming over context-free languages with linear constraints for combinatorial optimization, apply this method to several variants of the multidimensional knapsack problem, and discuss its performance relative to Michalewicz's genetic algorithm with penalty functions. With respect to Michalewicz's approach, we demonstrate that genetic programming over context-free languages with linear constraints improves convergence. A final result is that genetic programming over context-free languages with linear constraints is ideally suited to modeling complementarities between items in a knapsack problem: The more complementarities in the problem, the stronger the performance in comparison to its competitors.

The generalized pole assignment problem. [dynamic output feedback problems

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

Two dynamic output feedback problems for a linear, strictly proper system are considered, along with their interrelationships. The problems are formulated in the frequency domain and investigated in terms of linear equations over rings of polynomials. Necessary and sufficient conditions are expressed using genericity.

Wiener sliding-mode control for artificial pancreas: a new nonlinear approach to glucose regulation.

PubMed

Abu-Rmileh, Amjad; Garcia-Gabin, Winston

2012-08-01

Type 1 diabetic patients need insulin therapy to keep their blood glucose close to normal. In this paper an attempt is made to show how nonlinear control-oriented model may be used to improve the performance of closed-loop control of blood glucose in diabetic patients. The nonlinear Wiener model is used as a novel modeling approach to be applied to the glucose control problem. The identified Wiener model is used in the design of a robust nonlinear sliding mode control strategy. Two configurations of the nonlinear controller are tested and compared to a controller designed with a linear model. The controllers are designed in a Smith predictor structure to reduce the effect of system time delay. To improve the meal compensation features, the controllers are provided with a simple feedforward controller to inject an insulin bolus at meal time. Different simulation scenarios have been used to evaluate the proposed controllers. The obtained results show that the new approach outperforms the linear control scheme, and regulates the glucose level within safe limits in the presence of measurement and modeling errors, meal uncertainty and patient variations. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Enhancing roll stability of heavy vehicle by LQR active anti-roll bar control using electronic servo-valve hydraulic actuators

NASA Astrophysics Data System (ADS)

Vu, Van Tan; Sename, Olivier; Dugard, Luc; Gaspar, Peter

2017-09-01

Rollover of heavy vehicle is an important road safety problem world-wide. Although rollovers are relatively rare events, they are usually deadly accidents when they occur. The roll stability loss is the main cause of rollover accidents in which heavy vehicles are involved. In order to improve the roll stability, most of modern heavy vehicles are equipped with passive anti-roll bars to reduce roll motion during cornering or riding on uneven roads. However these may be not sufficient to overcome critical situations. This paper introduces the active anti-roll bars made of four electronic servo-valve hydraulic actuators, which are modelled and integrated in a yaw-roll model of a single unit heavy vehicle. The control signal is the current entering the electronic servo-valve and the output is the force generated by the hydraulic actuator. The active control design is achieved solving a linear optimal control problem based on the linear quadratic regulator (LQR) approach. A comparison of several LQR controllers is provided to allow for tackling the considered multi-objective problems. Simulation results in frequency and time domains show that the use of two active anti-roll bars (front and rear axles) drastically improves the roll stability of the single unit heavy vehicle compared with the passive anti-roll bar.

Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

NASA Astrophysics Data System (ADS)

Dubinskii, Yu A.; Osipenko, A. S.

2000-02-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

NASA Astrophysics Data System (ADS)

Ebrahimnejad, Ali

2015-08-01

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.

Study of quality assurance regulations for linear accelerators in Korea: A comparison study between the current status in Korea and the international guidelines

NASA Astrophysics Data System (ADS)

Lee, Hyunho; Jeong, Seonghoon; Jo, Yunhui; Yoon, Myonggeun

2015-07-01

Quality assurance (QA) for medical linear accelerators is indispensable for appropriate cancer treatment. Some international organizations and advanced Western countries have provided QA guidelines for linear accelerators. Currently, QA regulations for linear accelerators in Korean hospitals specify a system in which each hospital stipulates its independent hospital-based protocols for QA procedures (HP_QAPs) and conducts QA based on those HP_QAPs while regulatory authorities verify whether items under those HP_QAPs have been performed. However, because this regulatory method cannot guarantee the quality of universal treatment and QA items with tolerance criteria are different in many hospitals, the presentation of standardized QA items and tolerance criteria is essential. In this study, QA items in HP_QAPs from various hospitals and those presented by international organizations, such as the International Atomic Energy Agency, the European Union, and the American Association of Physicist in Medicine, and by advanced Western countries, such as the USA, the UK, and Canada, were compared. Concordance rates between QA items for linear accelerators that were presented by the aforementioned organizations and those currently being implemented in Korean hospitals were shown to exhibit a daily QA of 50%, a weekly QA of 22%, a monthly QA of 43%, and an annual QA of 65%, and the overall concordance rates of all QA items were approximately 48%. In the comparison between QA items being implemented in Korean hospitals and those being implemented in advanced Western countries, concordance rates were shown to exhibit a daily QA of 50%, a weekly QA of 33%, a monthly QA of 60%, and an annual QA of 67%, and the overall concordance rates of all QA items were approximately 57%. The results of this study indicate that the HP_QAPs currently implemented by Korean hospitals as QA standards for linear accelerators used in radiation therapy do not meet international standards. If this problem is to be solved, national standardized QA items and procedures for linear accelerators need to be developed.

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.

Linear Programming and Its Application to Pattern Recognition Problems

NASA Technical Reports Server (NTRS)

Omalley, M. J.

1973-01-01

Linear programming and linear programming like techniques as applied to pattern recognition problems are discussed. Three relatively recent research articles on such applications are summarized. The main results of each paper are described, indicating the theoretical tools needed to obtain them. A synopsis of the author's comments is presented with regard to the applicability or non-applicability of his methods to particular problems, including computational results wherever given.

Voltage regulation in linear induction accelerators

DOEpatents

Parsons, William M.

1992-01-01

Improvement in voltage regulation in a Linear Induction Accelerator wherein a varistor, such as a metal oxide varistor, is placed in parallel with the beam accelerating cavity and the magnetic core. The non-linear properties of the varistor result in a more stable voltage across the beam accelerating cavity than with a conventional compensating resistance.

The application of LQR synthesis techniques to the turboshaft engine control problem

NASA Technical Reports Server (NTRS)

Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.

1984-01-01

A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

THE SUCCESSIVE LINEAR ESTIMATOR: A REVISIT. (R827114)

EPA Science Inventory

This paper examines the theoretical basis of the successive linear estimator (SLE) that has been developed for the inverse problem in subsurface hydrology. We show that the SLE algorithm is a non-linear iterative estimator to the inverse problem. The weights used in the SLE al...

Consideration of computer limitations in implementing on-line controls. M.S. Thesis

NASA Technical Reports Server (NTRS)

Roberts, G. K.

1976-01-01

A formal statement of the optimal control problem which includes the interval of dicretization as an optimization parameter, and extend this to include selection of a control algorithm as part of the optimization procedure, is formulated. The performance of the scalar linear system depends on the discretization interval. Discrete-time versions of the output feedback regulator and an optimal compensator, and the use of these results in presenting an example of a system for which fast partial-state-feedback control better minimizes a quadratic cost than either a full-state feedback control or a compensator, are developed.

Analysis and discussion on the experimental data of electrolyte analyzer

NASA Astrophysics Data System (ADS)

Dong, XinYu; Jiang, JunJie; Liu, MengJun; Li, Weiwei

2018-06-01

In the subsequent verification of electrolyte analyzer, we found that the instrument can achieve good repeatability and stability in repeated measurements with a short period of time, in line with the requirements of verification regulation of linear error and cross contamination rate, but the phenomenon of large indication error is very common, the measurement results of different manufacturers have great difference, in order to find and solve this problem, help enterprises to improve quality of product, to obtain accurate and reliable measurement data, we conducted the experimental evaluation of electrolyte analyzer, and the data were analyzed by statistical analysis.

A neural network approach to job-shop scheduling.

PubMed

Zhou, D N; Cherkassky, V; Baldwin, T R; Olson, D E

1991-01-01

A novel analog computational network is presented for solving NP-complete constraint satisfaction problems, i.e. job-shop scheduling. In contrast to most neural approaches to combinatorial optimization based on quadratic energy cost function, the authors propose to use linear cost functions. As a result, the network complexity (number of neurons and the number of resistive interconnections) grows only linearly with problem size, and large-scale implementations become possible. The proposed approach is related to the linear programming network described by D.W. Tank and J.J. Hopfield (1985), which also uses a linear cost function for a simple optimization problem. It is shown how to map a difficult constraint-satisfaction problem onto a simple neural net in which the number of neural processors equals the number of subjobs (operations) and the number of interconnections grows linearly with the total number of operations. Simulations show that the authors' approach produces better solutions than existing neural approaches to job-shop scheduling, i.e. the traveling salesman problem-type Hopfield approach and integer linear programming approach of J.P.S. Foo and Y. Takefuji (1988), in terms of the quality of the solution and the network complexity.

A feasible DY conjugate gradient method for linear equality constraints

NASA Astrophysics Data System (ADS)

LI, Can

2017-09-01

In this paper, we propose a feasible conjugate gradient method for solving linear equality constrained optimization problem. The method is an extension of the Dai-Yuan conjugate gradient method proposed by Dai and Yuan to linear equality constrained optimization problem. It can be applied to solve large linear equality constrained problem due to lower storage requirement. An attractive property of the method is that the generated direction is always feasible and descent direction. Under mild conditions, the global convergence of the proposed method with exact line search is established. Numerical experiments are also given which show the efficiency of the method.

Linear systems on balancing chemical reaction problem

NASA Astrophysics Data System (ADS)

Kafi, R. A.; Abdillah, B.

2018-01-01

The concept of linear systems appears in a variety of applications. This paper presents a small sample of the wide variety of real-world problems regarding our study of linear systems. We show that the problem in balancing chemical reaction can be described by homogeneous linear systems. The solution of the systems is obtained by performing elementary row operations. The obtained solution represents the finding coefficients of chemical reaction. In addition, we present a computational calculation to show that mathematical software such as Matlab can be used to simplify completion of the systems, instead of manually using row operations.

Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer

NASA Astrophysics Data System (ADS)

Pikichyan, H. V.

2017-07-01

In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.

Voltage regulation in linear induction accelerators

DOEpatents

Parsons, W.M.

1992-12-29

Improvement in voltage regulation in a linear induction accelerator wherein a varistor, such as a metal oxide varistor, is placed in parallel with the beam accelerating cavity and the magnetic core is disclosed. The non-linear properties of the varistor result in a more stable voltage across the beam accelerating cavity than with a conventional compensating resistance. 4 figs.

Linear and Quadratic Change: A Problem from Japan

ERIC Educational Resources Information Center

Peterson, Blake E.

2006-01-01

In the fall of 2003, the author conducted research on the student teaching process in Japan. The basis for most of the lessons observed was rich mathematics problems. Upon returning to the US, the author used one such problem while teaching an algebra 2 class. This article introduces that problem, which gives rise to both linear and quadratic…

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

NASA Astrophysics Data System (ADS)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

Robust preview control for a class of uncertain discrete-time systems with time-varying delay.

PubMed

Li, Li; Liao, Fucheng

2018-02-01

This paper proposes a concept of robust preview tracking control for uncertain discrete-time systems with time-varying delay. Firstly, a model transformation is employed for an uncertain discrete system with time-varying delay. Then, the auxiliary variables related to the system state and input are introduced to derive an augmented error system that includes future information on the reference signal. This leads to the tracking problem being transformed into a regulator problem. Finally, for the augmented error system, a sufficient condition of asymptotic stability is derived and the preview controller design method is proposed based on the scaled small gain theorem and linear matrix inequality (LMI) technique. The method proposed in this paper not only solves the difficulty problem of applying the difference operator to the time-varying matrices but also simplifies the structure of the augmented error system. The numerical simulation example also illustrates the effectiveness of the results presented in the paper. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

NASA Astrophysics Data System (ADS)

Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

2004-12-01

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

NASA Astrophysics Data System (ADS)

Denevi, Giulia; Garbarino, Sara; Sorrentino, Alberto

2017-08-01

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out-perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Addona, Davide, E-mail: d.addona@campus.unimib.it

2015-08-15

We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

NASA Astrophysics Data System (ADS)

Xu, Jiuping; Li, Jun

2002-09-01

In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

Linear decomposition approach for a class of nonconvex programming problems.

PubMed

Shen, Peiping; Wang, Chunfeng

2017-01-01

This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.

Design and Implement of Low Ripple and Quasi-digital Power Supply

NASA Astrophysics Data System (ADS)

Xiangli, Li; Yanjun, Wei; Hanhong, Qi; Yan, Ma

A switch linearity hybrid power supply based on single chip microcomputer is designed which merged the merits of the switching and linear power supply. Main circuit includes pre-regulator which works in switching mode and series regulator which works in linear mode. Two-stage regulation mode was adopted in the main circuit of the power. A single chip computer (SCM) and high resolution of series D/A and A/D converters are applied to control and measurement which achieved continuous adjustable and low ripple constant current or voltage power supply

Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

NASA Astrophysics Data System (ADS)

Basin, M.; Maldonado, J. J.; Zendejo, O.

2016-07-01

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

Semilinear programming: applications and implementation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohan, S.

Semilinear programming is a method of solving optimization problems with linear constraints where the non-negativity restrictions on the variables are dropped and the objective function coefficients can take on different values depending on whether the variable is positive or negative. The simplex method for linear programming is modified in this thesis to solve general semilinear and piecewise linear programs efficiently without having to transform them into equivalent standard linear programs. Several models in widely different areas of optimization such as production smoothing, facility locations, goal programming and L/sub 1/ estimation are presented first to demonstrate the compact formulation that arisesmore » when such problems are formulated as semilinear programs. A code SLP is constructed using the semilinear programming techniques. Problems in aggregate planning and L/sub 1/ estimation are solved using SLP and equivalent linear programs using a linear programming simplex code. Comparisons of CPU times and number iterations indicate SLP to be far superior. The semilinear programming techniques are extended to piecewise linear programming in the implementation of the code PLP. Piecewise linear models in aggregate planning are solved using PLP and equivalent standard linear programs using a simple upper bounded linear programming code SUBLP.« less

Computer Power. Part 2: Electrical Power Problems and Their Amelioration.

ERIC Educational Resources Information Center

Price, Bennett J.

1989-01-01

Describes electrical power problems that affect computer users, including spikes, sags, outages, noise, frequency variations, and static electricity. Ways in which these problems may be diagnosed and cured are discussed. Sidebars consider transformers; power distribution units; surge currents/linear and non-linear loads; and sizing the power…

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

Reduced-Size Integer Linear Programming Models for String Selection Problems: Application to the Farthest String Problem.

PubMed

Zörnig, Peter

2015-08-01

We present integer programming models for some variants of the farthest string problem. The number of variables and constraints is substantially less than that of the integer linear programming models known in the literature. Moreover, the solution of the linear programming-relaxation contains only a small proportion of noninteger values, which considerably simplifies the rounding process. Numerical tests have shown excellent results, especially when a small set of long sequences is given.

Optimal multi-floor plant layout based on the mathematical programming and particle swarm optimization.

PubMed

Lee, Chang Jun

2015-01-01

In the fields of researches associated with plant layout optimization, the main goal is to minimize the costs of pipelines and pumping between connecting equipment under various constraints. However, what is the lacking of considerations in previous researches is to transform various heuristics or safety regulations into mathematical equations. For example, proper safety distances between equipments have to be complied for preventing dangerous accidents on a complex plant. Moreover, most researches have handled single-floor plant. However, many multi-floor plants have been constructed for the last decade. Therefore, the proper algorithm handling various regulations and multi-floor plant should be developed. In this study, the Mixed Integer Non-Linear Programming (MINLP) problem including safety distances, maintenance spaces, etc. is suggested based on mathematical equations. The objective function is a summation of pipeline and pumping costs. Also, various safety and maintenance issues are transformed into inequality or equality constraints. However, it is really hard to solve this problem due to complex nonlinear constraints. Thus, it is impossible to use conventional MINLP solvers using derivatives of equations. In this study, the Particle Swarm Optimization (PSO) technique is employed. The ethylene oxide plant is illustrated to verify the efficacy of this study.

Sixth SIAM conference on applied linear algebra: Final program and abstracts. Final technical report

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1997-12-31

Linear algebra plays a central role in mathematics and applications. The analysis and solution of problems from an amazingly wide variety of disciplines depend on the theory and computational techniques of linear algebra. In turn, the diversity of disciplines depending on linear algebra also serves to focus and shape its development. Some problems have special properties (numerical, structural) that can be exploited. Some are simply so large that conventional approaches are impractical. New computer architectures motivate new algorithms, and fresh ways to look at old ones. The pervasive nature of linear algebra in analyzing and solving problems means that peoplemore » from a wide spectrum--universities, industrial and government laboratories, financial institutions, and many others--share an interest in current developments in linear algebra. This conference aims to bring them together for their mutual benefit. Abstracts of papers presented are included.« less

Noisy covariance matrices and portfolio optimization

NASA Astrophysics Data System (ADS)

Pafka, S.; Kondor, I.

2002-05-01

According to recent findings [#!bouchaud!#,#!stanley!#], empirical covariance matrices deduced from financial return series contain such a high amount of noise that, apart from a few large eigenvalues and the corresponding eigenvectors, their structure can essentially be regarded as random. In [#!bouchaud!#], e.g., it is reported that about 94% of the spectrum of these matrices can be fitted by that of a random matrix drawn from an appropriately chosen ensemble. In view of the fundamental role of covariance matrices in the theory of portfolio optimization as well as in industry-wide risk management practices, we analyze the possible implications of this effect. Simulation experiments with matrices having a structure such as described in [#!bouchaud!#,#!stanley!#] lead us to the conclusion that in the context of the classical portfolio problem (minimizing the portfolio variance under linear constraints) noise has relatively little effect. To leading order the solutions are determined by the stable, large eigenvalues, and the displacement of the solution (measured in variance) due to noise is rather small: depending on the size of the portfolio and on the length of the time series, it is of the order of 5 to 15%. The picture is completely different, however, if we attempt to minimize the variance under non-linear constraints, like those that arise e.g. in the problem of margin accounts or in international capital adequacy regulation. In these problems the presence of noise leads to a serious instability and a high degree of degeneracy of the solutions.

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Performance and limitations of p-version finite element method for problems containing singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, K.K.; Surana, K.S.

1996-10-01

In this paper, the authors investigate the performance of p-version Least Squares Finite Element Formulation (LSFEF) for a hyperbolic system of equations describing a one-dimensional radial flow of an upper-convected Maxwell fluid. This problem has r{sup 2} singularity in stress and r{sup {minus}1} singularity in velocity at r = 0. By carefully controlling the inner radius r{sub j}, Deborah number DE and Reynolds number Re, this problem can be used to simulate the following four classes of problems: (a) smooth linear problems, (b) smooth non-linear problems, (c) singular linear problems and (d) singular non-linear problems. They demonstrate that in casesmore » (a) and (b) the p-version method, in particular p-version LSFEF is meritorious. However, for cases (c) and (d) p-version LSFEF, even with extreme mesh refinement and very high p-levels, either produces wrong solutions, or results in the failure of the iterative solution procedure. Even though in the numerical studies they have considered p-version LSFEF for the radial flow of the upper-convected Maxwell fluid, the findings and conclusions are equally valid for other smooth and singular problems as well, regardless of the formulation strategy chosen and element approximation functions employed.« less

Chromosome structures: reduction of certain problems with unequal gene content and gene paralogs to integer linear programming.

PubMed

Lyubetsky, Vassily; Gershgorin, Roman; Gorbunov, Konstantin

2017-12-06

Chromosome structure is a very limited model of the genome including the information about its chromosomes such as their linear or circular organization, the order of genes on them, and the DNA strand encoding a gene. Gene lengths, nucleotide composition, and intergenic regions are ignored. Although highly incomplete, such structure can be used in many cases, e.g., to reconstruct phylogeny and evolutionary events, to identify gene synteny, regulatory elements and promoters (considering highly conserved elements), etc. Three problems are considered; all assume unequal gene content and the presence of gene paralogs. The distance problem is to determine the minimum number of operations required to transform one chromosome structure into another and the corresponding transformation itself including the identification of paralogs in two structures. We use the DCJ model which is one of the most studied combinatorial rearrangement models. Double-, sesqui-, and single-operations as well as deletion and insertion of a chromosome region are considered in the model; the single ones comprise cut and join. In the reconstruction problem, a phylogenetic tree with chromosome structures in the leaves is given. It is necessary to assign the structures to inner nodes of the tree to minimize the sum of distances between terminal structures of each edge and to identify the mutual paralogs in a fairly large set of structures. A linear algorithm is known for the distance problem without paralogs, while the presence of paralogs makes it NP-hard. If paralogs are allowed but the insertion and deletion operations are missing (and special constraints are imposed), the reduction of the distance problem to integer linear programming is known. Apparently, the reconstruction problem is NP-hard even in the absence of paralogs. The problem of contigs is to find the optimal arrangements for each given set of contigs, which also includes the mutual identification of paralogs. We proved that these problems can be reduced to integer linear programming formulations, which allows an algorithm to redefine the problems to implement a very special case of the integer linear programming tool. The results were tested on synthetic and biological samples. Three well-known problems were reduced to a very special case of integer linear programming, which is a new method of their solutions. Integer linear programming is clearly among the main computational methods and, as generally accepted, is fast on average; in particular, computation systems specifically targeted at it are available. The challenges are to reduce the size of the corresponding integer linear programming formulations and to incorporate a more detailed biological concept in our model of the reconstruction.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

On some problems in a theory of thermally and mechanically interacting continuous media. Ph.D. Thesis; [linearized theory of interacting mixture of elastic solid and viscous fluid

NASA Technical Reports Server (NTRS)

Lee, Y. M.

1971-01-01

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

Control problem for a system of linear loaded differential equations

NASA Astrophysics Data System (ADS)

Barseghyan, V. R.; Barseghyan, T. V.

2018-04-01

The problem of control and optimal control for a system of linear loaded differential equations is considered. Necessary and sufficient conditions for complete controllability and conditions for the existence of a program control and the corresponding motion are formulated. The explicit form of control action for the control problem is constructed and a method for solving the problem of optimal control is proposed.

Guidance and Control System for a Satellite Constellation

NASA Technical Reports Server (NTRS)

Bryson, Jonathan Lamar; Cox, James; Mays, Paul Richard; Neidhoefer, James Christian; Ephrain, Richard

2010-01-01

A distributed guidance and control algorithm was developed for a constellation of satellites. The system repositions satellites as required, regulates satellites to desired orbits, and prevents collisions. 1. Optimal methods are used to compute nominal transfers from orbit to orbit. 2. Satellites are regulated to maintain the desired orbits once the transfers are complete. 3. A simulator is used to predict potential collisions or near-misses. 4. Each satellite computes perturbations to its controls so as to increase any unacceptable distances of nearest approach to other objects. a. The avoidance problem is recast in a distributed and locally-linear form to arrive at a tractable solution. b. Plant matrix values are approximated via simulation at each time step. c. The Linear Quadratic Gaussian (LQG) method is used to compute perturbations to the controls that will result in increased miss distances. 5. Once all danger is passed, the satellites return to their original orbits, all the while avoiding each other as above. 6. The delta-Vs are reasonable. The controller begins maneuvers as soon as practical to minimize delta-V. 7. Despite the inclusion of trajectory simulations within the control loop, the algorithm is sufficiently fast for available satellite computer hardware. 8. The required measurement accuracies are within the capabilities of modern inertial measurement devices and modern positioning devices.

EZLP: An Interactive Computer Program for Solving Linear Programming Problems. Final Report.

ERIC Educational Resources Information Center

Jarvis, John J.; And Others

Designed for student use in solving linear programming problems, the interactive computer program described (EZLP) permits the student to input the linear programming model in exactly the same manner in which it would be written on paper. This report includes a brief review of the development of EZLP; narrative descriptions of program features,…

Updating QR factorization procedure for solution of linear least squares problem with equality constraints.

PubMed

Zeb, Salman; Yousaf, Muhammad

2017-01-01

In this article, we present a QR updating procedure as a solution approach for linear least squares problem with equality constraints. We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem. The QR factorization of the subproblem is calculated and then we apply updating techniques to its upper triangular factor R to obtain its solution. We carry out the error analysis of the proposed algorithm to show that it is backward stable. We also illustrate the implementation and accuracy of the proposed algorithm by providing some numerical experiments with particular emphasis on dense problems.

Single-machine common/slack due window assignment problems with linear decreasing processing times

NASA Astrophysics Data System (ADS)

Zhang, Xingong; Lin, Win-Chin; Wu, Wen-Hsiang; Wu, Chin-Chia

2017-08-01

This paper studies linear non-increasing processing times and the common/slack due window assignment problems on a single machine, where the actual processing time of a job is a linear non-increasing function of its starting time. The aim is to minimize the sum of the earliness cost, tardiness cost, due window location and due window size. Some optimality results are discussed for the common/slack due window assignment problems and two O(n log n) time algorithms are presented to solve the two problems. Finally, two examples are provided to illustrate the correctness of the corresponding algorithms.

Krylov subspace methods - Theory, algorithms, and applications

NASA Technical Reports Server (NTRS)

Sad, Youcef

1990-01-01

Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

Fuzzy bi-objective linear programming for portfolio selection problem with magnitude ranking function

NASA Astrophysics Data System (ADS)

Kusumawati, Rosita; Subekti, Retno

2017-04-01

Fuzzy bi-objective linear programming (FBOLP) model is bi-objective linear programming model in fuzzy number set where the coefficients of the equations are fuzzy number. This model is proposed to solve portfolio selection problem which generate an asset portfolio with the lowest risk and the highest expected return. FBOLP model with normal fuzzy numbers for risk and expected return of stocks is transformed into linear programming (LP) model using magnitude ranking function.

An Introduction to Multilinear Formula Score Theory. Measurement Series 84-4.

ERIC Educational Resources Information Center

Levine, Michael V.

Formula score theory (FST) associates each multiple choice test with a linear operator and expresses all of the real functions of item response theory as linear combinations of the operator's eigenfunctions. Hard measurement problems can then often be reformulated as easier, standard mathematical problems. For example, the problem of estimating…

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

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.

A Linear Programming Approach to Routing Control in Networks of Constrained Nonlinear Positive Systems with Concave Flow Rates

NASA Technical Reports Server (NTRS)

Arneson, Heather M.; Dousse, Nicholas; Langbort, Cedric

2014-01-01

We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.

Global dynamic optimization approach to predict activation in metabolic pathways.

PubMed

de Hijas-Liste, Gundián M; Klipp, Edda; Balsa-Canto, Eva; Banga, Julio R

2014-01-06

During the last decade, a number of authors have shown that the genetic regulation of metabolic networks may follow optimality principles. Optimal control theory has been successfully used to compute optimal enzyme profiles considering simple metabolic pathways. However, applying this optimal control framework to more general networks (e.g. branched networks, or networks incorporating enzyme production dynamics) yields problems that are analytically intractable and/or numerically very challenging. Further, these previous studies have only considered a single-objective framework. In this work we consider a more general multi-objective formulation and we present solutions based on recent developments in global dynamic optimization techniques. We illustrate the performance and capabilities of these techniques considering two sets of problems. First, we consider a set of single-objective examples of increasing complexity taken from the recent literature. We analyze the multimodal character of the associated non linear optimization problems, and we also evaluate different global optimization approaches in terms of numerical robustness, efficiency and scalability. Second, we consider generalized multi-objective formulations for several examples, and we show how this framework results in more biologically meaningful results. The proposed strategy was used to solve a set of single-objective case studies related to unbranched and branched metabolic networks of different levels of complexity. All problems were successfully solved in reasonable computation times with our global dynamic optimization approach, reaching solutions which were comparable or better than those reported in previous literature. Further, we considered, for the first time, multi-objective formulations, illustrating how activation in metabolic pathways can be explained in terms of the best trade-offs between conflicting objectives. This new methodology can be applied to metabolic networks with arbitrary topologies, non-linear dynamics and constraints.

Quantum annealing versus classical machine learning applied to a simplified computational biology problem

PubMed Central

Li, Richard Y.; Di Felice, Rosa; Rohs, Remo; Lidar, Daniel A.

2018-01-01

Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. Here we studied the ability of a quantum machine learning approach to predict binding specificity. Using simplified datasets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding. The results were compared to state-of-the-art classical approaches for the same simplified datasets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems. PMID:29652405

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.

Another look at zonal flows: Resonance, shearing, and frictionless saturation

NASA Astrophysics Data System (ADS)

Li, J. C.; Diamond, P. H.

2018-04-01

We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, wave-flow resonance enters turbulence regulation, both linearly and nonlinearly. Resonance suppresses the linear instability by wave absorption. Flow shear can weaken the resonance, and thus destabilize drift waves, in contrast to the near-universal conventional shear suppression paradigm. Furthermore, consideration of wave-flow resonance resolves the long-standing problem of how zonal flows (ZFs) saturate in the limit of weak or zero frictional drag, and also determines the ZF scale. We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective at regulating the Dimits up-shift regime. Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator-prey model of drift-ZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as LZ F˜f3 /16(1-f ) 1 /8ρs5/8l03 /8 in the (relevant) adiabatic limit (i.e., τckk‖2D‖≫1 ). f is the fraction of turbulence energy coupled to ZF and l0 is the base state mixing length, absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional, and strongly frictional regimes. In the frictionless limit, the results differ significantly from conventionally quoted scalings derived for frictional regimes. To leading order, the flow is independent of turbulence intensity. The turbulence level scales as E ˜(γL/εc) 2 , which indicates the extent of the "near-marginal" regime to be γL<εc , for the case of avalanche-induced profile variability. Here, εc is the rate of dissipation of potential enstrophy and γL is the characteristic linear growth rate of fluctuations. The implications for dynamics near marginality of the strong scaling of saturated E with γL are discussed.

Investigating the linearity assumption between lumber grade mix and yield using design of experiments (DOE)

Treesearch

Xiaoqiu Zuo; Urs Buehlmann; R. Edward Thomas

2004-01-01

Solving the least-cost lumber grade mix problem allows dimension mills to minimize the cost of dimension part production. This problem, due to its economic importance, has attracted much attention from researchers and industry in the past. Most solutions used linear programming models and assumed that a simple linear relationship existed between lumber grade mix and...

Deformed Palmprint Matching Based on Stable Regions.

PubMed

Wu, Xiangqian; Zhao, Qiushi

2015-12-01

Palmprint recognition (PR) is an effective technology for personal recognition. A main problem, which deteriorates the performance of PR, is the deformations of palmprint images. This problem becomes more severe on contactless occasions, in which images are acquired without any guiding mechanisms, and hence critically limits the applications of PR. To solve the deformation problems, in this paper, a model for non-linearly deformed palmprint matching is derived by approximating non-linear deformed palmprint images with piecewise-linear deformed stable regions. Based on this model, a novel approach for deformed palmprint matching, named key point-based block growing (KPBG), is proposed. In KPBG, an iterative M-estimator sample consensus algorithm based on scale invariant feature transform features is devised to compute piecewise-linear transformations to approximate the non-linear deformations of palmprints, and then, the stable regions complying with the linear transformations are decided using a block growing algorithm. Palmprint feature extraction and matching are performed over these stable regions to compute matching scores for decision. Experiments on several public palmprint databases show that the proposed models and the KPBG approach can effectively solve the deformation problem in palmprint verification and outperform the state-of-the-art methods.

A Resume of Stochastic, Time-Varying, Linear System Theory with Application to Active-Sonar Signal-Processing Problems

DTIC Science & Technology

1981-06-15

relationships 5 3. Normalized energy in ambiguity function for i = 0 14 k ilI SACLANTCEN SR-50 A RESUME OF STOCHASTIC, TIME-VARYING, LINEAR SYSTEM THEORY WITH...the order in which systems are concatenated is unimportant. These results are exactly analogous to the results of time-invariant linear system theory in...REFERENCES 1. MEIER, L. A rdsum6 of deterministic time-varying linear system theory with application to active sonar signal processing problems, SACLANTCEN

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Digital program for solving the linear stochastic optimal control and estimation problem

NASA Technical Reports Server (NTRS)

Geyser, L. C.; Lehtinen, B.

1975-01-01

A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.

Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes

NASA Astrophysics Data System (ADS)

Amsallem, David; Tezaur, Radek; Farhat, Charbel

2016-12-01

A comprehensive approach for real-time computations using a database of parametric, linear, projection-based reduced-order models (ROMs) based on arbitrary underlying meshes is proposed. In the offline phase of this approach, the parameter space is sampled and linear ROMs defined by linear reduced operators are pre-computed at the sampled parameter points and stored. Then, these operators and associated ROMs are transformed into counterparts that satisfy a certain notion of consistency. In the online phase of this approach, a linear ROM is constructed in real-time at a queried but unsampled parameter point by interpolating the pre-computed linear reduced operators on matrix manifolds and therefore computing an interpolated linear ROM. The proposed overall model reduction framework is illustrated with two applications: a parametric inverse acoustic scattering problem associated with a mockup submarine, and a parametric flutter prediction problem associated with a wing-tank system. The second application is implemented on a mobile device, illustrating the capability of the proposed computational framework to operate in real-time.

Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data

NASA Astrophysics Data System (ADS)

Courdurier, M.; Monard, F.; Osses, A.; Romero, F.

2015-09-01

In medical single-photon emission computed tomography (SPECT) imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first-order scattering measurements and assuming a very specific scattering regime. The problem is modeled using the radiative transfer equation by means of an explicit non-linear operator that gives the ballistic and scattering measurements as a function of the radioactive source and attenuation distributions. First, by differentiating this non-linear operator we obtain a linearized inverse problem. Then, under regularity hypothesis for the source distribution and attenuation map and considering small attenuations, we rigorously prove that the linear operator is invertible and we compute its inverse explicitly. This allows proof of local uniqueness for the non-linear inverse problem. Finally, using the previous inversion result for the linear operator, we propose a new type of iterative algorithm for simultaneous source and attenuation recovery for SPECT based on the Neumann series and a Newton-Raphson algorithm.

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.

1998-01-01

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

Linear decentralized systems with special structure. [for twin lift helicopters

NASA Technical Reports Server (NTRS)

Martin, C. F.

1982-01-01

Certain fundamental structures associated with linear systems having internal symmetries are outlined. It is shown that the theory of finite-dimensional algebras and their representations are closely related to such systems. It is also demonstrated that certain problems in the decentralized control of symmetric systems are equivalent to long-standing problems of linear systems theory. Even though the structure imposed arose in considering the problems of twin-lift helicopters, any large system composed of several identical intercoupled control systems can be modeled by a linear system that satisfies the constraints imposed. Internal symmetry can be exploited to yield new system-theoretic invariants and a better understanding of the way in which the underlying structure affects overall system performance.

Finite Element Based Structural Damage Detection Using Artificial Boundary Conditions

DTIC Science & Technology

2007-09-01

C. (2005). Elementary Linear Algebra . New York: John Wiley and Sons. Avitable, Peter (2001, January) Experimental Modal Analysis, A Simple Non...variables under consideration. 3 Frequency sensitivities are the basis for a linear approximation to compute the change in the natural frequencies of a...THEORY The general problem statement for a non- linear constrained optimization problem is: To minimize ( )f x Objective Function Subject to

Stability of multiloop LQ regulators with nonlinearities. I - Regions of attraction. II - Regions of ultimate boundedness

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1986-01-01

An investigation is conducted for the closed loop stability of linear time-invariant systems controlled by linear quadratic (LQ) regulators, in cases where nonlinearities exist in the control channels lying outside the stability sector in regions away from the origin. The estimate of the region of attraction thus obtained furnishes methods for the selection of performance function weights for more robust LQ designs. Attention is then given to the closed loop stability of linear time-invariant systems controlled by the LQ regulators when the nonlinearities in the loops escape the stability sector in a bounded region containing the origin.

Automation of multi-agent control for complex dynamic systems in heterogeneous computational network

NASA Astrophysics Data System (ADS)

Oparin, Gennady; Feoktistov, Alexander; Bogdanova, Vera; Sidorov, Ivan

2017-01-01

The rapid progress of high-performance computing entails new challenges related to solving large scientific problems for various subject domains in a heterogeneous distributed computing environment (e.g., a network, Grid system, or Cloud infrastructure). The specialists in the field of parallel and distributed computing give the special attention to a scalability of applications for problem solving. An effective management of the scalable application in the heterogeneous distributed computing environment is still a non-trivial issue. Control systems that operate in networks, especially relate to this issue. We propose a new approach to the multi-agent management for the scalable applications in the heterogeneous computational network. The fundamentals of our approach are the integrated use of conceptual programming, simulation modeling, network monitoring, multi-agent management, and service-oriented programming. We developed a special framework for an automation of the problem solving. Advantages of the proposed approach are demonstrated on the parametric synthesis example of the static linear regulator for complex dynamic systems. Benefits of the scalable application for solving this problem include automation of the multi-agent control for the systems in a parallel mode with various degrees of its detailed elaboration.

Dynamic hysteresis in a one-dimensional Ising model: application to allosteric proteins.

PubMed

Graham, I; Duke, T A J

2005-06-01

We solve exactly the problem of dynamic hysteresis for a finite one-dimensional Ising model at low temperature. We find that the area of the hysteresis loop, as the field is varied periodically, scales as the square root of the field frequency for a large range of frequencies. Below a critical frequency there is a correction to the scaling law, resulting in a linear relationship between hysteresis area and frequency. The one-dimensional Ising model provides a simplified description of switchlike behavior in allosteric proteins, such as hemoglobin. Thus our analysis predicts the switching dynamics of allosteric proteins when they are exposed to a ligand concentration which changes with time. Many allosteric proteins bind a regulator that is maintained at a nonequilibrium concentration by active signal transduction processes. In the light of our analysis, we discuss to what extent allosteric proteins can respond to changes in regulator concentration caused by an upstream signaling event, while remaining insensitive to the intrinsic nonequilibrium fluctuations in regulator level which occur in the absence of a signal.

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Frequency assignments for HFDF receivers in a search and rescue network

NASA Astrophysics Data System (ADS)

Johnson, Krista E.

1990-03-01

This thesis applies a multiobjective linear programming approach to the problem of assigning frequencies to high frequency direction finding (HFDF) receivers in a search-and-rescue network in order to maximize the expected number of geolocations of vessels in distress. The problem is formulated as a multiobjective integer linear programming problem. The integrality of the solutions is guaranteed by the totally unimodularity of the A-matrix. Two approaches are taken to solve the multiobjective linear programming problem: (1) the multiobjective simplex method as implemented in ADBASE; and (2) an iterative approach. In this approach, the individual objective functions are weighted and combined in a single additive objective function. The resulting single objective problem is expressed as a network programming problem and solved using SAS NETFLOW. The process is then repeated with different weightings for the objective functions. The solutions obtained from the multiobjective linear programs are evaluated using a FORTRAN program to determine which solution provides the greatest expected number of geolocations. This solution is then compared to the sample mean and standard deviation for the expected number of geolocations resulting from 10,000 random frequency assignments for the network.

Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method

NASA Astrophysics Data System (ADS)

Bekhoucha, F.; Rechak, S.; Cadou, J. M.

2016-12-01

In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.

Genetic Network Inference: From Co-Expression Clustering to Reverse Engineering

NASA Technical Reports Server (NTRS)

Dhaeseleer, Patrik; Liang, Shoudan; Somogyi, Roland

2000-01-01

Advances in molecular biological, analytical, and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using high-throughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-duster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e., who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting, and bioengineering.

Sensitivity method for integrated structure/active control law design

NASA Technical Reports Server (NTRS)

Gilbert, Michael G.

1987-01-01

The development is described of an integrated structure/active control law design methodology for aeroelastic aircraft applications. A short motivating introduction to aeroservoelasticity is given along with the need for integrated structures/controls design algorithms. Three alternative approaches to development of an integrated design method are briefly discussed with regards to complexity, coordination and tradeoff strategies, and the nature of the resulting solutions. This leads to the formulation of the proposed approach which is based on the concepts of sensitivity of optimum solutions and multi-level decompositions. The concept of sensitivity of optimum is explained in more detail and compared with traditional sensitivity concepts of classical control theory. The analytical sensitivity expressions for the solution of the linear, quadratic cost, Gaussian (LQG) control problem are summarized in terms of the linear regulator solution and the Kalman Filter solution. Numerical results for a state space aeroelastic model of the DAST ARW-II vehicle are given, showing the changes in aircraft responses to variations of a structural parameter, in this case first wing bending natural frequency.

A New Pattern of Getting Nasty Number in Graphical Method

NASA Astrophysics Data System (ADS)

Sumathi, P.; Indhumathi, N.

2018-04-01

This paper proposed a new technique of getting nasty numbers using graphical method in linear programming problem and it has been proved for various Linear programming problems. And also some characterisation of nasty numbers is discussed in this paper.

Program for the solution of multipoint boundary value problems of quasilinear differential equations

NASA Technical Reports Server (NTRS)

1973-01-01

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

The Vertical Linear Fractional Initialization Problem

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

A study of the use of linear programming techniques to improve the performance in design optimization problems

NASA Technical Reports Server (NTRS)

Young, Katherine C.; Sobieszczanski-Sobieski, Jaroslaw

1988-01-01

This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

Investigating the interaction between the homeostatic and circadian processes of sleep-wake regulation for the prediction of waking neurobehavioural performance

NASA Technical Reports Server (NTRS)

Van Dongen, Hans P A.; Dinges, David F.

2003-01-01

The two-process model of sleep regulation has been applied successfully to describe, predict, and understand sleep-wake regulation in a variety of experimental protocols such as sleep deprivation and forced desynchrony. A non-linear interaction between the homeostatic and circadian processes was reported when the model was applied to describe alertness and performance data obtained during forced desynchrony. This non-linear interaction could also be due to intrinsic non-linearity in the metrics used to measure alertness and performance, however. Distinguishing these possibilities would be of theoretical interest, but could also have important implications for the design and interpretation of experiments placing sleep at different circadian phases or varying the duration of sleep and/or wakefulness. Although to date no resolution to this controversy has been found, here we show that the issue can be addressed with existing data sets. The interaction between the homeostatic and circadian processes of sleep-wake regulation was investigated using neurobehavioural performance data from a laboratory experiment involving total sleep deprivation. The results provided evidence of an actual non-linear interaction between the homeostatic and circadian processes of sleep-wake regulation for the prediction of waking neurobehavioural performance.

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

NASA Technical Reports Server (NTRS)

Jacquotte, Olivier P.; Oden, J. Tinsley

1994-01-01

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Electroosmosis modulated biomechanical transport through asymmetric microfluidics channel

NASA Astrophysics Data System (ADS)

Jhorar, R.; Tripathi, D.; Bhatti, M. M.; Ellahi, R.

2018-05-01

This article addresses the electrokinetically modulated biomechanical transport through a two-dimensional asymmetric microchannel induced by peristaltic waves. Electrokinetic transport with peristaltic phenomena grabbed a significant attention due to its novel applications in engineering. Electrical fields also provide an excellent mode for regulating flows. The electrohydrodynamics problem is modified by means of Debye-Hückel linearization. Firstly, the governing flow problem is described by continuity and momentum equations in the presence of electrokinetic forces in Cartesian coordinates, then long wavelength and low/zero Reynolds ("neglecting the inertial forces") approximations are applied to modify the governing flow problem. The resulting differential equations are solved analytically in order to obtain exact solutions for velocity profile whereas the numerical integration is carried out to analyze the pumping characteristics. The physical behaviour of sundry parameters is discussed for velocity profile, pressure rise and volume flow rate. In particular, the behaviour of electro-osmotic parameter, phase difference, and Helmholtz-Smoluchowski velocity is examined and discussed. The trapping mechanism is also visualized by drawing streamlines against the governing parameters. The present study offers various interesting results that warrant further study on electrokinetic transport with peristalsis.

Convergence of the standard RLS method and UDUT factorisation of covariance matrix for solving the algebraic Riccati equation of the DLQR via heuristic approximate dynamic programming

NASA Astrophysics Data System (ADS)

Moraes Rêgo, Patrícia Helena; Viana da Fonseca Neto, João; Ferreira, Ernesto M.

2015-08-01

The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor-critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.

Commande optimale minimisant la consommation d'energie d'un drone utilise comme relai de communication

NASA Astrophysics Data System (ADS)

Mechirgui, Monia

The purpose of this project is to implement an optimal control regulator, particularly the linear quadratic regulator in order to control the position of an unmanned aerial vehicle known as a quadrotor. This type of UAV has a symmetrical and simple structure. Thus, its control is relatively easy compared to conventional helicopters. Optimal control can be proven to be an ideal controller to reconcile between the tracking performance and energy consumption. In practice, the linearity requirements are not met, but some elaborations of the linear quadratic regulator have been used in many nonlinear applications with good results. The linear quadratic controller used in this thesis is presented in two forms: simple and adapted to the state of charge of the battery. Based on the traditional structure of the linear quadratic regulator, we introduced a new criterion which relies on the state of charge of the battery, in order to optimize energy consumption. This command is intended to be used to monitor and maintain the desired trajectory during several maneuvers while minimizing energy consumption. Both simple and adapted, linear quadratic controller are implemented in Simulink in discrete time. The model simulates the dynamics and control of a quadrotor. Performance and stability of the system are analyzed with several tests, from the simply hover to the complex trajectories in closed loop.

Linear SFM: A hierarchical approach to solving structure-from-motion problems by decoupling the linear and nonlinear components

NASA Astrophysics Data System (ADS)

Zhao, Liang; Huang, Shoudong; Dissanayake, Gamini

2018-07-01

This paper presents a novel hierarchical approach to solving structure-from-motion (SFM) problems. The algorithm begins with small local reconstructions based on nonlinear bundle adjustment (BA). These are then joined in a hierarchical manner using a strategy that requires solving a linear least squares optimization problem followed by a nonlinear transform. The algorithm can handle ordered monocular and stereo image sequences. Two stereo images or three monocular images are adequate for building each initial reconstruction. The bulk of the computation involves solving a linear least squares problem and, therefore, the proposed algorithm avoids three major issues associated with most of the nonlinear optimization algorithms currently used for SFM: the need for a reasonably accurate initial estimate, the need for iterations, and the possibility of being trapped in a local minimum. Also, by summarizing all the original observations into the small local reconstructions with associated information matrices, the proposed Linear SFM manages to preserve all the information contained in the observations. The paper also demonstrates that the proposed problem formulation results in a sparse structure that leads to an efficient numerical implementation. The experimental results using publicly available datasets show that the proposed algorithm yields solutions that are very close to those obtained using a global BA starting with an accurate initial estimate. The C/C++ source code of the proposed algorithm is publicly available at https://github.com/LiangZhaoPKUImperial/LinearSFM.

Nonexpansiveness of a linearized augmented Lagrangian operator for hierarchical convex optimization

NASA Astrophysics Data System (ADS)

Yamagishi, Masao; Yamada, Isao

2017-04-01

Hierarchical convex optimization concerns two-stage optimization problems: the first stage problem is a convex optimization; the second stage problem is the minimization of a convex function over the solution set of the first stage problem. For the hierarchical convex optimization, the hybrid steepest descent method (HSDM) can be applied, where the solution set of the first stage problem must be expressed as the fixed point set of a certain nonexpansive operator. In this paper, we propose a nonexpansive operator that yields a computationally efficient update when it is plugged into the HSDM. The proposed operator is inspired by the update of the linearized augmented Lagrangian method. It is applicable to characterize the solution set of recent sophisticated convex optimization problems found in the context of inverse problems, where the sum of multiple proximable convex functions involving linear operators must be minimized to incorporate preferable properties into the minimizers. For such a problem formulation, there has not yet been reported any nonexpansive operator that yields an update free from the inversions of linear operators in cases where it is utilized in the HSDM. Unlike previously known nonexpansive operators, the proposed operator yields an inversion-free update in such cases. As an application of the proposed operator plugged into the HSDM, we also present, in the context of the so-called superiorization, an algorithmic solution to a convex optimization problem over the generalized convex feasible set where the intersection of the hard constraints is not necessarily simple.

A Study of Strong Stability of Distributed Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Cataltepe, Tayfun

1989-01-01

The strong stability of distributed systems is studied and the problem of characterizing strongly stable semigroups of operators associated with distributed systems is addressed. Main emphasis is on contractive systems. Three different approaches to characterization of strongly stable contractive semigroups are developed. The first one is an operator theoretical approach. Using the theory of dilations, it is shown that every strongly stable contractive semigroup is related to the left shift semigroup on an L(exp 2) space. Then, a decomposition for the state space which identifies strongly stable and unstable states is introduced. Based on this decomposition, conditions for a contractive semigroup to be strongly stable are obtained. Finally, extensions of Lyapunov's equation for distributed parameter systems are investigated. Sufficient conditions for weak and strong stabilities of uniformly bounded semigroups are obtained by relaxing the equivalent norm condition on the right hand side of the Lyanupov equation. These characterizations are then applied to the problem of feedback stabilization. First, it is shown via the state space decomposition that under certain conditions a contractive system (A,B) can be strongly stabilized by the feedback -B(*). Then, application of the extensions of the Lyapunov equation results in sufficient conditions for weak, strong, and exponential stabilizations of contractive systems by the feedback -B(*). Finally, it is shown that for a contractive system, the first derivative of x with respect to time = Ax + Bu (where B is any linear bounded operator), there is a related linear quadratic regulator problem and a corresponding steady state Riccati equation which always has a bounded nonnegative solution.

Numerical methods on some structured matrix algebra problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1996-06-01

This proposal concerned the design, analysis, and implementation of serial and parallel algorithms for certain structured matrix algebra problems. It emphasized large order problems and so focused on methods that can be implemented efficiently on distributed-memory MIMD multiprocessors. Such machines supply the computing power and extensive memory demanded by the large order problems. We proposed to examine three classes of matrix algebra problems: the symmetric and nonsymmetric eigenvalue problems (especially the tridiagonal cases) and the solution of linear systems with specially structured coefficient matrices. As all of these are of practical interest, a major goal of this work was tomore » translate our research in linear algebra into useful tools for use by the computational scientists interested in these and related applications. Thus, in addition to software specific to the linear algebra problems, we proposed to produce a programming paradigm and library to aid in the design and implementation of programs for distributed-memory MIMD computers. We now report on our progress on each of the problems and on the programming tools.« less

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Beyond behavior modification: Benefits of social-emotional/self-regulation training for preschoolers with behavior problems.

PubMed

Graziano, Paulo A; Hart, Katie

2016-10-01

The current study evaluated the initial efficacy of three intervention programs aimed at improving school readiness in preschool children with externalizing behavior problems (EBP). Participants for this study included 45 preschool children (76% boys; Mage=5.16years; 84% Hispanic/Latino background) with at-risk or clinically elevated levels of EBP. During the summer between preschool and kindergarten, children were randomized to receive three newly developed intervention packages. The first and most cost effective intervention package was an 8-week School Readiness Parenting Program (SRPP). Families randomized into the second and third intervention packages received not only the weekly SRPP, but children also attended two different versions of an intensive kindergarten summer readiness class (M-F, 8a.m.-5p.m.) that was part of an 8-week summer treatment program for pre-kindergarteners (STP-PreK). One version included the standard behavioral modification system and academic curriculum (STP-PreK) while the other additionally contained social-emotional and self-regulation training (STP-PreK Enhanced). Baseline, post-intervention, and 6-month follow-up data were collected on children's school readiness outcomes including parent, teacher, and objective assessment measures. Analyses using linear mixed models indicated that children's behavioral functioning significantly improved across all groups in a similar magnitude. Children in the STP-PreK Enhanced group, however, experienced greater growth across time in academic achievement, emotion knowledge, emotion regulation, and executive functioning compared to children in the other groups. These findings suggest that while parent training is sufficient to address children's behavioral difficulties, an intensive summer program that goes beyond behavioral modification and academic preparation by targeting socio-emotional and self-regulation skills can have incremental benefits across multiple aspects of school readiness. Published by Elsevier Ltd.

Sparse Substring Pattern Set Discovery Using Linear Programming Boosting

NASA Astrophysics Data System (ADS)

Kashihara, Kazuaki; Hatano, Kohei; Bannai, Hideo; Takeda, Masayuki

In this paper, we consider finding a small set of substring patterns which classifies the given documents well. We formulate the problem as 1 norm soft margin optimization problem where each dimension corresponds to a substring pattern. Then we solve this problem by using LPBoost and an optimal substring discovery algorithm. Since the problem is a linear program, the resulting solution is likely to be sparse, which is useful for feature selection. We evaluate the proposed method for real data such as movie reviews.

Domain decomposition in time for PDE-constrained optimization

DOE PAGES

Barker, Andrew T.; Stoll, Martin

2015-08-28

Here, PDE-constrained optimization problems have a wide range of applications, but they lead to very large and ill-conditioned linear systems, especially if the problems are time dependent. In this paper we outline an approach for dealing with such problems by decomposing them in time and applying an additive Schwarz preconditioner in time, so that we can take advantage of parallel computers to deal with the very large linear systems. We then illustrate the performance of our method on a variety of problems.

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

2018-01-01

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.

Externalizing problems, attention regulation, and household chaos: a longitudinal behavioral genetic study.

PubMed

Wang, Zhe; Deater-Deckard, Kirby; Petrill, Stephen A; Thompson, Lee A

2012-08-01

Previous research documented a robust link between difficulties in self-regulation and development of externalizing problems (i.e., aggression and delinquency). In this study, we examined the longitudinal additive and interactive genetic and environmental covariation underlying this well-established link using a twin design. The sample included 131 pairs of monozygotic twins and 173 pairs of same-sex dizygotic twins who participated in three waves of annual assessment. Mothers and fathers provided reports of externalizing problems. Teacher report and observer rating were used to assess twin's attention regulation. The etiology underlying the link between externalizing problems and attention regulation shifted from a common genetic mechanism to a common environmental mechanism in the transition across middle childhood. Household chaos moderated the genetic variance of and covariance between externalizing problems and attention regulation. The genetic influence on individual differences in both externalizing problems and attention regulation was stronger in more chaotic households. However, higher levels of household chaos attenuated the genetic link between externalizing problems and attention regulation.

Externalizing problems, attention regulation, and household chaos: A longitudinal behavioral genetic study

PubMed Central

Wang, Zhe; Deater-Deckard, Kirby; Petrill, Stephen A.; Thompson, Lee A.

2015-01-01

Previous research has documented a robust link between difficulties in self-regulation and development of externalizing problems (i.e., aggression and delinquency). In the current study, we examined the longitudinal additive and interactive genetic and environmental covariation underlying this well-established link using a twin design. The sample included 131 pairs of monozygotic twins and 173 pairs of same-sex dizygotic twins who participated in three waves of annual assessment. Mothers and fathers provided reports of externalizing problems. Teacher report and observer rating were used to assess twin’s attention regulation. The etiology underlying the link between externalizing problems and attention regulation shifted from a common genetic mechanism to a common environmental mechanism in the transition across middle childhood. Household chaos moderated the genetic variance of and covariance between externalizing problems and attention regulation. The genetic influence on individual differences in both externalizing problems and attention regulation was stronger in more chaotic household. However, higher levels of household chaos attenuated the genetic link between externalizing problems and attention regulation. PMID:22781853

High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1999-01-01

Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

Does Preschool Self-Regulation Predict Later Behavior Problems in General or Specific Problem Behaviors?

PubMed

Lonigan, Christopher J; Spiegel, Jamie A; Goodrich, J Marc; Morris, Brittany M; Osborne, Colleen M; Lerner, Matthew D; Phillips, Beth M

2017-11-01

Findings from prior research have consistently indicated significant associations between self-regulation and externalizing behaviors. Significant associations have also been reported between children's language skills and both externalizing behaviors and self-regulation. Few studies to date, however, have examined these relations longitudinally, simultaneously, or with respect to unique clusters of externalizing problems. The current study examined the influence of preschool self-regulation on general and specific externalizing behavior problems in early elementary school and whether these relations were independent of associations between language, self-regulation, and externalizing behaviors in a sample of 815 children (44% female). Additionally, given a general pattern of sex differences in the presentations of externalizing behavior problems, self-regulation, and language skills, sex differences for these associations were examined. Results indicated unique relations of preschool self-regulation and language with both general externalizing behavior problems and specific problems of inattention. In general, self-regulation was a stronger longitudinal correlate of externalizing behavior for boys than it was for girls, and language was a stronger longitudinal predictor of hyperactive/impulsive behavior for girls than it was for boys.

A high-accuracy optical linear algebra processor for finite element applications

NASA Technical Reports Server (NTRS)

Casasent, D.; Taylor, B. K.

1984-01-01

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

Anxiety, Depression and Emotion Regulation Among Regular Online Poker Players.

PubMed

Barrault, Servane; Bonnaire, Céline; Herrmann, Florian

2017-12-01

Poker is a type of gambling that has specific features, including the need to regulate one's emotion to be successful. The aim of the present study is to assess emotion regulation, anxiety and depression in a sample of regular poker players, and to compare the results of problem and non-problem gamblers. 416 regular online poker players completed online questionnaires including sociodemographic data, measures of problem gambling (CPGI), anxiety and depression (HAD scale), and emotion regulation (ERQ). The CPGI was used to divide participants into four groups according to the intensity of their gambling practice (non-problem, low risk, moderate risk and problem gamblers). Anxiety and depression were significantly higher among severe-problem gamblers than among the other groups. Both significantly predicted problem gambling. On the other hand, there was no difference between groups in emotion regulation (cognitive reappraisal and expressive suppression), which was linked neither to problem gambling nor to anxiety and depression (except for cognitive reappraisal, which was significantly correlated to anxiety). Our results underline the links between anxiety, depression and problem gambling among poker players. If emotion regulation is involved in problem gambling among poker players, as strongly suggested by data from the literature, the emotion regulation strategies we assessed (cognitive reappraisal and expressive suppression) may not be those involved. Further studies are thus needed to investigate the involvement of other emotion regulation strategies.

A comparison of Heuristic method and Llewellyn’s rules for identification of redundant constraints

NASA Astrophysics Data System (ADS)

Estiningsih, Y.; Farikhin; Tjahjana, R. H.

2018-03-01

Important techniques in linear programming is modelling and solving practical optimization. Redundant constraints are consider for their effects on general linear programming problems. Identification and reduce redundant constraints are for avoidance of all the calculations associated when solving an associated linear programming problems. Many researchers have been proposed for identification redundant constraints. This paper a compararison of Heuristic method and Llewellyn’s rules for identification of redundant constraints.

Discrete Methods and their Applications

DTIC Science & Technology

1993-02-03

problem of finding all near-optimal solutions to a linear program. In paper [18], we give a brief and elementary proof of a result of Hoffman [1952) about...relies only on linear programming duality; second, we obtain geometric and algebraic representations of the bounds that are determined explicitly in...same. We have studied the problem of finding the minimum n such that a given unit interval graph is an n--graph. A linear time algorithm to compute

An improved error bound for linear complementarity problems for B-matrices.

PubMed

Gao, Lei; Li, Chaoqian

2017-01-01

A new error bound for the linear complementarity problem when the matrix involved is a B -matrix is presented, which improves the corresponding result in (Li et al. in Electron. J. Linear Algebra 31(1):476-484, 2016). In addition some sufficient conditions such that the new bound is sharper than that in (García-Esnaola and Peña in Appl. Math. Lett. 22(7):1071-1075, 2009) are provided.

Simple Test Functions in Meshless Local Petrov-Galerkin Methods

NASA Technical Reports Server (NTRS)

Raju, Ivatury S.

2016-01-01

Two meshless local Petrov-Galerkin (MLPG) methods based on two different trial functions but that use a simple linear test function were developed for beam and column problems. These methods used generalized moving least squares (GMLS) and radial basis (RB) interpolation functions as trial functions. These two methods were tested on various patch test problems. Both methods passed the patch tests successfully. Then the methods were applied to various beam vibration problems and problems involving Euler and Beck's columns. Both methods yielded accurate solutions for all problems studied. The simple linear test function offers considerable savings in computing efforts as the domain integrals involved in the weak form are avoided. The two methods based on this simple linear test function method produced accurate results for frequencies and buckling loads. Of the two methods studied, the method with radial basis trial functions is very attractive as the method is simple, accurate, and robust.

The linear Boltzmann equation in slab geometry - Development and verification of a reliable and efficient solution

NASA Technical Reports Server (NTRS)

Stamnes, K.; Lie-Svendsen, O.; Rees, M. H.

1991-01-01

The linear Boltzmann equation can be cast in a form mathematically identical to the radiation-transport equation. A multigroup procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative-transfer problem, and existing software is used to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well-suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of the formalism to include external forces and spherical geometry are also feasible.

A new neural network model for solving random interval linear programming problems.

PubMed

Arjmandzadeh, Ziba; Safi, Mohammadreza; Nazemi, Alireza

2017-05-01

This paper presents a neural network model for solving random interval linear programming problems. The original problem involving random interval variable coefficients is first transformed into an equivalent convex second order cone programming problem. A neural network model is then constructed for solving the obtained convex second order cone problem. Employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact satisfactory solution of the original problem. Several illustrative examples are solved in support of this technique. Copyright © 2017 Elsevier Ltd. All rights reserved.

Train repathing in emergencies based on fuzzy linear programming.

PubMed

Meng, Xuelei; Cui, Bingmou

2014-01-01

Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

NASA Astrophysics Data System (ADS)

Greenough, J. A.; Rider, W. J.

2004-05-01

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube problem, (3) the "peak" shock tube problem, (4) a version of the Shu and Osher shock entropy wave interaction and (5) the Woodward and Colella interacting shock wave problem. For each problem and method, run times, density error norms and convergence rates are reported for each method as produced from a common code test-bed. The linear problem exhibits the advertised convergence rate for both methods as well as the expected large disparity in overall error levels; WENO5 has the smaller errors and an enormous advantage in overall efficiency (in accuracy per unit CPU time). For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid. The overall comparison of error levels shows some variation from problem to problem. For Sod's shock tube, PLMDE has nearly half the error, while on the peak problem the errors are nearly the same. For the interacting blast wave problem the two methods again produce a similar level of error with a slight edge for the PLMDE. On the other hand, for the Shu-Osher problem, the errors are similar on the coarser grids, but favors WENO by a factor of nearly 1.5 on the finer grids used. In all cases holding mesh resolution constant though, PLMDE is less costly in terms of CPU time by approximately a factor of 6. If the CPU cost is taken as fixed, that is run times are equal for both numerical methods, then PLMDE uniformly produces lower errors than WENO for the fixed computation cost on the test problems considered here.

Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method

NASA Astrophysics Data System (ADS)

Vasant, Pandian

2011-06-01

Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

Particle swarm optimization - Genetic algorithm (PSOGA) on linear transportation problem

NASA Astrophysics Data System (ADS)

Rahmalia, Dinita

2017-08-01

Linear Transportation Problem (LTP) is the case of constrained optimization where we want to minimize cost subject to the balance of the number of supply and the number of demand. The exact method such as northwest corner, vogel, russel, minimal cost have been applied at approaching optimal solution. In this paper, we use heurisitic like Particle Swarm Optimization (PSO) for solving linear transportation problem at any size of decision variable. In addition, we combine mutation operator of Genetic Algorithm (GA) at PSO to improve optimal solution. This method is called Particle Swarm Optimization - Genetic Algorithm (PSOGA). The simulations show that PSOGA can improve optimal solution resulted by PSO.

Anomaly General Circulation Models.

NASA Astrophysics Data System (ADS)

Navarra, Antonio

The feasibility of the anomaly model is assessed using barotropic and baroclinic models. In the barotropic case, both a stationary and a time-dependent model has been formulated and constructed, whereas only the stationary, linear case is considered in the baroclinic case. Results from the barotropic model indicate that a relation between the stationary solution and the time-averaged non-linear solution exists. The stationary linear baroclinic solution can therefore be considered with some confidence. The linear baroclinic anomaly model poses a formidable mathematical problem because it is necessary to solve a gigantic linear system to obtain the solution. A new method to find solution of large linear system, based on a projection on the Krylov subspace is shown to be successful when applied to the linearized baroclinic anomaly model. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be inverted to obtain the solution. With an appropriate setting of the damping parameters, the iterative Krylov method reaches a solution even using a Krylov subspace ten times smaller than the original space of the problem. This generality allows the treatment of the important problem of linear waves in the atmosphere. A larger class (nonzonally symmetric) of basic states can now be treated for the baroclinic primitive equations. These problem leads to large unsymmetrical linear systems of order 10000 and more which can now be successfully tackled by the Krylov method. The (R7) linear anomaly model is used to investigate extensively the linear response to equatorial and mid-latitude prescribed heating. The results indicate that the solution is deeply affected by the presence of the stationary waves in the basic state. The instability of the asymmetric flows, first pointed out by Simmons et al. (1983), is active also in the baroclinic case. However, the presence of baroclinic processes modifies the dominant response. The most sensitive areas are identified; they correspond to north Japan, the Pole and Greenland regions. A limited set of higher resolution (R15) experiments indicate that this situation is still present and enhanced at higher resolution. The linear anomaly model is also applied to a realistic case. (Abstract shortened with permission of author.).

Nonlinearity measure and internal model control based linearization in anti-windup design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perev, Kamen

2013-12-18

This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequencymore » ranges.« less

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

NASA Astrophysics Data System (ADS)

Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

2018-02-01

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

Generalised Assignment Matrix Methodology in Linear Programming

ERIC Educational Resources Information Center

Jerome, Lawrence

2012-01-01

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

Numerical methods in Markov chain modeling

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef; Stewart, William J.

1989-01-01

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

Image reconstruction

NASA Astrophysics Data System (ADS)

Vasilenko, Georgii Ivanovich; Taratorin, Aleksandr Markovich

Linear, nonlinear, and iterative image-reconstruction (IR) algorithms are reviewed. Theoretical results are presented concerning controllable linear filters, the solution of ill-posed functional minimization problems, and the regularization of iterative IR algorithms. Attention is also given to the problem of superresolution and analytical spectrum continuation, the solution of the phase problem, and the reconstruction of images distorted by turbulence. IR in optical and optical-digital systems is discussed with emphasis on holographic techniques.

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.

Enhanced algorithms for stochastic programming

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishna, Alamuru S.

1993-09-01

In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean ofmore » a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.« less

The principle of superposition and its application in ground-water hydraulics

USGS Publications Warehouse

Reilly, T.E.; Franke, O.L.; Bennett, G.D.

1984-01-01

The principle of superposition, a powerful methematical technique for analyzing certain types of complex problems in many areas of science and technology, has important application in ground-water hydraulics and modeling of ground-water systems. The principle of superposition states that solutions to individual problems can be added together to obtain solutions to complex problems. This principle applies to linear systems governed by linear differential equations. This report introduces the principle of superposition as it applies to groundwater hydrology and provides background information, discussion, illustrative problems with solutions, and problems to be solved by the reader. (USGS)

Autonomous spacecraft attitude control using magnetic torquing only

NASA Technical Reports Server (NTRS)

Musser, Keith L.; Ebert, Ward L.

1989-01-01

Magnetic torquing of spacecraft has been an important mechanism for attitude control since the earliest satellites were launched. Typically a magnetic control system has been used for precession/nutation damping for gravity-gradient stabilized satellites, momentum dumping for systems equipped with reaction wheels, or momentum-axis pointing for spinning and momentum-biased spacecraft. Although within the small satellite community there has always been interest in expensive, light-weight, and low-power attitude control systems, completely magnetic control systems have not been used for autonomous three-axis stabilized spacecraft due to the large computational requirements involved. As increasingly more powerful microprocessors have become available, this has become less of an impediment. These facts have motivated consideration of the all-magnetic attitude control system presented here. The problem of controlling spacecraft attitude using only magnetic torquing is cast into the form of the Linear Quadratic Regulator (LQR), resulting in a linear feedback control law. Since the geomagnetic field along a satellite trajectory is not constant, the system equations are time varying. As a result, the optimal feedback gains are time-varying. Orbit geometry is exploited to treat feedback gains as a function of position rather than time, making feasible the onboard solution of the optimal control problem. In simulations performed to date, the control laws have shown themselves to be fairly robust and a good candidate for an onboard attitude control system.

Weak stability of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Catania, Davide; D'Abbicco, Marcello; Secchi, Paolo

2016-09-01

We consider the free boundary problem for the two-dimensional plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. We study the linear stability of rectilinear plasma-vacuum interfaces by computing the Kreiss-Lopatinskiĭ determinant of an associated linearized boundary value problem. Apart from possible resonances, we obtain that the piecewise constant plasma-vacuum interfaces are always weakly linearly stable, independently of the size of tangential velocity, magnetic and electric fields on both sides of the characteristic discontinuity. We also prove that solutions to the linearized problem obey an energy estimate with a loss of regularity with respect to the source terms, both in the interior domain and on the boundary, due to the failure of the uniform Kreiss-Lopatinskiĭ condition, as the Kreiss-Lopatinskiĭ determinant associated with this linearized boundary value problem has roots on the boundary of the frequency space. In the proof of the a priori estimates, a crucial part is played by the construction of symmetrizers for a reduced differential system, which has poles at which the Kreiss-Lopatinskiĭ condition may fail simultaneously.

Nonlinearization and waves in bounded media: old wine in a new bottle

NASA Astrophysics Data System (ADS)

Mortell, Michael P.; Seymour, Brian R.

2017-02-01

We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.

Probabilistic dual heuristic programming-based adaptive critic

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.

The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

PubMed

Pang, Haotian; Liu, Han; Vanderbei, Robert

2014-02-01

We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization

PubMed Central

Li, Zukui; Ding, Ran; Floudas, Christodoulos A.

2011-01-01

Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented. PMID:21935263

An Extended Microcomputer-Based Network Optimization Package.

DTIC Science & Technology

1982-10-01

Analysis, Laxenberq, Austria, 1981, pp. 781-808. 9. Anton , H., Elementary Linear Algebra , John Wiley & Sons, New York, 1977. 10. Koopmans, T. C...fCaRUlue do leVee. aide It 001100"M OW eedea9f’ OF Nooke~e Network, generalized network, microcomputer, optimization, network with gains, linear ...Oboe &111111041 network problem, in turn, can be viewed as a specialization of a linear programuing problem having at most two non-zero entries in each

A Linear Algebraic Approach to Teaching Interpolation

ERIC Educational Resources Information Center

Tassa, Tamir

2007-01-01

A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach…

SOME PROBLEMS IN THE CONSTRUCTION OF AN ELECTRON LINEAR ACCELERATOR (in Dutch)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verhaeghe, J.; Vanhuyse, V.; Van Leuven, P.

1959-01-01

Special problems encountered in the construction of the electron linear accelerator of the Natuurkundig Laboratorium der Rijksuniversiteit of Ghent are discussed. The subjects considered are magnetic focusing, magnetic screening of the electron gun cathode, abnormal attenuation-multipactor effects, and electron energy control. (J.S.R.)

Technology, Linear Equations, and Buying a Car.

ERIC Educational Resources Information Center

Sandefur, James T.

1992-01-01

Discusses the use of technology in solving compound interest-rate problems that can be modeled by linear relationships. Uses a graphing calculator to solve the specific problem of determining the amount of money that can be borrowed to buy a car for a given monthly payment and interest rate. (MDH)

The mean-square error optimal linear discriminant function and its application to incomplete data vectors

NASA Technical Reports Server (NTRS)

Walker, H. F.

1979-01-01

In many pattern recognition problems, data vectors are classified although one or more of the data vector elements are missing. This problem occurs in remote sensing when the ground is obscured by clouds. Optimal linear discrimination procedures for classifying imcomplete data vectors are discussed.

Finding Optimal Gains In Linear-Quadratic Control Problems

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

Preventing intimate partner violence via the Internet: A randomized controlled trial of emotion-regulation and conflict-management training for individuals with aggression problems.

PubMed

Hesser, Hugo; Axelsson, Sandra; Bäcke, Victoria; Engstrand, Jonna; Gustafsson, Tina; Holmgren, Elin; Jeppsson, Ulrika; Pollack, Maria; Nordén, Kjell; Rosenqvist, Dan; Andersson, Gerhard

2017-09-01

The aim of this randomized controlled trial was to investigate the effect of an Internet-delivered cognitive behaviour therapy (iCBT), which incorporated emotion-regulation and conflict-resolution techniques, on intimate partner violence (IPV). Another aim was to test the theoretical underpinnings of the treatment model using mediation analysis. Sixty-five participants with aggression problems in intimate adult relationships were recruited from the community and were randomly assigned to iCBT or to a monitored waitlist control. Participants were assessed with standardized self-report measures of IPV or aggression (Multidimensional Measure of Emotional Abuse, Revised Conflict Tactics Scale, and Aggression Questionnaire), relationship quality (Dyadic Adjustment Scale), anxiety or depression symptomatology (Patient Health Questionnaire; Generalized Anxiety Disorder Screener), at pretreatment, posttreatment (8 weeks), and 1-year follow-up. Process variables (subscales of Dysfunctional and Emotional Regulation Scale and Anger Rumination Scale) were assessed weekly over the active treatment phase. Robust linear regression analysis of all randomized participants showed significant treatment effects on emotional abuse relative to control at postassessment. Mediation analysis using growth curve modeling revealed that the treatment effect was partially mediated by changes in emotion-regulation ability. Controlled effects on secondary outcomes were also observed. Analyses of uncontrolled effects indicted that gains on IPV were maintained at 1-year follow-up. iCBT focusing on enhancing conflict-resolution skills and emotion-regulation ability has the potential to reduce IPV among self-recruited individuals with mild forms of abusive behaviour in intimate relationships. Emotion-regulation ability is potentially a key therapeutic process of change. Internet-delivered clinician-guided cognitive behaviour therapy is a viable treatment option for reducing intimate partner violence among self-recruited individuals with mild forms of abusive behaviour. For persons who display patterns of frequent and severe violence, other treatments are most likely needed. Emotion-regulation training is potentially a key therapeutic component that ought to be incorporated in interventions targeting IPV. Copyright © 2017 John Wiley & Sons, Ltd.

A Non-linear Geodetic Data Inversion Using ABIC for Slip Distribution on a Fault With an Unknown dip Angle

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Wright, T. J.

2006-12-01

We developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. When fault geometry is unknown, the problem of geodetic data inversion is non-linear. A common strategy for obtaining slip distribution is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. In addition, in obtaining a uniform slip fault model, we have to simultaneously determine the values of the nine mutually dependent parameters, which is a highly non-linear, complicated process. Although the inverse problem is non-linear for cases with unknown fault geometries, the non-linearity of the problems is actually weak, when we can assume the fault surface to be flat. In particular, when a clear fault trace is observed on the EarthOs surface after an earthquake, we can precisely estimate the strike and the location of the fault. In this case only the dip angle has large ambiguity. In geodetic data inversion we usually need to introduce smoothness constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. Strictly speaking, the inverse problem with smoothness constraints is also non-linear, even if the fault geometry is known. The non-linearity has been dissolved by introducing AkaikeOs Bayesian Information Criterion (ABIC), with which the optimal value of the relative weight of observed data to smoothness constraints is objectively determined. In this study, using ABIC in determining the optimal dip angle, we dissolved the non-linearity of the inverse problem. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much shallower dip angle than before.

Research on fuzzy PID control to electronic speed regulator

NASA Astrophysics Data System (ADS)

Xu, Xiao-gang; Chen, Xue-hui; Zheng, Sheng-guo

2007-12-01

As an important part of diesel engine, the speed regulator plays an important role in stabilizing speed and improving engine's performance. Because there are so many model parameters of diesel-engine considered in traditional PID control and these parameters present non-linear characteristic.The method to adjust engine speed using traditional PID is not considered as a best way. Especially for the diesel-engine generator set. In this paper, the Fuzzy PID control strategy is proposed. Some problems about its utilization in electronic speed regulator are discussed. A mathematical model of electric control system for diesel-engine generator set is established and the way of the PID parameters in the model to affect the function of system is analyzed. And then it is proposed the differential coefficient must be applied in control design for reducing dynamic deviation of system and adjusting time. Based on the control theory, a study combined control with PID calculation together for turning fuzzy PID parameter is implemented. And also a simulation experiment about electronic speed regulator system was conducted using Matlab/Simulink and the Fuzzy-Toolbox. Compared with the traditional PID Algorithm, the simulated results presented obvious improvements in the instantaneous speed governing rate and steady state speed governing rate of diesel-engine generator set when the fuzzy logic control strategy used.

Turnover of regulated nurses in long-term care facilities.

PubMed

Chu, Charlene H; Wodchis, Walter P; McGilton, Katherine S

2014-07-01

To describe the relationship between nursing staff turnover in long-term care (LTC) homes and organisational factors consisting of leadership practices and behaviours, supervisory support, burnout, job satisfaction and work environment satisfaction. The turnover of regulated nursing staff [Registered Nurses (RNs) and Registered Practical Nurses (RPNs)] in LTC facilities is a pervasive problem, but there is a scarcity of research examining this issue in Canada. The study was conceptualized using a Stress Process model. Distinct surveys were distributed to administrators to measure organisational factors and to regulated nurses to measure personal and job-related sources of stress and workplace support. In total, 324 surveys were used in the linear regression analysis to examine factors associated with high turnover rates. Higher leadership practice scores were associated with lower nursing turnover; a one score increase in leadership correlated with a 49% decrease in nursing turnover. A significant inverse relationship between leadership turnover and nurse turnover was found: the higher the administrator turnover the lower the nurse turnover rate. Leadership practices and administrator turnover are significant in influencing regulated nurse turnover in LTC. Long-term care facilities may want to focus on building good leadership and communication as an upstream method to minimize nurse turnover. © 2013 John Wiley & Sons Ltd.

Convergence of a sequence of dual variables at the solution of a completely degenerate problem of linear programming

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dikin, I.

1994-12-31

We survey results about the convergence of the primal affine scaling method at solutions of a completely degenerate problem of linear programming. Moreover we are studying the case when a next approximation is on the boundary of the affine scaling ellipsoid. Convergence of successive approximation to an interior point u of the solution for the dual problem is proved. Coordinates of the vector u are determined only by the input data of the problem; they do not depend of the choice of the starting point.

Interior point techniques for LP and NLP

DOE Office of Scientific and Technical Information (OSTI.GOV)

Evtushenko, Y.

By using surjective mapping the initial constrained optimization problem is transformed to a problem in a new space with only equality constraints. For the numerical solution of the latter problem we use the generalized gradient-projection method and Newton`s method. After inverse transformation to the initial space we obtain the family of numerical methods for solving optimization problems with equality and inequality constraints. In the linear programming case after some simplification we obtain Dikin`s algorithm, affine scaling algorithm and generalized primal dual interior point linear programming algorithm.

Kernel-imbedded Gaussian processes for disease classification using microarray gene expression data

PubMed Central

Zhao, Xin; Cheung, Leo Wang-Kit

2007-01-01

Background Designing appropriate machine learning methods for identifying genes that have a significant discriminating power for disease outcomes has become more and more important for our understanding of diseases at genomic level. Although many machine learning methods have been developed and applied to the area of microarray gene expression data analysis, the majority of them are based on linear models, which however are not necessarily appropriate for the underlying connection between the target disease and its associated explanatory genes. Linear model based methods usually also bring in false positive significant features more easily. Furthermore, linear model based algorithms often involve calculating the inverse of a matrix that is possibly singular when the number of potentially important genes is relatively large. This leads to problems of numerical instability. To overcome these limitations, a few non-linear methods have recently been introduced to the area. Many of the existing non-linear methods have a couple of critical problems, the model selection problem and the model parameter tuning problem, that remain unsolved or even untouched. In general, a unified framework that allows model parameters of both linear and non-linear models to be easily tuned is always preferred in real-world applications. Kernel-induced learning methods form a class of approaches that show promising potentials to achieve this goal. Results A hierarchical statistical model named kernel-imbedded Gaussian process (KIGP) is developed under a unified Bayesian framework for binary disease classification problems using microarray gene expression data. In particular, based on a probit regression setting, an adaptive algorithm with a cascading structure is designed to find the appropriate kernel, to discover the potentially significant genes, and to make the optimal class prediction accordingly. A Gibbs sampler is built as the core of the algorithm to make Bayesian inferences. Simulation studies showed that, even without any knowledge of the underlying generative model, the KIGP performed very close to the theoretical Bayesian bound not only in the case with a linear Bayesian classifier but also in the case with a very non-linear Bayesian classifier. This sheds light on its broader usability to microarray data analysis problems, especially to those that linear methods work awkwardly. The KIGP was also applied to four published microarray datasets, and the results showed that the KIGP performed better than or at least as well as any of the referred state-of-the-art methods did in all of these cases. Conclusion Mathematically built on the kernel-induced feature space concept under a Bayesian framework, the KIGP method presented in this paper provides a unified machine learning approach to explore both the linear and the possibly non-linear underlying relationship between the target features of a given binary disease classification problem and the related explanatory gene expression data. More importantly, it incorporates the model parameter tuning into the framework. The model selection problem is addressed in the form of selecting a proper kernel type. The KIGP method also gives Bayesian probabilistic predictions for disease classification. These properties and features are beneficial to most real-world applications. The algorithm is naturally robust in numerical computation. The simulation studies and the published data studies demonstrated that the proposed KIGP performs satisfactorily and consistently. PMID:17328811

Contextual risk, maternal parenting and adolescent externalizing behaviour problems: the role of emotion regulation.

PubMed

Walton, A; Flouri, Eirini

2010-03-01

The objective of this study was to test if emotion regulation mediates the association between mothers' parenting and adolescents' externalizing behaviour problems (conduct problems and hyperactivity). The parenting dimensions were warmth, psychological control and behavioural control (measured with knowledge, monitoring and discipline). Adjustment was made for contextual risk (measured with the number of proximal adverse life events experienced), gender, age and English as an additional language. Data were from a UK community sample of adolescents aged 11-18 from a comprehensive school in a disadvantaged area. At the multivariate level, none of the parenting variables predicted hyperactivity, which was associated only with difficulties in emotion regulation, contextual risk and English as a first language. The parenting variables predicting conduct problems at the multivariate level were warmth and knowledge. Knowledge did not predict emotion regulation. However, warmth predicted emotion regulation, which was negatively associated with conduct problems. Contextual risk was a significant predictor of both difficulties in emotion regulation and externalizing behaviour problems. Its effect on conduct problems was independent of parenting and was not via its association with difficulties in emotion regulation. The findings add to the evidence for the importance of maternal warmth and contextual risk for both regulated emotion and regulated behaviour. The small maternal control effects on both emotion regulation and externalizing behaviour could suggest the importance of paternal control for adolescent outcomes.

The Association between Motivation, Affect, and Self-regulated Learning When Solving Problems.

PubMed

Baars, Martine; Wijnia, Lisette; Paas, Fred

2017-01-01

Self-regulated learning (SRL) skills are essential for learning during school years, particularly in complex problem-solving domains, such as biology and math. Although a lot of studies have focused on the cognitive resources that are needed for learning to solve problems in a self-regulated way, affective and motivational resources have received much less research attention. The current study investigated the relation between affect (i.e., Positive Affect and Negative Affect Scale), motivation (i.e., autonomous and controlled motivation), mental effort, SRL skills, and problem-solving performance when learning to solve biology problems in a self-regulated online learning environment. In the learning phase, secondary education students studied video-modeling examples of how to solve hereditary problems, solved hereditary problems which they chose themselves from a set of problems with different complexity levels (i.e., five levels). In the posttest, students solved hereditary problems, self-assessed their performance, and chose a next problem from the set of problems but did not solve these problems. The results from this study showed that negative affect, inaccurate self-assessments during the posttest, and higher perceptions of mental effort during the posttest were negatively associated with problem-solving performance after learning in a self-regulated way.

Infant Sleep Predicts Attention Regulation and Behavior Problems at 3-4 Years of Age.

PubMed

Sadeh, Avi; De Marcas, Gali; Guri, Yael; Berger, Andrea; Tikotzky, Liat; Bar-Haim, Yair

2015-01-01

This longitudinal study assessed the role of early sleep patterns in predicting attention regulation and behavior problems. Sleep of 43 infants was assessed using actigraphy at 12 months of age and then reassessed when the children were 3-4 years old. During this follow-up, their attention regulation and behavior problems were also assessed using a computerized test and parental reports. Lower quality of sleep in infancy significantly predicted compromised attention regulation and behavior problems. These findings underscore the need to identify and treat early sleep problems.

A Mixed Integer Linear Programming Approach to Electrical Stimulation Optimization Problems.

PubMed

Abouelseoud, Gehan; Abouelseoud, Yasmine; Shoukry, Amin; Ismail, Nour; Mekky, Jaidaa

2018-02-01

Electrical stimulation optimization is a challenging problem. Even when a single region is targeted for excitation, the problem remains a constrained multi-objective optimization problem. The constrained nature of the problem results from safety concerns while its multi-objectives originate from the requirement that non-targeted regions should remain unaffected. In this paper, we propose a mixed integer linear programming formulation that can successfully address the challenges facing this problem. Moreover, the proposed framework can conclusively check the feasibility of the stimulation goals. This helps researchers to avoid wasting time trying to achieve goals that are impossible under a chosen stimulation setup. The superiority of the proposed framework over alternative methods is demonstrated through simulation examples.

The Relations of Regulation and Emotionality to Children's Externalizing and Internalizing Problem Behavior.

ERIC Educational Resources Information Center

Eisenberg, Nancy; Cumberland, Amanda; Spinrad, Tracy L.; Fabes, Richard A.; Shepard, Stephanie A.; Reiser, Mark; Murphy, Bridget C.; LoSaga, Sandra H.; Guthrie, Ivanna K.

2001-01-01

Examined relation of different types of negative emotion and regulation and control to 55- to 97-month-olds' internalizing and externalizing problem behaviors. Found that children with externalizing problems, compared to children with internalizing problems and nondisordered children, were more prone to anger, impulsivity, and low regulation.…

Detangling the Interrelationships between Self- Regulation and Ill-Structured Problem Solving in Problem-Based Learning

ERIC Educational Resources Information Center

Ge, Xun; Law, Victor; Huang, Kun

2016-01-01

One of the goals for problem-based learning (PBL) is to promote self-regulation. Although self-regulation has been studied extensively, its interrelationships with ill-structured problem solving have been unclear. In order to clarify the interrelationships, this article proposes a conceptual framework illustrating the iterative processes among…

Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application

NASA Technical Reports Server (NTRS)

Ustino, Eugene A.

2006-01-01

This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches

The Dynamics of Small-Scale Turbulence Driven Flows

NASA Astrophysics Data System (ADS)

Beer, M. A.; Hammett, G. W.

1997-11-01

The dynamics of small-scale fluctuation driven flows are of great interest for micro-instability driven turbulence, since nonlinear toroidal simulations have shown that these flows play an important role in the regulation of the turbulence and transport levels. The gyrofluid treatment of these flows was shown to be accurate for times shorter than a bounce time.(Beer, M. A., Ph. D. thesis, Princeton University (1995).) Since the decorrelation times of the turbulence are generally shorter than a bounce time, our original hypothesis was that this description was adequate. Recent work(Hinton, F. L., Rosenbluth, M. N., and Waltz, R. E., International Sherwood Fusion Theory Conference (1997).) pointed out possible problems with this hypothesis, emphasizing the existence of a linearly undamped component of the flow which could build up in time and lower the final turbulence level. While our original gyrofluid model reproduces some aspects of the linear flow, there are differences between the long time gyrofluid and kinetic linear results in some cases. On the other hand, if the long time behavior of these flows is dominated by nonlinear damping (which seems reasonable), then the existing nonlinear gyrofluid simulations may be sufficiently accurate. We test these possibilities by modifying the gyrofluid description of these flows and diagnosing the flow evolution in nonlinear simulations.

The dynamics and control of large flexible space structures, 2. Part A: Shape and orientation control using point actuators

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Reddy, A. S. S. R.

1979-01-01

The equations of planar motion for a flexible beam in orbit which includes the effects of gravity gradient torques and control torques from point actuators located along the beam was developed. Two classes of theorems are applied to the linearized form of these equations to establish necessary conditions for controlability for preselected actuator configurations. The feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping, and (2) by applying the linear regulator problem to the individual model coordinates separately. The linear control laws obtained using both techniques were evaluated by numerical integration of the nonlinear system equations. Numerical examples considering pitch and various number of modes with different combination of actuator numbers and locations are presented. The independent model control concept used earlier with a discretized model of the thin beam in orbit was reviewed for the case where the number of actuators is less than the number of modes. Results indicate that although the system is controllable it is not stable about the nominal (local vertical) orientation when the control is based on modal decoupling. An alternate control law not based on modal decoupling ensures stability of all the modes.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

Linearly Adjustable International Portfolios

NASA Astrophysics Data System (ADS)

Fonseca, R. J.; Kuhn, D.; Rustem, B.

2010-09-01

We present an approach to multi-stage international portfolio optimization based on the imposition of a linear structure on the recourse decisions. Multiperiod decision problems are traditionally formulated as stochastic programs. Scenario tree based solutions however can become intractable as the number of stages increases. By restricting the space of decision policies to linear rules, we obtain a conservative tractable approximation to the original problem. Local asset prices and foreign exchange rates are modelled separately, which allows for a direct measure of their impact on the final portfolio value.

Efficiency of energy conversion in model biological pumps. Optimization by linear nonequilibrium thermodynamic relations.

PubMed

Stucki, J W; Compiani, M; Caplan, S R

1983-09-01

Experimental investigations showed linear relations between flows and forces in some biological energy converters operating far from equilibrium. This observation cannot be understood on the basis of conventional nonequilibrium thermodynamics. Therefore, the efficiencies of a linear and a nonlinear mode of operation of an energy converter (a hypothetical redox-driven H+ pump) were compared. This comparison revealed that at physiological values of the forces and degrees of coupling (1) the force ratio permitting optimal efficiency was much higher in the linear than in the nonlinear mode and (2) the linear mode of operation was at least 10(6)-times more efficient that the nonlinear one. These observations suggest that the experimentally observed linear relations between flows and forces, particularly in the case of oxidative phosphorylation, may be due to a feedback regulation maintaining linear thermodynamic relations far from equilibrium. This regulation may have come about as the consequence of an evolutionary drive towards higher efficiency.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.

When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modularmore » In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.« less

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Homotopy approach to optimal, linear quadratic, fixed architecture compensation

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1991-01-01

Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

Global optimization algorithm for heat exchanger networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quesada, I.; Grossmann, I.E.

This paper deals with the global optimization of heat exchanger networks with fixed topology. It is shown that if linear area cost functions are assumed, as well as arithmetic mean driving force temperature differences in networks with isothermal mixing, the corresponding nonlinear programming (NLP) optimization problem involves linear constraints and a sum of linear fractional functions in the objective which are nonconvex. A rigorous algorithm is proposed that is based on a convex NLP underestimator that involves linear and nonlinear estimators for fractional and bilinear terms which provide a tight lower bound to the global optimum. This NLP problem ismore » used within a spatial branch and bound method for which branching rules are given. Basic properties of the proposed method are presented, and its application is illustrated with several example problems. The results show that the proposed method only requires few nodes in the branch and bound search.« less

Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C.

1992-11-01

The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schrödinger equation as an example, we show that all types of solutions of the linear problems, as well as spectral data known in the literature, are given as specific values of this unique function — the resolvent function. A new form of the inverse problem is formulated.

Design of Distributed Controllers Seeking Optimal Power Flow Solutions Under Communication Constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall'Anese, Emiliano; Simonetto, Andrea; Dhople, Sairaj

This paper focuses on power distribution networks featuring inverter-interfaced distributed energy resources (DERs), and develops feedback controllers that drive the DER output powers to solutions of time-varying AC optimal power flow (OPF) problems. Control synthesis is grounded on primal-dual-type methods for regularized Lagrangian functions, as well as linear approximations of the AC power-flow equations. Convergence and OPF-solution-tracking capabilities are established while acknowledging: i) communication-packet losses, and ii) partial updates of control signals. The latter case is particularly relevant since it enables asynchronous operation of the controllers where DER setpoints are updated at a fast time scale based on local voltagemore » measurements, and information on the network state is utilized if and when available, based on communication constraints. As an application, the paper considers distribution systems with high photovoltaic integration, and demonstrates that the proposed framework provides fast voltage-regulation capabilities, while enabling the near real-time pursuit of solutions of AC OPF problems.« less

Design of Distributed Controllers Seeking Optimal Power Flow Solutions under Communication Constraints: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall'Anese, Emiliano; Simonetto, Andrea; Dhople, Sairaj

This paper focuses on power distribution networks featuring inverter-interfaced distributed energy resources (DERs), and develops feedback controllers that drive the DER output powers to solutions of time-varying AC optimal power flow (OPF) problems. Control synthesis is grounded on primal-dual-type methods for regularized Lagrangian functions, as well as linear approximations of the AC power-flow equations. Convergence and OPF-solution-tracking capabilities are established while acknowledging: i) communication-packet losses, and ii) partial updates of control signals. The latter case is particularly relevant since it enables asynchronous operation of the controllers where DER setpoints are updated at a fast time scale based on local voltagemore » measurements, and information on the network state is utilized if and when available, based on communication constraints. As an application, the paper considers distribution systems with high photovoltaic integration, and demonstrates that the proposed framework provides fast voltage-regulation capabilities, while enabling the near real-time pursuit of solutions of AC OPF problems.« less

The dynamics and control of large flexible space structures - 13

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Li, Feiyue; Xu, Jianke

1990-01-01

The optimal control of three-dimensional large angle maneuvers and vibrations of a Shuttle-mast-reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam subject to three-dimensional deformations. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem is then solved by using the quasilinearization algorithm and the method of particular solutions. The study of the large angle maneuvering of the Shuttle-beam-reflector spacecraft in the plane of a circular earth orbit is extended to consider the effects of the structural offset connection, the axial shortening, and the gravitational torque on the slewing motion. Finally the effect of additional design parameters (such as related to additional payload requirement) on the linear quadratic regulator based design of an orbiting control/structural system is examined.

A Mathematical Formulation of the SCOLE Control Problem. Part 2: Optimal Compensator Design

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1988-01-01

The study initiated in Part 1 of this report is concluded and optimal feedback control (compensator) design for stability augmentation is considered, following the mathematical formulation developed in Part 1. Co-located (rate) sensors and (force and moment) actuators are assumed, and allowing for both sensor and actuator noise, stabilization is formulated as a stochastic regulator problem. Specializing the general theory developed by the author, a complete, closed form solution (believed to be new with this report) is obtained, taking advantage of the fact that the inherent structural damping is light. In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation formulation. The results thus hold for any multibody system so long as the basic model is linear.

Quantum annealing versus classical machine learning applied to a simplified computational biology problem

NASA Astrophysics Data System (ADS)

Li, Richard Y.; Di Felice, Rosa; Rohs, Remo; Lidar, Daniel A.

2018-03-01

Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. Here we studied the ability of a quantum machine learning approach to classify and rank binding affinities. Using simplified data sets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding. The results were compared to state-of-the-art classical approaches for the same simplified data sets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems.

Cutting planes for the multistage stochastic unit commitment problem

DOE PAGES

Jiang, Ruiwei; Guan, Yongpei; Watson, Jean -Paul

2016-04-20

As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use to enhance the reliability unit commitment process for day-ahead power system operations. In our approach, we first develop a deterministic equivalent formulation for the problem, which leads to a large-scale mixed-integer linear program.more » Then, we verify that the turn on/off inequalities provide a convex hull representation of the minimum-up/down time polytope under the stochastic setting. Next, we develop several families of strong valid inequalities mainly through lifting schemes. In particular, by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes, we obtain strong valid inequalities for the ramping and general load balance polytopes. Lastly, branch-and-cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem. Our computational results verify the effectiveness of the proposed approach.« less

Cutting planes for the multistage stochastic unit commitment problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Ruiwei; Guan, Yongpei; Watson, Jean -Paul

As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use to enhance the reliability unit commitment process for day-ahead power system operations. In our approach, we first develop a deterministic equivalent formulation for the problem, which leads to a large-scale mixed-integer linear program.more » Then, we verify that the turn on/off inequalities provide a convex hull representation of the minimum-up/down time polytope under the stochastic setting. Next, we develop several families of strong valid inequalities mainly through lifting schemes. In particular, by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes, we obtain strong valid inequalities for the ramping and general load balance polytopes. Lastly, branch-and-cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem. Our computational results verify the effectiveness of the proposed approach.« less

Visual, Algebraic and Mixed Strategies in Visually Presented Linear Programming Problems.

ERIC Educational Resources Information Center

Shama, Gilli; Dreyfus, Tommy

1994-01-01

Identified and classified solution strategies of (n=49) 10th-grade students who were presented with linear programming problems in a predominantly visual setting in the form of a computerized game. Visual strategies were developed more frequently than either algebraic or mixed strategies. Appendix includes questionnaires. (Contains 11 references.)…

Robust Neighboring Optimal Guidance for the Advanced Launch System

NASA Technical Reports Server (NTRS)

Hull, David G.

1993-01-01

In recent years, optimization has become an engineering tool through the availability of numerous successful nonlinear programming codes. Optimal control problems are converted into parameter optimization (nonlinear programming) problems by assuming the control to be piecewise linear, making the unknowns the nodes or junction points of the linear control segments. Once the optimal piecewise linear control (suboptimal) control is known, a guidance law for operating near the suboptimal path is the neighboring optimal piecewise linear control (neighboring suboptimal control). Research conducted under this grant has been directed toward the investigation of neighboring suboptimal control as a guidance scheme for an advanced launch system.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

PubMed

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-06-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION

PubMed Central

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-01-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression. PMID:25598560

Accommodation of practical constraints by a linear programming jet select. [for Space Shuttle

NASA Technical Reports Server (NTRS)

Bergmann, E.; Weiler, P.

1983-01-01

An experimental spacecraft control system will be incorporated into the Space Shuttle flight software and exercised during a forthcoming mission to evaluate its performance and handling qualities. The control system incorporates a 'phase space' control law to generate rate change requests and a linear programming jet select to compute jet firings. Posed as a linear programming problem, jet selection must represent the rate change request as a linear combination of jet acceleration vectors where the coefficients are the jet firing times, while minimizing the fuel expended in satisfying that request. This problem is solved in real time using a revised Simplex algorithm. In order to implement the jet selection algorithm in the Shuttle flight control computer, it was modified to accommodate certain practical features of the Shuttle such as limited computer throughput, lengthy firing times, and a large number of control jets. To the authors' knowledge, this is the first such application of linear programming. It was made possible by careful consideration of the jet selection problem in terms of the properties of linear programming and the Simplex algorithm. These modifications to the jet select algorithm may by useful for the design of reaction controlled spacecraft.

A comparison of several methods of solving nonlinear regression groundwater flow problems

USGS Publications Warehouse

Cooley, Richard L.

1985-01-01

Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear-regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi-linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi-Newton method, and last was the Fletcher-Reeves method, which did not converge in 100 iterations for two of the problems. The fastest method per iteration was the Fletcher-Reeves method, and this was followed closely by the quasi-Newton method. The Marquardt and quasi-linearization methods were slower. For all four methods the speed per iteration was directly related to the number of parameters in the model. However, this effect was much more pronounced for the Marquardt and quasi-linearization methods than for the other two. Hence the quasi-Newton (and perhaps Fletcher-Reeves) method might be more efficient than either the Marquardt or quasi-linearization methods if the number of parameters in a particular model were large, although this remains to be proven. The Marquardt method required somewhat less central memory than the quasi-linearization metilod for three of the four problems. For all four problems the quasi-Newton method required roughly two thirds to three quarters of the memory required by the Marquardt method, and the Fletcher-Reeves method required slightly less memory than the quasi-Newton method. Memory requirements were not excessive for any of the four methods.

Graph-cut based discrete-valued image reconstruction.

PubMed

Tuysuzoglu, Ahmet; Karl, W Clem; Stojanovic, Ivana; Castañòn, David; Ünlü, M Selim

2015-05-01

Efficient graph-cut methods have been used with great success for labeling and denoising problems occurring in computer vision. Unfortunately, the presence of linear image mappings has prevented the use of these techniques in most discrete-amplitude image reconstruction problems. In this paper, we develop a graph-cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations. We first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph-cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator. We then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph-cut frameworks. We use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems. We first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter. Then we focus on nonlocal, tomographic examples where we consider limited-angle data problems. We compare our technique with state-of-the-art discrete and continuous image reconstruction techniques. Experiments show that the proposed method outperforms state-of-the-art techniques in challenging scenarios involving discrete valued unknowns.

Angular Impulse and Balance Regulation During the Golf Swing.

PubMed

Peterson, Travis J; Wilcox, Rand R; McNitt-Gray, Jill L

2016-08-01

Our aim was to determine how skilled players regulate linear and angular impulse while maintaining balance during the golf swing. Eleven highly-skilled golf players performed swings with a 6-iron and driver. Components contributing to linear and angular impulse generated by the rear and target legs (resultant horizontal reaction force [RFh], RFh-angle, and moment arm) were quantified and compared across the group and within a player (α = .05). Net angular impulse generated by both the rear and target legs was greater for the driver than the 6-iron. Mechanisms used to regulate angular impulse generation between clubs varied across players and required coordination between the legs. Increases in net angular impulse with a driver involved increases in target leg RFh. Rear leg RFh-angle was maintained between clubs whereas target leg RFh became more aligned with the target line. Net linear impulse perpendicular to the target line remained near zero, preserving balance, while net linear impulse along the target line decreased in magnitude. These results indicate that the net angular impulse was regulated between clubs by coordinating force generation of the rear and target legs while sustaining balance throughout the task.

Solving a mixture of many random linear equations by tensor decomposition and alternating minimization.

DOT National Transportation Integrated Search

2016-09-01

We consider the problem of solving mixed random linear equations with k components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample...

The checkpoint ordering problem

PubMed Central

Hungerländer, P.

2017-01-01

Abstract We suggest a new variant of a row layout problem: Find an ordering of n departments with given lengths such that the total weighted sum of their distances to a given checkpoint is minimized. The Checkpoint Ordering Problem (COP) is both of theoretical and practical interest. It has several applications and is conceptually related to some well-studied combinatorial optimization problems, namely the Single-Row Facility Layout Problem, the Linear Ordering Problem and a variant of parallel machine scheduling. In this paper we study the complexity of the (COP) and its special cases. The general version of the (COP) with an arbitrary but fixed number of checkpoints is NP-hard in the weak sense. We propose both a dynamic programming algorithm and an integer linear programming approach for the (COP) . Our computational experiments indicate that the (COP) is hard to solve in practice. While the run time of the dynamic programming algorithm strongly depends on the length of the departments, the integer linear programming approach is able to solve instances with up to 25 departments to optimality. PMID:29170574

Three-dimensional Finite Element Formulation and Scalable Domain Decomposition for High Fidelity Rotor Dynamic Analysis

NASA Technical Reports Server (NTRS)

Datta, Anubhav; Johnson, Wayne R.

2009-01-01

This paper has two objectives. The first objective is to formulate a 3-dimensional Finite Element Model for the dynamic analysis of helicopter rotor blades. The second objective is to implement and analyze a dual-primal iterative substructuring based Krylov solver, that is parallel and scalable, for the solution of the 3-D FEM analysis. The numerical and parallel scalability of the solver is studied using two prototype problems - one for ideal hover (symmetric) and one for a transient forward flight (non-symmetric) - both carried out on up to 48 processors. In both hover and forward flight conditions, a perfect linear speed-up is observed, for a given problem size, up to the point of substructure optimality. Substructure optimality and the linear parallel speed-up range are both shown to depend on the problem size as well as on the selection of the coarse problem. With a larger problem size, linear speed-up is restored up to the new substructure optimality. The solver also scales with problem size - even though this conclusion is premature given the small prototype grids considered in this study.

Towards lexicographic multi-objective linear programming using grossone methodology

NASA Astrophysics Data System (ADS)

Cococcioni, Marco; Pappalardo, Massimo; Sergeyev, Yaroslav D.

2016-10-01

Lexicographic Multi-Objective Linear Programming (LMOLP) problems can be solved in two ways: preemptive and nonpreemptive. The preemptive approach requires the solution of a series of LP problems, with changing constraints (each time the next objective is added, a new constraint appears). The nonpreemptive approach is based on a scalarization of the multiple objectives into a single-objective linear function by a weighted combination of the given objectives. It requires the specification of a set of weights, which is not straightforward and can be time consuming. In this work we present both mathematical and software ingredients necessary to solve LMOLP problems using a recently introduced computational methodology (allowing one to work numerically with infinities and infinitesimals) based on the concept of grossone. The ultimate goal of such an attempt is an implementation of a simplex-like algorithm, able to solve the original LMOLP problem by solving only one single-objective problem and without the need to specify finite weights. The expected advantages are therefore obvious.

Numerical Solution of Systems of Loaded Ordinary Differential Equations with Multipoint Conditions

NASA Astrophysics Data System (ADS)

Assanova, A. T.; Imanchiyev, A. E.; Kadirbayeva, Zh. M.

2018-04-01

A system of loaded ordinary differential equations with multipoint conditions is considered. The problem under study is reduced to an equivalent boundary value problem for a system of ordinary differential equations with parameters. A system of linear algebraic equations for the parameters is constructed using the matrices of the loaded terms and the multipoint condition. The conditions for the unique solvability and well-posedness of the original problem are established in terms of the matrix made up of the coefficients of the system of linear algebraic equations. The coefficients and the righthand side of the constructed system are determined by solving Cauchy problems for linear ordinary differential equations. The solutions of the system are found in terms of the values of the desired function at the initial points of subintervals. The parametrization method is numerically implemented using the fourth-order accurate Runge-Kutta method as applied to the Cauchy problems for ordinary differential equations. The performance of the constructed numerical algorithms is illustrated by examples.

Ultralow-quiescent-current and wide-load-range low-dropout linear regulator with self-biasing technique for micropower battery management

NASA Astrophysics Data System (ADS)

Ozaki, Toshihiro; Hirose, Tetsuya; Asano, Hiroki; Kuroki, Nobutaka; Numa, Masahiro

2017-04-01

In this paper, we present a 151 nA quiescent and 6.8 mA maximum-output-current low-dropout (LDO) linear regulator for micropower battery management. The LDO regulator employs self-biasing and multiple-stacked cascode techniques to achieve efficient, accurate, and high-voltage-input-tolerant operation. Measurement results demonstrated that the proposed LDO regulator operates with an ultralow quiescent current of 151 nA. The maximum output currents with a 4.16 V output were 1.0 and 6.8 mA when the input voltages were 4.25 and 5.0 V, respectively.

Linear time-varying models can reveal non-linear interactions of biomolecular regulatory networks using multiple time-series data.

PubMed

Kim, Jongrae; Bates, Declan G; Postlethwaite, Ian; Heslop-Harrison, Pat; Cho, Kwang-Hyun

2008-05-15

Inherent non-linearities in biomolecular interactions make the identification of network interactions difficult. One of the principal problems is that all methods based on the use of linear time-invariant models will have fundamental limitations in their capability to infer certain non-linear network interactions. Another difficulty is the multiplicity of possible solutions, since, for a given dataset, there may be many different possible networks which generate the same time-series expression profiles. A novel algorithm for the inference of biomolecular interaction networks from temporal expression data is presented. Linear time-varying models, which can represent a much wider class of time-series data than linear time-invariant models, are employed in the algorithm. From time-series expression profiles, the model parameters are identified by solving a non-linear optimization problem. In order to systematically reduce the set of possible solutions for the optimization problem, a filtering process is performed using a phase-portrait analysis with random numerical perturbations. The proposed approach has the advantages of not requiring the system to be in a stable steady state, of using time-series profiles which have been generated by a single experiment, and of allowing non-linear network interactions to be identified. The ability of the proposed algorithm to correctly infer network interactions is illustrated by its application to three examples: a non-linear model for cAMP oscillations in Dictyostelium discoideum, the cell-cycle data for Saccharomyces cerevisiae and a large-scale non-linear model of a group of synchronized Dictyostelium cells. The software used in this article is available from http://sbie.kaist.ac.kr/software

Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

NASA Astrophysics Data System (ADS)

Rosenberg, D. E.; Alafifi, A.

2016-12-01

Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one step to any point in the near-optimal region, and each iterate generates a new, feasible alternative. We use the method to generate alternatives that span the near-optimal regions of simple and more complicated water management problems and may be preferred to optimal solutions. We also discuss extensions to handle non-linear equity constraints.

The Association between Motivation, Affect, and Self-regulated Learning When Solving Problems

PubMed Central

Baars, Martine; Wijnia, Lisette; Paas, Fred

2017-01-01

Self-regulated learning (SRL) skills are essential for learning during school years, particularly in complex problem-solving domains, such as biology and math. Although a lot of studies have focused on the cognitive resources that are needed for learning to solve problems in a self-regulated way, affective and motivational resources have received much less research attention. The current study investigated the relation between affect (i.e., Positive Affect and Negative Affect Scale), motivation (i.e., autonomous and controlled motivation), mental effort, SRL skills, and problem-solving performance when learning to solve biology problems in a self-regulated online learning environment. In the learning phase, secondary education students studied video-modeling examples of how to solve hereditary problems, solved hereditary problems which they chose themselves from a set of problems with different complexity levels (i.e., five levels). In the posttest, students solved hereditary problems, self-assessed their performance, and chose a next problem from the set of problems but did not solve these problems. The results from this study showed that negative affect, inaccurate self-assessments during the posttest, and higher perceptions of mental effort during the posttest were negatively associated with problem-solving performance after learning in a self-regulated way. PMID:28848467

High profile students’ growth of mathematical understanding in solving linier programing problems

NASA Astrophysics Data System (ADS)

Utomo; Kusmayadi, TA; Pramudya, I.

2018-04-01

Linear program has an important role in human’s life. This linear program is learned in senior high school and college levels. This material is applied in economy, transportation, military and others. Therefore, mastering linear program is useful for provision of life. This research describes a growth of mathematical understanding in solving linear programming problems based on the growth of understanding by the Piere-Kieren model. Thus, this research used qualitative approach. The subjects were students of grade XI in Salatiga city. The subjects of this study were two students who had high profiles. The researcher generally chose the subjects based on the growth of understanding from a test result in the classroom; the mark from the prerequisite material was ≥ 75. Both of the subjects were interviewed by the researcher to know the students’ growth of mathematical understanding in solving linear programming problems. The finding of this research showed that the subjects often folding back to the primitive knowing level to go forward to the next level. It happened because the subjects’ primitive understanding was not comprehensive.

Linearized-moment analysis of the temperature jump and temperature defect in the Knudsen layer of a rarefied gas.

PubMed

Gu, Xiao-Jun; Emerson, David R

2014-06-01

Understanding the thermal behavior of a rarefied gas remains a fundamental problem. In the present study, we investigate the predictive capabilities of the regularized 13 and 26 moment equations. In this paper, we consider low-speed problems with small gradients, and to simplify the analysis, a linearized set of moment equations is derived to explore a classic temperature problem. Analytical solutions obtained for the linearized 26 moment equations are compared with available kinetic models and can reliably capture all qualitative trends for the temperature-jump coefficient and the associated temperature defect in the thermal Knudsen layer. In contrast, the linearized 13 moment equations lack the necessary physics to capture these effects and consistently underpredict kinetic theory. The deviation from kinetic theory for the 13 moment equations increases significantly for specular reflection of gas molecules, whereas the 26 moment equations compare well with results from kinetic theory. To improve engineering analyses, expressions for the effective thermal conductivity and Prandtl number in the Knudsen layer are derived with the linearized 26 moment equations.

Optimal control problem for linear fractional-order systems, described by equations with Hadamard-type derivative

NASA Astrophysics Data System (ADS)

Postnov, Sergey

2017-11-01

Two kinds of optimal control problem are investigated for linear time-invariant fractional-order systems with lumped parameters which dynamics described by equations with Hadamard-type derivative: the problem of control with minimal norm and the problem of control with minimal time at given restriction on control norm. The problem setting with nonlocal initial conditions studied. Admissible controls allowed to be the p-integrable functions (p > 1) at half-interval. The optimal control problem studied by moment method. The correctness and solvability conditions for the corresponding moment problem are derived. For several special cases the optimal control problems stated are solved analytically. Some analogies pointed for results obtained with the results which are known for integer-order systems and fractional-order systems describing by equations with Caputo- and Riemann-Liouville-type derivatives.

The principle of superposition and its application in ground-water hydraulics

USGS Publications Warehouse

Reilly, Thomas E.; Franke, O. Lehn; Bennett, Gordon D.

1987-01-01

The principle of superposition, a powerful mathematical technique for analyzing certain types of complex problems in many areas of science and technology, has important applications in ground-water hydraulics and modeling of ground-water systems. The principle of superposition states that problem solutions can be added together to obtain composite solutions. This principle applies to linear systems governed by linear differential equations. This report introduces the principle of superposition as it applies to ground-water hydrology and provides background information, discussion, illustrative problems with solutions, and problems to be solved by the reader.

Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations

NASA Astrophysics Data System (ADS)

Podlipenko, Yu. K.; Shestopalov, Yu. V.

2017-09-01

We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

Fleet Assignment Using Collective Intelligence

NASA Technical Reports Server (NTRS)

Antoine, Nicolas E.; Bieniawski, Stefan R.; Kroo, Ilan M.; Wolpert, David H.

2004-01-01

Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).

Piecewise linear approximation for hereditary control problems

NASA Technical Reports Server (NTRS)

Propst, Georg

1987-01-01

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

The Relationship between Mathematical Problem-Solving Skills and Self-Regulated Learning through Homework Behaviours, Motivation, and Metacognition

ERIC Educational Resources Information Center

Özcan, Zeynep Çigdem

2016-01-01

Studies highlight that using appropriate strategies during problem solving is important to improve problem-solving skills and draw attention to the fact that using these skills is an important part of students' self-regulated learning ability. Studies on this matter view the self-regulated learning ability as key to improving problem-solving…

Investigating High-School Students' Reasoning Strategies when They Solve Linear Equations

ERIC Educational Resources Information Center

Huntley, Mary Ann; Marcus, Robin; Kahan, Jeremy; Miller, Jane Lincoln

2007-01-01

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third-year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from one problem that involved solving a set of three linear equations of…

Enriched Imperialist Competitive Algorithm for system identification of magneto-rheological dampers

NASA Astrophysics Data System (ADS)

Talatahari, Siamak; Rahbari, Nima Mohajer

2015-10-01

In the current research, the imperialist competitive algorithm is dramatically enhanced and a new optimization method dubbed as Enriched Imperialist Competitive Algorithm (EICA) is effectively introduced to deal with high non-linear optimization problems. To conduct a close examination of its functionality and efficacy, the proposed metaheuristic optimization approach is actively employed to sort out the parameter identification of two different types of hysteretic Bouc-Wen models which are simulating the non-linear behavior of MR dampers. Two types of experimental data are used for the optimization problems to minutely examine the robustness of the proposed EICA. The obtained results self-evidently demonstrate the high adaptability of EICA to suitably get to the bottom of such non-linear and hysteretic problems.

Hybrid Genetic Agorithms and Line Search Method for Industrial Production Planning with Non-Linear Fitness Function

NASA Astrophysics Data System (ADS)

Vasant, Pandian; Barsoum, Nader

2008-10-01

Many engineering, science, information technology and management optimization problems can be considered as non linear programming real world problems where the all or some of the parameters and variables involved are uncertain in nature. These can only be quantified using intelligent computational techniques such as evolutionary computation and fuzzy logic. The main objective of this research paper is to solve non linear fuzzy optimization problem where the technological coefficient in the constraints involved are fuzzy numbers which was represented by logistic membership functions by using hybrid evolutionary optimization approach. To explore the applicability of the present study a numerical example is considered to determine the production planning for the decision variables and profit of the company.

An Obstruction to the Integrability of a Class of Non-linear Wave Equations by 1-Stable Cartan Characteristics

NASA Astrophysics Data System (ADS)

Fackerell, E. D.; Hartley, D.; Tucker, R. W.

We examine in detail the Cauchy problem for a class of non-linear hyperbolic equations in two independent variables. This class is motivated by the analysis of the dynamics of a line of non-linearly coupled particles by Fermi, Pasta, and Ulam and extends the recent investigation of this problem by Gardner and Kamran. We find conditions for the existence of a 1-stable Cartan characteristic of a Pfaffian exterior differential system whose integral curves provide a solution to the Cauchy problem. The same obstruction to involution is exposed in Darboux's method of integration and the two approaches are compared. A class of particular solutions to the obstruction is constructed.

Application of a stochastic inverse to the geophysical inverse problem

NASA Technical Reports Server (NTRS)

Jordan, T. H.; Minster, J. B.

1972-01-01

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

Topology optimization of embedded piezoelectric actuators considering control spillover effects

NASA Astrophysics Data System (ADS)

Gonçalves, Juliano F.; De Leon, Daniel M.; Perondi, Eduardo A.

2017-02-01

This article addresses the problem of active structural vibration control by means of embedded piezoelectric actuators. The topology optimization method using the solid isotropic material with penalization (SIMP) approach is employed in this work to find the optimum design of actuators taken into account the control spillover effects. A coupled finite element model of the structure is derived assuming a two-phase material and this structural model is written into the state-space representation. The proposed optimization formulation aims to determine the distribution of piezoelectric material which maximizes the controllability for a given vibration mode. The undesirable effects of the feedback control on the residual modes are limited by including a spillover constraint term containing the residual controllability Gramian eigenvalues. The optimization of the shape and placement of the conventionally embedded piezoelectric actuators are performed using a Sequential Linear Programming (SLP) algorithm. Numerical examples are presented considering the control of the bending vibration modes for a cantilever and a fixed beam. A Linear-Quadratic Regulator (LQR) is synthesized for each case of controlled structure in order to compare the influence of the additional constraint.

Active control of acoustic pressure fields using smart material technologies

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, R. C.

1993-01-01

An overview describing the use of piezoceramic patches in reducing noise in a structural acoustics setting is presented. The passive and active contributions due to patches which are bonded to an Euler-Bernoulli beam or thin shell are briefly discussed and the results are incorporated into a 2-D structural acoustics model. In this model, an exterior noise source causes structural vibrations which in turn lead to interior noise as a result of nonlinear fluid/structure coupling mechanism. Interior sound pressure levels are reduced via patches bonded to the flexible boundary (a beam in this case) which generate pure bending moments when an out-of-phase voltage is applied. Well-posedness results for the infinite dimensional system are discussed and a Galerkin scheme for approximating the system dynamics is outlined. Control is implemented by using linear quadratic regulator (LQR) optimal control theory to calculate gains for the linearized system and then feeding these gains back into the nonlinear system of interest. The effectiveness of this strategy for this problem is illustrated in an example.

The Glycosylphosphatidylinositol-PLC in Trypanosoma brucei Forms a Linear Array on the Exterior of the Flagellar Membrane Before and After Activation

PubMed Central

Hanrahan, Orla; Webb, Helena; O'Byrne, Robert; Brabazon, Elaine; Treumann, Achim; Sunter, Jack D.; Carrington, Mark; Voorheis, H. Paul

2009-01-01

Bloodstream forms of Trypanosoma brucei contain a glycosylphosphatidylinositol-specific phospholipase C (GPI-PLC) that cleaves the GPI-anchor of the variable surface glycoprotein (VSG). Its location in trypanosomes has been controversial. Here, using confocal microscopy and surface labelling techniques, we show that the GPI-PLC is located exclusively in a linear array on the outside of the flagellar membrane, close to the flagellar attachment zone, but does not co-localize with the flagellar attachment zone protein, FAZ1. Consequently, the GPI-PLC and the VSG occupy the same plasma membrane leaflet, which resolves the topological problem associated with the cleavage reaction if the VSG and the GPI-PLC were on opposite sides of the membrane. The exterior location requires the enzyme to be tightly regulated to prevent VSG release under basal conditions. During stimulated VSG release in intact cells, the GPI-PLC did not change location, suggesting that the release mechanism involves lateral diffusion of the VSG in the plane of the membrane to the fixed position of the GPI-PLC. PMID:19503825

An Improved Search Approach for Solving Non-Convex Mixed-Integer Non Linear Programming Problems

NASA Astrophysics Data System (ADS)

Sitopu, Joni Wilson; Mawengkang, Herman; Syafitri Lubis, Riri

2018-01-01

The nonlinear mathematical programming problem addressed in this paper has a structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method, has been developed. This strategy is used to force the appropriate non-integer basic variables to move to their neighbourhood integer points. Successful implementation of these algorithms was achieved on various test problems.

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

On the Problems of Construction and Statistical Inference Associated with a Generalization of Canonical Variables.

DTIC Science & Technology

1982-02-01

of them are pre- sented in this paper. As an application, important practical problems similar to the one posed by Gnanadesikan (1977), p. 77 can be... Gnanadesikan and Wilk (1969) to search for a non-linear combination, giving rise to non-linear first principal component. So, a p-dinensional vector can...distribution, Gnanadesikan and Gupta (1970) and earlier Eaton (1967) have considered the problem of ranking the r underlying populations according to the

Proceedings of the Tenth Annual National Conference on Ada Technology. Held in Arlington, VA, on February 24-28, 1992

DTIC Science & Technology

1992-02-01

Newsletter, Vol. 5, No. 1, January 1983 be translated from HAL’S. 4. Klumpp, Allan R., An Ada Linear Algebra Software development costs for using the...a linear algebra approach to As noted above, the concept of the problem and address the problem of unitdimensional analysis extends beyond problems...you will join us again next year. The 11th Annual Conference on Ada Technology (1993) will be held here at the Hyatt Regency - Crystal City

The effect of discovery learning and problem-based learning on middle school students’ self-regulated learning

NASA Astrophysics Data System (ADS)

Miatun, A.; Muntazhimah

2018-01-01

The aim of this research was to determine the effect of learning models on mathematics achievement viewed from student’s self-regulated learning. The learning model compared were discovery learning and problem-based learning. The population was all students at the grade VIII of Junior High School in Boyolali regency. The samples were students of SMPN 4 Boyolali, SMPN 6 Boyolali, and SMPN 4 Mojosongo. The instruments used were mathematics achievement tests and self-regulated learning questionnaire. The data were analyzed using unbalanced two-ways Anova. The conclusion was as follows: (1) discovery learning gives better achievement than problem-based learning. (2) Achievement of students who have high self-regulated learning was better than students who have medium and low self-regulated learning. (3) For discovery learning, achievement of students who have high self-regulated learning was better than students who have medium and low self-regulated learning. For problem-based learning, students who have high and medium self-regulated learning have the same achievement. (4) For students who have high self-regulated learning, discovery learning gives better achievement than problem-based learning. Students who have medium and low self-regulated learning, both learning models give the same achievement.

The near optimality of the stabilizing control in a weakly nonlinear system with state-dependent coefficients

NASA Astrophysics Data System (ADS)

Dmitriev, Mikhail G.; Makarov, Dmitry A.

2016-08-01

We carried out analysis of near optimality of one computationally effective nonlinear stabilizing control built for weakly nonlinear systems with coefficients depending on the state and the formal small parameter. First investigation of that problem was made in [M. G. Dmitriev, and D. A. Makarov, "The suboptimality of stabilizing regulator in a quasi-linear system with state-depended coefficients," in 2016 International Siberian Conference on Control and Communications (SIBCON) Proceedings, National Research University, Moscow, 2016]. In this paper, another optimal control and gain matrix representations were used and theoretical results analogous to cited work above were obtained. Also as in the cited work above the form of quality criterion on which this close-loop control is optimal was constructed.

Microgravity vibration isolation: Optimal preview and feedback control

NASA Technical Reports Server (NTRS)

Hampton, R. D.; Knospe, C. R.; Grodsinsky, C. M.; Allaire, P. E.; Lewis, D. W.

1992-01-01

In order to achieve adequate low-frequency vibration isolation for certain space experiments an active control is needed, due to inherent passive-isolator limitations. Proposed here are five possible state-space models for a one-dimensional vibration isolation system with a quadratic performance index. The five models are subsets of a general set of nonhomogeneous state space equations which includes disturbance terms. An optimal control is determined, using a differential equations approach, for this class of problems. This control is expressed in terms of constant, Linear Quadratic Regulator (LQR) feedback gains and constant feedforward (preview) gains. The gains can be easily determined numerically. They result in a robust controller and offers substantial improvements over a control that uses standard LQR feedback alone.

The Algebra of Sleepiness: Investigating the Interaction of Homeostatic (S) and Circadian (C) Processes in Sleepiness Using Linear Metrics"

ERIC Educational Resources Information Center

Mairesse, Olivier; Hofmans, Joeri; Neu, Daniel; Dinis Monica de Oliveira, Armando Luis; Cluydts, Raymond; Theuns, Peter

2010-01-01

The present studies were conducted to contribute to the debate on the interaction between circadian (C) and homeostatic (S) processes in models of sleep regulation. The Two-Process Model of Sleep Regulation assumes a linear relationship between processes S and C. However, recent elaborations of the model, based on data from forced desynchrony…

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

NASA Astrophysics Data System (ADS)

Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

2018-02-01

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

Graph cuts via l1 norm minimization.

PubMed

Bhusnurmath, Arvind; Taylor, Camillo J

2008-10-01

Graph cuts have become an increasingly important tool for solving a number of energy minimization problems in computer vision and other fields. In this paper, the graph cut problem is reformulated as an unconstrained l1 norm minimization that can be solved effectively using interior point methods. This reformulation exposes connections between the graph cuts and other related continuous optimization problems. Eventually the problem is reduced to solving a sequence of sparse linear systems involving the Laplacian of the underlying graph. The proposed procedure exploits the structure of these linear systems in a manner that is easily amenable to parallel implementations. Experimental results obtained by applying the procedure to graphs derived from image processing problems are provided.

Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations.

PubMed

Lee, UnJin; Skinner, John J; Reinitz, John; Rosner, Marsha Rich; Kim, Eun-Jin

2015-01-01

There has been increasing awareness in the wider biological community of the role of clonal phenotypic heterogeneity in playing key roles in phenomena such as cellular bet-hedging and decision making, as in the case of the phage-λ lysis/lysogeny and B. Subtilis competence/vegetative pathways. Here, we report on the effect of stochasticity in growth rate, cellular memory/intermittency, and its relation to phenotypic heterogeneity. We first present a linear stochastic differential model with finite auto-correlation time, where a randomly fluctuating growth rate with a negative average is shown to result in exponential growth for sufficiently large fluctuations in growth rate. We then present a non-linear stochastic self-regulation model where the loss of coherent self-regulation and an increase in noise can induce a shift from bounded to unbounded growth. An important consequence of these models is that while the average change in phenotype may not differ for various parameter sets, the variance of the resulting distributions may considerably change. This demonstrates the necessity of understanding the influence of variance and heterogeneity within seemingly identical clonal populations, while providing a mechanism for varying functional consequences of such heterogeneity. Our results highlight the importance of a paradigm shift from a deterministic to a probabilistic view of clonality in understanding selection as an optimization problem on noise-driven processes, resulting in a wide range of biological implications, from robustness to environmental stress to the development of drug resistance.

The Riesz-Radon-Fréchet problem of characterization of integrals

NASA Astrophysics Data System (ADS)

Zakharov, Valerii K.; Mikhalev, Aleksandr V.; Rodionov, Timofey V.

2010-11-01

This paper is a survey of results on characterizing integrals as linear functionals. It starts from the familiar result of F. Riesz (1909) on integral representation of bounded linear functionals by Riemann-Stieltjes integrals on a closed interval, and is directly connected with Radon's famous theorem (1913) on integral representation of bounded linear functionals by Lebesgue integrals on a compact subset of {R}^n. After the works of Radon, Fréchet, and Hausdorff, the problem of characterizing integrals as linear functionals took the particular form of the problem of extending Radon's theorem from {R}^n to more general topological spaces with Radon measures. This problem turned out to be difficult, and its solution has a long and rich history. Therefore, it is natural to call it the Riesz-Radon-Fréchet problem of characterization of integrals. Important stages of its solution are associated with such eminent mathematicians as Banach (1937-1938), Saks (1937-1938), Kakutani (1941), Halmos (1950), Hewitt (1952), Edwards (1953), Prokhorov (1956), Bourbaki (1969), and others. Essential ideas and technical tools were developed by A.D. Alexandrov (1940-1943), Stone (1948-1949), Fremlin (1974), and others. Most of this paper is devoted to the contemporary stage of the solution of the problem, connected with papers of König (1995-2008), Zakharov and Mikhalev (1997-2009), and others. The general solution of the problem is presented in the form of a parametric theorem on characterization of integrals which directly implies the characterization theorems of the indicated authors. Bibliography: 60 titles.

An analysis of hypercritical states in elastic and inelastic systems

NASA Astrophysics Data System (ADS)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

A longitudinal examination of the bidirectional association between sleep problems and social ties at university: the mediating role of emotion regulation.

PubMed

Tavernier, Royette; Willoughby, Teena

2015-02-01

Despite the growing body of research linking sleep problems and social ties, research investigating the direction of effects between these two constructs is lacking. Furthermore, there remains a dearth of research examining the mechanisms that may explain the association between sleep problems and social ties within a longitudinal design. The present 3-year longitudinal study addressed two research questions: (1) Is there a bidirectional association between sleep problems and social ties at university? and (2) Does emotion regulation mediate the association between sleep problems and social ties at university? Participants (N = 942, 71.5% female; M = 19.01 years at Time 1, SD = 0.90) were university students who completed annual assessments of sleep problems, social ties, and emotion regulation, for three consecutive years. Results of path analysis indicated that the bidirectional association between sleep problems and social ties was statistically significant (controlling for demographics, sleep-wake inconsistency, sleep duration, and alcohol). Analyses of indirect effects indicated that emotion regulation mediated this link, such that better sleep quality (i.e., less sleep problems) led to more effective emotion regulation, which, subsequently, led to more positive social ties. In addition, more positive social ties led to more effective emotion regulation, which, in turn, led to less sleep problems. The findings highlight the critical role that emotional regulation plays in the link between sleep problems and social ties, and emphasize the need for students as well as university administration to pay close attention to both the sleep and social environment of university students.

Stability of Linear Equations--Algebraic Approach

ERIC Educational Resources Information Center

Cherif, Chokri; Goldstein, Avraham; Prado, Lucio M. G.

2012-01-01

This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

Application of Hierarchical Linear Models/Linear Mixed-Effects Models in School Effectiveness Research

ERIC Educational Resources Information Center

Ker, H. W.

2014-01-01

Multilevel data are very common in educational research. Hierarchical linear models/linear mixed-effects models (HLMs/LMEs) are often utilized to analyze multilevel data nowadays. This paper discusses the problems of utilizing ordinary regressions for modeling multilevel educational data, compare the data analytic results from three regression…

A feedback linearization approach to spacecraft control using momentum exchange devices. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Dzielski, John Edward

1988-01-01

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

The Effects of the Concrete-Representational-Abstract Integration Strategy on the Ability of Students with Learning Disabilities to Multiply Linear Expressions within Area Problems

ERIC Educational Resources Information Center

Strickland, Tricia K.; Maccini, Paula

2013-01-01

We examined the effects of the Concrete-Representational-Abstract Integration strategy on the ability of secondary students with learning disabilities to multiply linear algebraic expressions embedded within contextualized area problems. A multiple-probe design across three participants was used. Results indicated that the integration of the…

A Quantitative and Combinatorial Approach to Non-Linear Meanings of Multiplication

ERIC Educational Resources Information Center

Tillema, Erik; Gatza, Andrew

2016-01-01

We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative…

On some Aitken-like acceleration of the Schwarz method

NASA Astrophysics Data System (ADS)

Garbey, M.; Tromeur-Dervout, D.

2002-12-01

In this paper we present a family of domain decomposition based on Aitken-like acceleration of the Schwarz method seen as an iterative procedure with a linear rate of convergence. We first present the so-called Aitken-Schwarz procedure for linear differential operators. The solver can be a direct solver when applied to the Helmholtz problem with five-point finite difference scheme on regular grids. We then introduce the Steffensen-Schwarz variant which is an iterative domain decomposition solver that can be applied to linear and nonlinear problems. We show that these solvers have reasonable numerical efficiency compared to classical fast solvers for the Poisson problem or multigrids for more general linear and nonlinear elliptic problems. However, the salient feature of our method is that our algorithm has high tolerance to slow network in the context of distributed parallel computing and is attractive, generally speaking, to use with computer architecture for which performance is limited by the memory bandwidth rather than the flop performance of the CPU. This is nowadays the case for most parallel. computer using the RISC processor architecture. We will illustrate this highly desirable property of our algorithm with large-scale computing experiments.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1985-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1986-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Linear complementarity formulation for 3D frictional sliding problems

USGS Publications Warehouse

Kaven, Joern; Hickman, Stephen H.; Davatzes, Nicholas C.; Mutlu, Ovunc

2012-01-01

Frictional sliding on quasi-statically deforming faults and fractures can be modeled efficiently using a linear complementarity formulation. We review the formulation in two dimensions and expand the formulation to three-dimensional problems including problems of orthotropic friction. This formulation accurately reproduces analytical solutions to static Coulomb friction sliding problems. The formulation accounts for opening displacements that can occur near regions of non-planarity even under large confining pressures. Such problems are difficult to solve owing to the coupling of relative displacements and tractions; thus, many geomechanical problems tend to neglect these effects. Simple test cases highlight the importance of including friction and allowing for opening when solving quasi-static fault mechanics models. These results also underscore the importance of considering the effects of non-planarity in modeling processes associated with crustal faulting.

Sleep and Self-Regulation from Birth to 7 Years: A Retrospective Study of Children with and Without Attention-Deficit Hyperactivity Disorder at 8 to 9 Years.

PubMed

Williams, Kate E; Sciberras, Emma

2016-06-01

To examine mean level differences and longitudinal and reciprocal relations among behavioral sleep problems, emotional dysregulation, and attentional regulation across early childhood for children with and without attention-deficit hyperactivity disorder (ADHD) at 8 to 9 years. This study used data from Growing Up in Australia: The Longitudinal Study of Australian Children (LSAC)-Infant Cohort (n = 4,109 analyzed). Children with and without ADHD were identified at age 8 to 9 years via parent report of ADHD diagnosis and the 5-item Inattention-Hyperactivity subscale from the Strengths and Difficulties Questionnaire. Maternal report of child sleep problems and self-regulation was collected at 0 to 1, 2 to 3, 4 to 5, and 6 to 7 years of age. Analysis of variance was used to compare mean level differences in sleep problems and emotional and attentional regulation by ADHD group. Longitudinal structural equation modeling examined the relations among sleep and self-regulation across time in children with and without ADHD. Children with ADHD had persistently elevated levels of sleep problems (from infancy) and emotional and attentional dysregulation compared to controls (from 2 to 3 years of age). Sleep problems, emotional dysregulation, and attentional regulation were stable over time for both groups. Sleep problems were associated with greater emotional dysregulation 2 years later from 2 to 3 years of age for both groups, which in turn was associated with poorer attentional regulation. There was no direct relationship between sleep problems and later attentional regulation. Sleep problems in children with and without ADHD are associated with emotional dysregulation, which in turn contributes to poorer attentional functioning. This study highlights the importance of assessing and managing sleep problems in young children.

ELAS: A general-purpose computer program for the equilibrium problems of linear structures. Volume 2: Documentation of the program. [subroutines and flow charts

NASA Technical Reports Server (NTRS)

Utku, S.

1969-01-01

A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.

Analysis of Slope Limiters on Irregular Grids

NASA Technical Reports Server (NTRS)

Berger, Marsha; Aftosmis, Michael J.

2005-01-01

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. Many slope limiters in standard use do not preserve linear solutions on irregular grids impacting both accuracy and convergence. We rewrite some well-known limiters to highlight their underlying symmetry, and use this form to examine the proper - ties of both traditional and novel limiter formulations on non-uniform meshes. A consistent method of handling stretched meshes is developed which is both linearity preserving for arbitrary mesh stretchings and reduces to common limiters on uniform meshes. In multiple dimensions we analyze the monotonicity region of the gradient vector and show that the multidimensional limiting problem may be cast as the solution of a linear programming problem. For some special cases we present a new directional limiting formulation that preserves linear solutions in multiple dimensions on irregular grids. Computational results using model problems and complex three-dimensional examples are presented, demonstrating accuracy, monotonicity and robustness.

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.

Emotional Reactivity and Regulation in Anxious and Non-anxious Youth: A Cell-Phone Ecological Momentary Assessment Study

PubMed Central

Tan, Patricia Z.; Forbes, Erika E.; Dahl, Ronald E.; Ryan, Neal D.; Siegle, Greg J.; Ladouceur, Cecile D.; Silk, Jennifer S.

2011-01-01

Background Reviews have highlighted anxious youths’ affective disturbances, specifically, elevated negative emotions and reliance on ineffective emotion regulation strategies. However, no study has examined anxious youth’s emotional reactivity and regulation in real-world contexts. Methods This study utilized an ecological momentary assessment approach to compare real-world emotional experiences of 65 youth with generalized anxiety disorder, social anxiety disorder, or social phobia (ANX) and 65 age-matched healthy controls (CON), ages 9–13 years. Results Hierarchical linear models revealed that ANX reported higher levels of average past-hour peak intensity of nervous, sad, and upset emotions than CON youth but similar levels during momentary reports of current emotion. As expected, ANX youth reported more frequent physiological reactions in response to a negative event; however there were no group differences in how frequently they used cognitive-behavioral strategies. Avoidance, distraction, and problem-solving were associated with the down-regulation of all negative emotions except nervousness for both ANX and CON youth; however, group differences emerged for acceptance, rumination, and physiological responding. Conclusions In real-world contexts, ANX youth do not report higher levels of momentary negative emotions but do report heightened negative emotions in response to challenging events. Moreover, ANX youth report no differences in how frequently they use adaptive regulatory strategies but are more likely to have physiological responses to challenging events. They are also less effective at using some strategies to down-regulate negative emotion than CON youth. PMID:22176136

Compressed modes for variational problems in mathematics and physics

PubMed Central

Ozoliņš, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-01-01

This article describes a general formalism for obtaining spatially localized (“sparse”) solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger’s equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support (“compressed modes”). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. PMID:24170861

Compressed modes for variational problems in mathematics and physics.

PubMed

Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-11-12

This article describes a general formalism for obtaining spatially localized ("sparse") solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support ("compressed modes"). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size.

A Cross-Domain Collaborative Filtering Algorithm Based on Feature Construction and Locally Weighted Linear Regression

PubMed Central

Jiang, Feng; Han, Ji-zhong

2018-01-01

Cross-domain collaborative filtering (CDCF) solves the sparsity problem by transferring rating knowledge from auxiliary domains. Obviously, different auxiliary domains have different importance to the target domain. However, previous works cannot evaluate effectively the significance of different auxiliary domains. To overcome this drawback, we propose a cross-domain collaborative filtering algorithm based on Feature Construction and Locally Weighted Linear Regression (FCLWLR). We first construct features in different domains and use these features to represent different auxiliary domains. Thus the weight computation across different domains can be converted as the weight computation across different features. Then we combine the features in the target domain and in the auxiliary domains together and convert the cross-domain recommendation problem into a regression problem. Finally, we employ a Locally Weighted Linear Regression (LWLR) model to solve the regression problem. As LWLR is a nonparametric regression method, it can effectively avoid underfitting or overfitting problem occurring in parametric regression methods. We conduct extensive experiments to show that the proposed FCLWLR algorithm is effective in addressing the data sparsity problem by transferring the useful knowledge from the auxiliary domains, as compared to many state-of-the-art single-domain or cross-domain CF methods. PMID:29623088

A Cross-Domain Collaborative Filtering Algorithm Based on Feature Construction and Locally Weighted Linear Regression.

PubMed

Yu, Xu; Lin, Jun-Yu; Jiang, Feng; Du, Jun-Wei; Han, Ji-Zhong

2018-01-01

Cross-domain collaborative filtering (CDCF) solves the sparsity problem by transferring rating knowledge from auxiliary domains. Obviously, different auxiliary domains have different importance to the target domain. However, previous works cannot evaluate effectively the significance of different auxiliary domains. To overcome this drawback, we propose a cross-domain collaborative filtering algorithm based on Feature Construction and Locally Weighted Linear Regression (FCLWLR). We first construct features in different domains and use these features to represent different auxiliary domains. Thus the weight computation across different domains can be converted as the weight computation across different features. Then we combine the features in the target domain and in the auxiliary domains together and convert the cross-domain recommendation problem into a regression problem. Finally, we employ a Locally Weighted Linear Regression (LWLR) model to solve the regression problem. As LWLR is a nonparametric regression method, it can effectively avoid underfitting or overfitting problem occurring in parametric regression methods. We conduct extensive experiments to show that the proposed FCLWLR algorithm is effective in addressing the data sparsity problem by transferring the useful knowledge from the auxiliary domains, as compared to many state-of-the-art single-domain or cross-domain CF methods.

Robust L1-norm two-dimensional linear discriminant analysis.

PubMed

Li, Chun-Na; Shao, Yuan-Hai; Deng, Nai-Yang

2015-05-01

In this paper, we propose an L1-norm two-dimensional linear discriminant analysis (L1-2DLDA) with robust performance. Different from the conventional two-dimensional linear discriminant analysis with L2-norm (L2-2DLDA), where the optimization problem is transferred to a generalized eigenvalue problem, the optimization problem in our L1-2DLDA is solved by a simple justifiable iterative technique, and its convergence is guaranteed. Compared with L2-2DLDA, our L1-2DLDA is more robust to outliers and noises since the L1-norm is used. This is supported by our preliminary experiments on toy example and face datasets, which show the improvement of our L1-2DLDA over L2-2DLDA. Copyright © 2015 Elsevier Ltd. All rights reserved.

Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

NASA Astrophysics Data System (ADS)

Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.

2012-11-01

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

NASA Technical Reports Server (NTRS)

Cheyney, H., III; Arking, A.

1976-01-01

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

Comparison of two-concentration with multi-concentration linear regressions: Retrospective data analysis of multiple regulated LC-MS bioanalytical projects.

PubMed

Musuku, Adrien; Tan, Aimin; Awaiye, Kayode; Trabelsi, Fethi

2013-09-01

Linear calibration is usually performed using eight to ten calibration concentration levels in regulated LC-MS bioanalysis because a minimum of six are specified in regulatory guidelines. However, we have previously reported that two-concentration linear calibration is as reliable as or even better than using multiple concentrations. The purpose of this research is to compare two-concentration with multiple-concentration linear calibration through retrospective data analysis of multiple bioanalytical projects that were conducted in an independent regulated bioanalytical laboratory. A total of 12 bioanalytical projects were randomly selected: two validations and two studies for each of the three most commonly used types of sample extraction methods (protein precipitation, liquid-liquid extraction, solid-phase extraction). When the existing data were retrospectively linearly regressed using only the lowest and the highest concentration levels, no extra batch failure/QC rejection was observed and the differences in accuracy and precision between the original multi-concentration regression and the new two-concentration linear regression are negligible. Specifically, the differences in overall mean apparent bias (square root of mean individual bias squares) are within the ranges of -0.3% to 0.7% and 0.1-0.7% for the validations and studies, respectively. The differences in mean QC concentrations are within the ranges of -0.6% to 1.8% and -0.8% to 2.5% for the validations and studies, respectively. The differences in %CV are within the ranges of -0.7% to 0.9% and -0.3% to 0.6% for the validations and studies, respectively. The average differences in study sample concentrations are within the range of -0.8% to 2.3%. With two-concentration linear regression, an average of 13% of time and cost could have been saved for each batch together with 53% of saving in the lead-in for each project (the preparation of working standard solutions, spiking, and aliquoting). Furthermore, examples are given as how to evaluate the linearity over the entire concentration range when only two concentration levels are used for linear regression. To conclude, two-concentration linear regression is accurate and robust enough for routine use in regulated LC-MS bioanalysis and it significantly saves time and cost as well. Copyright © 2013 Elsevier B.V. All rights reserved.

Associations of Students' Beliefs with Self-Regulated Problem Solving in College Algebra

ERIC Educational Resources Information Center

Cifarelli, Victor; Goodson-Espy, Tracy; Chae, Jeong-Lim

2010-01-01

This paper reports results from a study of self-regulated problem solving actions of students enrolled in College Algebra (N = 139). The study examined the associations between the expressed mathematical beliefs of students and the students' self-regulated actions in solving mathematics problems. The research questions are: (a) What are some…

Numerical solution of system of boundary value problems using B-spline with free parameter

NASA Astrophysics Data System (ADS)

Gupta, Yogesh

2017-01-01

This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.

A Mixed-Integer Linear Programming Problem which is Efficiently Solvable.

DTIC Science & Technology

1987-10-01

INTEGER LINEAR PROGRAMMING PROBLEM WHICH IS EFFICIENTLY SOLVABLE 12. PERSONAL AUTHOR(S) Leiserson, Charles, and Saxe, James B. 13a. TYPE OF REPORT j13b TIME...ger prongramn rg versions or the problem is not ac’hievable in genieral for sparse inistancves of’ P rolem(r Mi. Th le remrai nder or thris paper is...rClazes c:oIh edge (i,I*) by comlpli urg +- rnirr(z 3, ,x + a,j). A sirnI) le analysis (11 vto Nei [131 indicates why whe Iellinan-Ford algorithm works

Feedback linearization of singularly perturbed systems based on canonical similarity transformations

NASA Astrophysics Data System (ADS)

Kabanov, A. A.

2018-05-01

This paper discusses the problem of feedback linearization of a singularly perturbed system in a state-dependent coefficient form. The result is based on the introduction of a canonical similarity transformation. The transformation matrix is constructed from separate blocks for fast and slow part of an original singularly perturbed system. The transformed singular perturbed system has a linear canonical form that significantly simplifies a control design problem. Proposed similarity transformation allows accomplishing linearization of the system without considering the virtual output (as it is needed for normal form method), a technique of a transition from phase coordinates of the transformed system to state variables of the original system is simpler. The application of the proposed approach is illustrated through example.

Algorithms for sorting unsigned linear genomes by the DCJ operations.

PubMed

Jiang, Haitao; Zhu, Binhai; Zhu, Daming

2011-02-01

The double cut and join operation (abbreviated as DCJ) has been extensively used for genomic rearrangement. Although the DCJ distance between signed genomes with both linear and circular (uni- and multi-) chromosomes is well studied, the only known result for the NP-complete unsigned DCJ distance problem is an approximation algorithm for unsigned linear unichromosomal genomes. In this article, we study the problem of computing the DCJ distance on two unsigned linear multichromosomal genomes (abbreviated as UDCJ). We devise a 1.5-approximation algorithm for UDCJ by exploiting the distance formula for signed genomes. In addition, we show that UDCJ admits a weak kernel of size 2k and hence an FPT algorithm running in O(2(2k)n) time.

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

NASA Technical Reports Server (NTRS)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

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.

Linear quadratic regulators with eigenvalue placement in a specified region

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar

1988-01-01

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at + or - pi/2k (k = 2 or 3) from the negative real axis with a sector angle of pi/2 or less, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. The design method is mainly based on the solution of a linear matrix Liapunov equation, and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.

Correction for spatial averaging in laser speckle contrast analysis

PubMed Central

Thompson, Oliver; Andrews, Michael; Hirst, Evan

2011-01-01

Practical laser speckle contrast analysis systems face a problem of spatial averaging of speckles, due to the pixel size in the cameras used. Existing practice is to use a system factor in speckle contrast analysis to account for spatial averaging. The linearity of the system factor correction has not previously been confirmed. The problem of spatial averaging is illustrated using computer simulation of time-integrated dynamic speckle, and the linearity of the correction confirmed using both computer simulation and experimental results. The valid linear correction allows various useful compromises in the system design. PMID:21483623

The numerical solution of linear multi-term fractional differential equations: systems of equations

NASA Astrophysics Data System (ADS)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

Model checking for linear temporal logic: An efficient implementation

NASA Technical Reports Server (NTRS)

Sherman, Rivi; Pnueli, Amir

1990-01-01

This report provides evidence to support the claim that model checking for linear temporal logic (LTL) is practically efficient. Two implementations of a linear temporal logic model checker is described. One is based on transforming the model checking problem into a satisfiability problem; the other checks an LTL formula for a finite model by computing the cross-product of the finite state transition graph of the program with a structure containing all possible models for the property. An experiment was done with a set of mutual exclusion algorithms and tested safety and liveness under fairness for these algorithms.

48 CFR 2929.101 - Resolving tax problems.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 48 Federal Acquisition Regulations System 7 2010-10-01 2010-10-01 false Resolving tax problems. 2929.101 Section 2929.101 Federal Acquisition Regulations System DEPARTMENT OF LABOR GENERAL CONTRACTING REQUIREMENTS TAXES General 2929.101 Resolving tax problems. Contract tax problems or questions...

Lyapunov stability and its application to systems of ordinary differential equations

NASA Technical Reports Server (NTRS)

Kennedy, E. W.

1979-01-01

An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.

Some Issues about the Introduction of First Concepts in Linear Algebra during Tutorial Sessions at the Beginning of University

ERIC Educational Resources Information Center

Grenier-Boley, Nicolas

2014-01-01

Certain mathematical concepts were not introduced to solve a specific open problem but rather to solve different problems with the same tools in an economic formal way or to unify several approaches: such concepts, as some of those of linear algebra, are presumably difficult to introduce to students as they are potentially interwoven with many…

Extended Decentralized Linear-Quadratic-Gaussian Control

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2000-01-01

A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.

An automated system for reduction of the firm's employees under maximal overall efficiency

NASA Astrophysics Data System (ADS)

Yonchev, Yoncho; Nikolov, Simeon; Baeva, Silvia

2012-11-01

Achieving maximal overall efficiency is a priority in all companies. This problem is formulated as a knap-sack problem and afterwards as a linear assignment problem. An automated system is created for solving of this problem.

Analysis of junior high school students' attempt to solve a linear inequality problem

NASA Astrophysics Data System (ADS)

Taqiyuddin, Muhammad; Sumiaty, Encum; Jupri, Al

2017-08-01

Linear inequality is one of fundamental subjects within junior high school mathematics curricula. Several studies have been conducted to asses students' perform on linear inequality. However, it can hardly be found that linear inequality problems are in the form of "ax + b < dx + e" with "a, d ≠ 0", and "a ≠ d" as it can be seen on the textbook used by Indonesian students and several studies. This condition leads to the research questions concerning students' attempt on solving a simple linear inequality problem in this form. In order to do so, the written test was administered to 58 students from two schools in Bandung followed by interviews. The other sources of the data are from teachers' interview and mathematics books used by students. After that, the constant comparative method was used to analyse the data. The result shows that the majority approached the question by doing algebraic operations. Interestingly, most of them did it incorrectly. In contrast, algebraic operations were correctly used by some of them. Moreover, the others performed expected-numbers solution, rewriting the question, translating the inequality into words, and blank answer. Furthermore, we found that there is no one who was conscious of the existence of all-numbers solution. It was found that this condition is reasonably due to how little the learning components concern about why a procedure of solving a linear inequality works and possibilities of linear inequality solution.

Individualized Math Problems in Simple Equations. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require solution of linear equations, systems…

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions.

PubMed

Liu, Qingshan; Wang, Jun

2011-04-01

This paper presents a one-layer recurrent neural network for solving a class of constrained nonsmooth optimization problems with piecewise-linear objective functions. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter in the model. The number of neurons in the neural network is the same as the number of decision variables of the optimization problem. Compared with existing neural networks for optimization, the proposed neural network has a couple of salient features such as finite-time convergence and a low model complexity. Specific models for two important special cases, namely, linear programming and nonsmooth optimization, are also presented. In addition, applications to the shortest path problem and constrained least absolute deviation problem are discussed with simulation results to demonstrate the effectiveness and characteristics of the proposed neural network.

A geometric approach to failure detection and identification in linear systems

NASA Technical Reports Server (NTRS)

Massoumnia, M. A.

1986-01-01

Using concepts of (C,A)-invariant and unobservability (complementary observability) subspaces, a geometric formulation of the failure detection and identification filter problem is stated. Using these geometric concepts, it is shown that it is possible to design a causal linear time-invariant processor that can be used to detect and uniquely identify a component failure in a linear time-invariant system, assuming: (1) The components can fail simultaneously, and (2) The components can fail only one at a time. In addition, a geometric formulation of Beard's failure detection filter problem is stated. This new formulation completely clarifies of output separability and mutual detectability introduced by Beard and also exploits the dual relationship between a restricted version of the failure detection and identification problem and the control decoupling problem. Moreover, the frequency domain interpretation of the results is used to relate the concepts of failure sensitive observers with the generalized parity relations introduced by Chow. This interpretation unifies the various failure detection and identification concepts and design procedures.

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

DOE PAGES

Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...

2012-01-01

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less

The quasi-optimality criterion in the linear functional strategy

NASA Astrophysics Data System (ADS)

Kindermann, Stefan; Pereverzyev, Sergiy, Jr.; Pilipenko, Andrey

2018-07-01

The linear functional strategy for the regularization of inverse problems is considered. For selecting the regularization parameter therein, we propose the heuristic quasi-optimality principle and some modifications including the smoothness of the linear functionals. We prove convergence rates for the linear functional strategy with these heuristic rules taking into account the smoothness of the solution and the functionals and imposing a structural condition on the noise. Furthermore, we study these noise conditions in both a deterministic and stochastic setup and verify that for mildly-ill-posed problems and Gaussian noise, these conditions are satisfied almost surely, where on the contrary, in the severely-ill-posed case and in a similar setup, the corresponding noise condition fails to hold. Moreover, we propose an aggregation method for adaptively optimizing the parameter choice rule by making use of improved rates for linear functionals. Numerical results indicate that this method yields better results than the standard heuristic rule.

Asymptotic Linear Spectral Statistics for Spiked Hermitian Random Matrices

NASA Astrophysics Data System (ADS)

Passemier, Damien; McKay, Matthew R.; Chen, Yang

2015-07-01

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked correlation), non-central Wishart with rank-one non-centrality, and a related class of non-central matrices. For a generic linear statistic, we derive simple and explicit CLT expressions as the matrix dimensions grow large. For all three ensembles under consideration, we find that the primary effect of the spike is to introduce an correction term to the asymptotic mean of the linear spectral statistic, which we characterize with simple formulas. The utility of our proposed framework is demonstrated through application to three different linear statistics problems: the classical likelihood ratio test for a population covariance, the capacity analysis of multi-antenna wireless communication systems with a line-of-sight transmission path, and a classical multiple sample significance testing problem.

A memory structure adapted simulated annealing algorithm for a green vehicle routing problem.

PubMed

Küçükoğlu, İlker; Ene, Seval; Aksoy, Aslı; Öztürk, Nursel

2015-03-01

Currently, reduction of carbon dioxide (CO2) emissions and fuel consumption has become a critical environmental problem and has attracted the attention of both academia and the industrial sector. Government regulations and customer demands are making environmental responsibility an increasingly important factor in overall supply chain operations. Within these operations, transportation has the most hazardous effects on the environment, i.e., CO2 emissions, fuel consumption, noise and toxic effects on the ecosystem. This study aims to construct vehicle routes with time windows that minimize the total fuel consumption and CO2 emissions. The green vehicle routing problem with time windows (G-VRPTW) is formulated using a mixed integer linear programming model. A memory structure adapted simulated annealing (MSA-SA) meta-heuristic algorithm is constructed due to the high complexity of the proposed problem and long solution times for practical applications. The proposed models are integrated with a fuel consumption and CO2 emissions calculation algorithm that considers the vehicle technical specifications, vehicle load, and transportation distance in a green supply chain environment. The proposed models are validated using well-known instances with different numbers of customers. The computational results indicate that the MSA-SA heuristic is capable of obtaining good G-VRPTW solutions within a reasonable amount of time by providing reductions in fuel consumption and CO2 emissions.

The Use of Efficient Broadcast Protocols in Asynchronous Distributed Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Schmuck, Frank Bernhard

1988-01-01

Reliable broadcast protocols are important tools in distributed and fault-tolerant programming. They are useful for sharing information and for maintaining replicated data in a distributed system. However, a wide range of such protocols has been proposed. These protocols differ in their fault tolerance and delivery ordering characteristics. There is a tradeoff between the cost of a broadcast protocol and how much ordering it provides. It is, therefore, desirable to employ protocols that support only a low degree of ordering whenever possible. This dissertation presents techniques for deciding how strongly ordered a protocol is necessary to solve a given application problem. It is shown that there are two distinct classes of application problems: problems that can be solved with efficient, asynchronous protocols, and problems that require global ordering. The concept of a linearization function that maps partially ordered sets of events to totally ordered histories is introduced. How to construct an asynchronous implementation that solves a given problem if a linearization function for it can be found is shown. It is proved that in general the question of whether a problem has an asynchronous solution is undecidable. Hence there exists no general algorithm that would automatically construct a suitable linearization function for a given problem. Therefore, an important subclass of problems that have certain commutativity properties are considered. Techniques for constructing asynchronous implementations for this class are presented. These techniques are useful for constructing efficient asynchronous implementations for a broad range of practical problems.

Drinking motives mediate emotion regulation difficulties and problem drinking in college students.

PubMed

Aurora, Pallavi; Klanecky, Alicia K

2016-05-01

Problem drinking in college places students at an increased risk for a wealth of negative consequences including alcohol use disorders. Most research has shown that greater emotion regulation difficulties are related to increased problem drinking, and studies generally assume that drinking is motivated by efforts to cope with or enhance affective experiences. However, there is a lack of research specifically testing this assumption. The current study sought to examine the mediating potential of drinking motives, specifically coping and enhancement, on the relationship between emotion regulation and problem drinking. College participants (N = 200) completed an online survey, consisting of a battery of measures assessing alcohol use behaviors and related variables. Coping drinking motives fully mediated the emotion regulation/problem drinking relationship, and enhancement motives partially mediated this relationship. Exploratory analyses indicated that all four drinking motives (i.e. coping, enhancement, social, and conformity) simultaneously mediated the relationship between emotion regulation and quantity/frequency of alcohol use. However, only coping and enhancement significantly mediated the relationship between emotion regulation and alcohol-related consequences (e.g. alcohol dependence symptoms, alcohol-related injuries). The current results offer direction for potentially modifying brief alcohol interventions in efforts to reduce students' engagement in problem drinking behaviors. For example, interventions might incorporate information on the risks of using alcohol as a means of emotion regulation and offer alternative emotion regulation strategies.

Economic analysis of a Japanese air pollution regulation : an optimal retirement problem under vehicle type regulation in the NOx-particulate matter law

DOT National Transportation Integrated Search

2008-06-01

This paper empirically examines the vehicle type regulation that was introduced under the : Automobile Nitrogen OxidesParticulate Matter Law to mitigate air pollution problems in Japanese metropolitan areas. The vehicle type regulation effectively...

An Inquiry-Oriented Approach to Span and Linear Independence: The Case of the Magic Carpet Ride Sequence

ERIC Educational Resources Information Center

Wawro, Megan; Rasmussen, Chris; Zandieh, Michelle; Sweeney, George Franklin; Larson, Christine

2012-01-01

In this paper we present an innovative instructional sequence for an introductory linear algebra course that supports students' reinvention of the concepts of span, linear dependence, and linear independence. Referred to as the Magic Carpet Ride sequence, the problems begin with an imaginary scenario that allows students to build rich imagery and…

Comparison of the Tangent Linear Properties of Tracer Transport Schemes Applied to Geophysical Problems.

NASA Technical Reports Server (NTRS)

Kent, James; Holdaway, Daniel

2015-01-01

A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.

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.

Solving deterministic non-linear programming problem using Hopfield artificial neural network and genetic programming techniques

NASA Astrophysics Data System (ADS)

Vasant, P.; Ganesan, T.; Elamvazuthi, I.

2012-11-01

A fairly reasonable result was obtained for non-linear engineering problems using the optimization techniques such as neural network, genetic algorithms, and fuzzy logic independently in the past. Increasingly, hybrid techniques are being used to solve the non-linear problems to obtain better output. This paper discusses the use of neuro-genetic hybrid technique to optimize the geological structure mapping which is known as seismic survey. It involves the minimization of objective function subject to the requirement of geophysical and operational constraints. In this work, the optimization was initially performed using genetic programming, and followed by hybrid neuro-genetic programming approaches. Comparative studies and analysis were then carried out on the optimized results. The results indicate that the hybrid neuro-genetic hybrid technique produced better results compared to the stand-alone genetic programming method.

Linear Programming across the Curriculum

ERIC Educational Resources Information Center

Yoder, S. Elizabeth; Kurz, M. Elizabeth

2015-01-01

Linear programming (LP) is taught in different departments across college campuses with engineering and management curricula. Modeling an LP problem is taught in every linear programming class. As faculty teaching in Engineering and Management departments, the depth to which teachers should expect students to master this particular type of…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au; Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem ofmore » optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.« less

Multicriterion problem of allocation of resources in the heterogeneous distributed information processing systems

NASA Astrophysics Data System (ADS)

Antamoshkin, O. A.; Kilochitskaya, T. R.; Ontuzheva, G. A.; Stupina, A. A.; Tynchenko, V. S.

2018-05-01

This study reviews the problem of allocation of resources in the heterogeneous distributed information processing systems, which may be formalized in the form of a multicriterion multi-index problem with the linear constraints of the transport type. The algorithms for solution of this problem suggest a search for the entire set of Pareto-optimal solutions. For some classes of hierarchical systems, it is possible to significantly speed up the procedure of verification of a system of linear algebraic inequalities for consistency due to the reducibility of them to the stream models or the application of other solution schemes (for strongly connected structures) that take into account the specifics of the hierarchies under consideration.

Very Efficient High-order Hyperbolic Schemes for Time-dependent Advection Diffusion Problems: Third-, Fourth-, and Sixth-order

DTIC Science & Technology

2014-07-07

boundary condition (x ¼ 7p =2; j ¼ 2p; U ¼ 1; m ¼ 1) on N ¼ 10 uniform nodes (Dt ¼ 0:01.) Table 10 Unsteady linear advection–diffusion problem with periodic...500 3rd 55 2 4th 55 2 6th 55 2 1000 3rd 116 2 4th 116 2 6th 116 2 Table 11 Unsteady linear advection–diffusion problem with oscillatory BC (x ¼ 7p =2; a...dependent problem with oscillatory BC (x ¼ 7p =2; a ¼ 1.) using the third-order RD-GT scheme with the BDF3 time discretization. Number of nodes Dt (BDF3

Modeling and simulation of different and representative engineering problems using Network Simulation Method

PubMed Central

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model. PMID:29518121

Modeling and simulation of different and representative engineering problems using Network Simulation Method.

PubMed

Sánchez-Pérez, J F; Marín, F; Morales, J L; Cánovas, M; Alhama, F

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model.

A Conforming Multigrid Method for the Pure Traction Problem of Linear Elasticity: Mixed Formulation

NASA Technical Reports Server (NTRS)

Lee, Chang-Ock

1996-01-01

A multigrid method using conforming P-1 finite element is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.

An algorithm for the split-feasibility problems with application to the split-equality problem.

PubMed

Chuang, Chih-Sheng; Chen, Chi-Ming

2017-01-01

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

Early Childhood Profiles of Sleep Problems and Self-Regulation Predict Later School Adjustment

ERIC Educational Resources Information Center

Williams, Kate E.; Nicholson, Jan M.; Walker, Sue; Berthelsen, Donna

2016-01-01

Background: Children's sleep problems and self-regulation problems have been independently associated with poorer adjustment to school, but there has been limited exploration of longitudinal early childhood profiles that include both indicators. Aims: This study explores the normative developmental pathway for sleep problems and self-regulation…

Optical systolic solutions of linear algebraic equations

NASA Technical Reports Server (NTRS)

Neuman, C. P.; Casasent, D.

1984-01-01

The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

A linear programming approach to max-sum problem: a review.

PubMed

Werner, Tomás

2007-07-01

The max-sum labeling problem, defined as maximizing a sum of binary (i.e., pairwise) functions of discrete variables, is a general NP-hard optimization problem with many applications, such as computing the MAP configuration of a Markov random field. We review a not widely known approach to the problem, developed by Ukrainian researchers Schlesinger et al. in 1976, and show how it contributes to recent results, most importantly, those on the convex combination of trees and tree-reweighted max-product. In particular, we review Schlesinger et al.'s upper bound on the max-sum criterion, its minimization by equivalent transformations, its relation to the constraint satisfaction problem, the fact that this minimization is dual to a linear programming relaxation of the original problem, and the three kinds of consistency necessary for optimality of the upper bound. We revisit problems with Boolean variables and supermodular problems. We describe two algorithms for decreasing the upper bound. We present an example application for structural image analysis.

A Linear Empirical Model of Self-Regulation on Flourishing, Health, Procrastination, and Achievement, Among University Students

PubMed Central

Garzón-Umerenkova, Angélica; de la Fuente, Jesús; Amate, Jorge; Paoloni, Paola V.; Fadda, Salvatore; Pérez, Javier Fiz

2018-01-01

This research aimed to analyze the linear bivariate correlation and structural relations between self-regulation -as a central construct-, with flow, health, procrastination and academic performance, in an academic context. A total of 363 college students took part, 101 men (27.8%) and 262 women (72.2%). Participants had an average age of 22 years and were between the first and fifth year of studies. They were from five different programs and two universities in Bogotá city (Colombia). A validated ad hoc questionnaire of physical and psychological health was applied along with a battery of tests to measure self-regulation, procrastination, and flourishing. To establish an association relationship, Pearson bivariate correlations were performed using SPSS software (v. 22.0), and structural relationship predictive analysis was performed using an SEM on AMOS software (v. 22.0). Regarding this linear association, it was established that (1) self-regulation has a significant positive association on flourishing and overall health, and a negative effect on procrastination. Regarding the structural relation, it confirmed that (2) self-regulation is a direct and positive predictor of flourishing and health; (3) self-regulation predicts procrastination directly and negatively, and academic performance indirectly and positively; and (4) age and gender have a prediction effect on the analyzed variables. Implications, limitations and future research scope are discussed. PMID:29706922

A Linear Empirical Model of Self-Regulation on Flourishing, Health, Procrastination, and Achievement, Among University Students.

PubMed

Garzón-Umerenkova, Angélica; de la Fuente, Jesús; Amate, Jorge; Paoloni, Paola V; Fadda, Salvatore; Pérez, Javier Fiz

2018-01-01

This research aimed to analyze the linear bivariate correlation and structural relations between self-regulation -as a central construct-, with flow, health, procrastination and academic performance, in an academic context. A total of 363 college students took part, 101 men (27.8%) and 262 women (72.2%). Participants had an average age of 22 years and were between the first and fifth year of studies. They were from five different programs and two universities in Bogotá city (Colombia). A validated ad hoc questionnaire of physical and psychological health was applied along with a battery of tests to measure self-regulation, procrastination, and flourishing. To establish an association relationship, Pearson bivariate correlations were performed using SPSS software (v. 22.0), and structural relationship predictive analysis was performed using an SEM on AMOS software (v. 22.0). Regarding this linear association, it was established that (1) self-regulation has a significant positive association on flourishing and overall health, and a negative effect on procrastination. Regarding the structural relation, it confirmed that (2) self-regulation is a direct and positive predictor of flourishing and health; (3) self-regulation predicts procrastination directly and negatively, and academic performance indirectly and positively; and (4) age and gender have a prediction effect on the analyzed variables. Implications, limitations and future research scope are discussed.

Teaching Linear Algebra: Must the Fog Always Roll In?

ERIC Educational Resources Information Center

Carlson, David

1993-01-01

Proposes methods to teach the more difficult concepts of linear algebra. Examines features of the Linear Algebra Curriculum Study Group Core Syllabus, and presents problems from the core syllabus that utilize the mathematical process skills of making conjectures, proving the results, and communicating the results to colleagues. Presents five…

Artificial Intelligence Methodologies in Flight Related Differential Game, Control and Optimization Problems

DTIC Science & Technology

1993-01-31

28 Controllability and Observability ............................. .32 ’ Separation of Learning and Control ... ... 37 Linearization via... Linearization via Transformation of Coordinates and Nonlinear Fedlback . .1 Main Result ......... .............................. 13 Discussion...9 2.1 Basic Structure of a NLM........................ .󈧟 2.2 General Structure of NNLM .......................... .28 2.3 Linear System

Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem

NASA Astrophysics Data System (ADS)

Lebovka, Nikolai I.; Tarasevich, Yuri Yu.; Vygornitskii, Nikolai V.

2018-02-01

The vertical drying of a two-dimensional colloidal film containing zero-thickness sticks (lines) was studied by means of kinetic Monte Carlo (MC) simulations. The continuous two-dimensional problem for both the positions and orientations was considered. The initial state before drying was produced using a model of random sequential adsorption with isotropic orientations of the sticks. During the evaporation, an upper interface falls with a linear velocity in the vertical direction, and the sticks undergo translational and rotational Brownian motions. The MC simulations were run at different initial number concentrations (the numbers of sticks per unit area), pi, and solvent evaporation rates, u . For completely dried films, the spatial distributions of the sticks, the order parameters, and the electrical conductivities of the films in both the horizontal, x , and vertical, y , directions were examined. Significant evaporation-driven self-assembly and stratification of the sticks in the vertical direction was observed. The extent of stratification increased with increasing values of u . The anisotropy of the electrical conductivity of the film can be finely regulated by changes in the values of pi and u .

Analysis of explicit model predictive control for path-following control

PubMed Central

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration. PMID:29534080

Analysis of explicit model predictive control for path-following control.

PubMed

Lee, Junho; Chang, Hyuk-Jun

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration.

Coping with post-war mental health problems among survivors of violence in Northern Uganda: Findings from the WAYS study.

PubMed

Amone-P'Olak, Kennedy; Omech, Bernard

2018-05-01

Cognitive emotion regulation strategies and mental health problems were assessed in a sample of war-affected youth in Northern Uganda. Univariable and multivariable regression models were fitted to assess the influence of CERS on mental health problems. Maladaptive cognitive emotion regulation strategies (e.g., rumination) were significantly associated with more mental health problems while adaptive cognitive emotion regulation strategies (e.g., putting into perspective) were associated with reporting fewer symptoms of mental health problems. The youth with significant scores on mental health problems (scores ≥ 85th percentile) reported more frequent use of maladaptive than adaptive strategies. Interventions to reduce mental health problems should focus on enhancing the use of adaptive strategies.

Computation of the shock-wave boundary layer interaction with flow separation

NASA Technical Reports Server (NTRS)

Ardonceau, P.; Alziary, T.; Aymer, D.

1980-01-01

The boundary layer concept is used to describe the flow near the wall. The external flow is approximated by a pressure displacement relationship (tangent wedge in linearized supersonic flow). The boundary layer equations are solved in finite difference form and the question of the presence and unicity of the solution is considered for the direct problem (assumed pressure) or converse problem (assumed displacement thickness, friction ratio). The coupling algorithm presented implicitly processes the downstream boundary condition necessary to correctly define the interacting boundary layer problem. The algorithm uses a Newton linearization technique to provide a fast convergence.

Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeff Linderoth

2011-11-06

the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.

A model for managing sources of groundwater pollution

USGS Publications Warehouse

Gorelick, Steven M.

1982-01-01

The waste disposal capacity of a groundwater system can be maximized while maintaining water quality at specified locations by using a groundwater pollutant source management model that is based upon linear programing and numerical simulation. The decision variables of the management model are solute waste disposal rates at various facilities distributed over space. A concentration response matrix is used in the management model to describe transient solute transport and is developed using the U.S. Geological Survey solute transport simulation model. The management model was applied to a complex hypothetical groundwater system. Large-scale management models were formulated as dual linear programing problems to reduce numerical difficulties and computation time. Linear programing problems were solved using a numerically stable, available code. Optimal solutions to problems with successively longer management time horizons indicated that disposal schedules at some sites are relatively independent of the number of disposal periods. Optimal waste disposal schedules exhibited pulsing rather than constant disposal rates. Sensitivity analysis using parametric linear programing showed that a sharp reduction in total waste disposal potential occurs if disposal rates at any site are increased beyond their optimal values.

Analytical Solution of Steady State Equations for Chemical Reaction Networks with Bilinear Rate Laws

PubMed Central

Halász, Ádám M.; Lai, Hong-Jian; McCabe, Meghan M.; Radhakrishnan, Krishnan; Edwards, Jeremy S.

2014-01-01

True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher dimensional space. We show that the linearized version of the steady state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1. PMID:24334389

A binary linear programming formulation of the graph edit distance.

PubMed

Justice, Derek; Hero, Alfred

2006-08-01

A binary linear programming formulation of the graph edit distance for unweighted, undirected graphs with vertex attributes is derived and applied to a graph recognition problem. A general formulation for editing graphs is used to derive a graph edit distance that is proven to be a metric, provided the cost function for individual edit operations is a metric. Then, a binary linear program is developed for computing this graph edit distance, and polynomial time methods for determining upper and lower bounds on the solution of the binary program are derived by applying solution methods for standard linear programming and the assignment problem. A recognition problem of comparing a sample input graph to a database of known prototype graphs in the context of a chemical information system is presented as an application of the new method. The costs associated with various edit operations are chosen by using a minimum normalized variance criterion applied to pairwise distances between nearest neighbors in the database of prototypes. The new metric is shown to perform quite well in comparison to existing metrics when applied to a database of chemical graphs.

Human Performance on Hard Non-Euclidean Graph Problems: Vertex Cover

ERIC Educational Resources Information Center

Carruthers, Sarah; Masson, Michael E. J.; Stege, Ulrike

2012-01-01

Recent studies on a computationally hard visual optimization problem, the Traveling Salesperson Problem (TSP), indicate that humans are capable of finding close to optimal solutions in near-linear time. The current study is a preliminary step in investigating human performance on another hard problem, the Minimum Vertex Cover Problem, in which…

A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty

NASA Astrophysics Data System (ADS)

Tian, Wenli; Cao, Chengxuan

2017-03-01

A generalized interval fuzzy mixed integer programming model is proposed for the multimodal freight transportation problem under uncertainty, in which the optimal mode of transport and the optimal amount of each type of freight transported through each path need to be decided. For practical purposes, three mathematical methods, i.e. the interval ranking method, fuzzy linear programming method and linear weighted summation method, are applied to obtain equivalents of constraints and parameters, and then a fuzzy expected value model is presented. A heuristic algorithm based on a greedy criterion and the linear relaxation algorithm are designed to solve the model.

Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

NASA Astrophysics Data System (ADS)

Guo, Sangang

2017-09-01

There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Some estimation formulae for continuous time-invariant linear systems

NASA Technical Reports Server (NTRS)

Bierman, G. J.; Sidhu, G. S.

1975-01-01

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Insights into linearized rotor dynamics, Part 2

NASA Astrophysics Data System (ADS)

Adams, M. L.

1987-01-01

This paper builds upon its 1981 namesake to extend and propose ideas which focus on some unique problems at the current center of interest in rotor vibration technology. These problems pertain to the ongoing extension of the linearized rotor-bearing model to include other rotor-stator interactive forces such as seals and turbomachinery stages. A unified linear model is proposed and contains an axiom which requires the coefficient matrix of the highest order term, in an interactive force model, to be symmetric. The paper ends on a fundamental question, namely, the potential weakness inherent in the whole idea of mechanical impedance modeling of rotor-stator interactive fluid flow fields.

The research of radar target tracking observed information linear filter method

NASA Astrophysics Data System (ADS)

Chen, Zheng; Zhao, Xuanzhi; Zhang, Wen

2018-05-01

Aiming at the problems of low precision or even precision divergent is caused by nonlinear observation equation in radar target tracking, a new filtering algorithm is proposed in this paper. In this algorithm, local linearization is carried out on the observed data of the distance and angle respectively. Then the kalman filter is performed on the linearized data. After getting filtered data, a mapping operation will provide the posteriori estimation of target state. A large number of simulation results show that this algorithm can solve above problems effectively, and performance is better than the traditional filtering algorithm for nonlinear dynamic systems.

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1972-01-01

A sequential adaptive experimental design procedure for a related problem is studied. It is assumed that a finite set of potential linear models relating certain controlled variables to an observed variable is postulated, and that exactly one of these models is correct. The problem is to sequentially design most informative experiments so that the correct model equation can be determined with as little experimentation as possible. Discussion includes: structure of the linear models; prerequisite distribution theory; entropy functions and the Kullback-Leibler information function; the sequential decision procedure; and computer simulation results. An example of application is given.

Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jesus, Isaías Pereira de, E-mail: isaias@ufpi.edu.br

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

Computing eigenfunctions and eigenvalues of boundary-value problems with the orthogonal spectral renormalization method

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Musslimani, Ziad H.; Schwarz, Lukas; Wunner, Günter

2018-03-01

The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian PT -symmetric models.

Word Problems: A "Meme" for Our Times.

ERIC Educational Resources Information Center

Leamnson, Robert N.

1996-01-01

Discusses a novel approach to word problems that involves linear relationships between variables. Argues that working stepwise through intermediates is the way our minds actually work and therefore this should be used in solving word problems. (JRH)

Managing stress: the influence of gender, age and emotion regulation on coping among university students in Botswana

PubMed Central

Monteiro, Nicole M.; Balogun, Shyngle K.; Oratile, Kutlo N.

2014-01-01

This study focused on the influence of gender, age and emotion regulation on coping strategies among university students in Botswana. Sixty-four males and 64 females, ranging in age from 18 to 29 years completed the Difficulty in Emotion Regulation Scale and the Coping Strategy Inventory. Female students used wishful thinking and problem-focused disengagement more than male students; however, there were no other significant gender differences in coping strategies. Older students were more likely to use problem-solving, cognitive restructuring and express emotion coping strategies. In addition, problems in emotion regulation significantly predicted problem-and emotion-focused engagement, problem- and emotion-focused disengagement and coping strategies. There was a unique finding that non-acceptance of emotional responses, a type of emotion suppression, was positively correlated with problem solving, cognitive restructuring, expressing emotion, social support, problem avoidance and wishful thinking coping strategies. Cultural context and implications for student well-being and university support are discussed. PMID:24910491

A Novel Joint Problem of Routing, Scheduling, and Variable-Width Channel Allocation in WMNs

PubMed Central

Liu, Wan-Yu; Chou, Chun-Hung

2014-01-01

This paper investigates a novel joint problem of routing, scheduling, and channel allocation for single-radio multichannel wireless mesh networks in which multiple channel widths can be adjusted dynamically through a new software technology so that more concurrent transmissions and suppressed overlapping channel interference can be achieved. Although the previous works have studied this joint problem, their linear programming models for the problem were not incorporated with some delicate constraints. As a result, this paper first constructs a linear programming model with more practical concerns and then proposes a simulated annealing approach with a novel encoding mechanism, in which the configurations of multiple time slots are devised to characterize the dynamic transmission process. Experimental results show that our approach can find the same or similar solutions as the optimal solutions for smaller-scale problems and can efficiently find good-quality solutions for a variety of larger-scale problems. PMID:24982990

An improved risk-explicit interval linear programming model for pollution load allocation for watershed management.

PubMed

Xia, Bisheng; Qian, Xin; Yao, Hong

2017-11-01

Although the risk-explicit interval linear programming (REILP) model has solved the problem of having interval solutions, it has an equity problem, which can lead to unbalanced allocation between different decision variables. Therefore, an improved REILP model is proposed. This model adds an equity objective function and three constraint conditions to overcome this equity problem. In this case, pollution reduction is in proportion to pollutant load, which supports balanced development between different regional economies. The model is used to solve the problem of pollution load allocation in a small transboundary watershed. Compared with the REILP original model result, our model achieves equity between the upstream and downstream pollutant loads; it also overcomes the problem of greatest pollution reduction, where sources are nearest to the control section. The model provides a better solution to the problem of pollution load allocation than previous versions.

Solving a class of generalized fractional programming problems using the feasibility of linear programs.

PubMed

Shen, Peiping; Zhang, Tongli; Wang, Chunfeng

2017-01-01

This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.

Linear quadratic optimization for positive LTI system

NASA Astrophysics Data System (ADS)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

Emotion Regulation and Parent Co-Regulation in Children with Autism Spectrum Disorder

ERIC Educational Resources Information Center

Ting, Victoria; Weiss, Jonathan A.

2017-01-01

Children with autism spectrum disorder (ASD) often exhibit emotional problems, which can be associated with emotion regulation (ER) difficulties. Parent co-regulation is often associated with child ER and emotional problems, though little work has been done with reference to youth with ASD. This study investigated the association among parent…

Using block pulse functions for seismic vibration semi-active control of structures with MR dampers

NASA Astrophysics Data System (ADS)

Rahimi Gendeshmin, Saeed; Davarnia, Daniel

2018-03-01

This article applied the idea of block pulse functions in the semi-active control of structures. The BP functions give effective tools to approximate complex problems. The applied control algorithm has a major effect on the performance of the controlled system and the requirements of the control devices. In control problems, it is important to devise an accurate analytical technique with less computational cost. It is proved that the BP functions are fundamental tools in approximation problems which have been applied in disparate areas in last decades. This study focuses on the employment of BP functions in control algorithm concerning reduction the computational cost. Magneto-rheological (MR) dampers are one of the well-known semi-active tools that can be used to control the response of civil Structures during earthquake. For validation purposes, numerical simulations of a 5-story shear building frame with MR dampers are presented. The results of suggested method were compared with results obtained by controlling the frame by the optimal control method based on linear quadratic regulator theory. It can be seen from simulation results that the suggested method can be helpful in reducing seismic structural responses. Besides, this method has acceptable accuracy and is in agreement with optimal control method with less computational costs.

Problems Relating Mathematics and Science in the High School.

ERIC Educational Resources Information Center

Morrow, Richard; Beard, Earl

This document contains various science problems which require a mathematical solution. The problems are arranged under two general areas. The first (algebra I) contains biology, chemistry, and physics problems which require solutions related to linear equations, exponentials, and nonlinear equations. The second (algebra II) contains physics…

Information fusion based optimal control for large civil aircraft system.

PubMed

Zhen, Ziyang; Jiang, Ju; Wang, Xinhua; Gao, Chen

2015-03-01

Wind disturbance has a great influence on landing security of Large Civil Aircraft. Through simulation research and engineering experience, it can be found that PID control is not good enough to solve the problem of restraining the wind disturbance. This paper focuses on anti-wind attitude control for Large Civil Aircraft in landing phase. In order to improve the riding comfort and the flight security, an information fusion based optimal control strategy is presented to restrain the wind in landing phase for maintaining attitudes and airspeed. Data of Boeing707 is used to establish a nonlinear mode with total variables of Large Civil Aircraft, and then two linear models are obtained which are divided into longitudinal and lateral equations. Based on engineering experience, the longitudinal channel adopts PID control and C inner control to keep longitudinal attitude constant, and applies autothrottle system for keeping airspeed constant, while an information fusion based optimal regulator in the lateral control channel is designed to achieve lateral attitude holding. According to information fusion estimation, by fusing hard constraint information of system dynamic equations and the soft constraint information of performance index function, optimal estimation of the control sequence is derived. Based on this, an information fusion state regulator is deduced for discrete time linear system with disturbance. The simulation results of nonlinear model of aircraft indicate that the information fusion optimal control is better than traditional PID control, LQR control and LQR control with integral action, in anti-wind disturbance performance in the landing phase. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Optimal GENCO bidding strategy

NASA Astrophysics Data System (ADS)

Gao, Feng

Electricity industries worldwide are undergoing a period of profound upheaval. The conventional vertically integrated mechanism is being replaced by a competitive market environment. Generation companies have incentives to apply novel technologies to lower production costs, for example: Combined Cycle units. Economic dispatch with Combined Cycle units becomes a non-convex optimization problem, which is difficult if not impossible to solve by conventional methods. Several techniques are proposed here: Mixed Integer Linear Programming, a hybrid method, as well as Evolutionary Algorithms. Evolutionary Algorithms share a common mechanism, stochastic searching per generation. The stochastic property makes evolutionary algorithms robust and adaptive enough to solve a non-convex optimization problem. This research implements GA, EP, and PS algorithms for economic dispatch with Combined Cycle units, and makes a comparison with classical Mixed Integer Linear Programming. The electricity market equilibrium model not only helps Independent System Operator/Regulator analyze market performance and market power, but also provides Market Participants the ability to build optimal bidding strategies based on Microeconomics analysis. Supply Function Equilibrium (SFE) is attractive compared to traditional models. This research identifies a proper SFE model, which can be applied to a multiple period situation. The equilibrium condition using discrete time optimal control is then developed for fuel resource constraints. Finally, the research discusses the issues of multiple equilibria and mixed strategies, which are caused by the transmission network. Additionally, an advantage of the proposed model for merchant transmission planning is discussed. A market simulator is a valuable training and evaluation tool to assist sellers, buyers, and regulators to understand market performance and make better decisions. A traditional optimization model may not be enough to consider the distributed, large-scale, and complex energy market. This research compares the performance and searching paths of different artificial life techniques such as Genetic Algorithm (GA), Evolutionary Programming (EP), and Particle Swarm (PS), and look for a proper method to emulate Generation Companies' (GENCOs) bidding strategies. After deregulation, GENCOs face risk and uncertainty associated with the fast-changing market environment. A profit-based bidding decision support system is critical for GENCOs to keep a competitive position in the new environment. Most past research do not pay special attention to the piecewise staircase characteristic of generator offer curves. This research proposes an optimal bidding strategy based on Parametric Linear Programming. The proposed algorithm is able to handle actual piecewise staircase energy offer curves. The proposed method is then extended to incorporate incomplete information based on Decision Analysis. Finally, the author develops an optimal bidding tool (GenBidding) and applies it to the RTS96 test system.

The condition of regular degeneration for singularly perturbed systems of linear differential-difference equations.

NASA Technical Reports Server (NTRS)

Cooke, K. L.; Meyer, K. R.

1966-01-01

Extension of problem of singular perturbation for linear scalar constant coefficient differential- difference equation with single retardation to several retardations, noting degenerate equation solution

Dynamical theory of stability for elastic rods with nonlinear curvature and twist

NASA Technical Reports Server (NTRS)

Wauer, J.

1977-01-01

Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.

The Shock and Vibration Digest, Volume 18, Number 3

DTIC Science & Technology

1986-03-01

Linear Distributed Parameter Des., Proc. Intl. Symp., 11th ONR Naval Struc. Systems by Shifted Legendre Polynomial Func- Mech. Symp., Tucson, AZ, pp...University, Atlanta, Georgia nonlinear problems with elementary algebra . It J. Sound Vib., 102 (2), pp 247-257 (Sept 22, uses i = -1, the Pascal’s...eigenvalues specified. The optimal avoid failure due to resonance under the action control problem of a linear distributed parameter 0School of Mechanical

A globally convergent LCL method for nonlinear optimization.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Friedlander, M. P.; Saunders, M. A.; Mathematics and Computer Science

2005-01-01

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form 'minimize an augmented Lagrangian function subject to linearized constraints.' Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the well-known software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an optionmore » to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.« less

A monolithic Lagrangian approach for fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Ryzhakov, P. B.; Rossi, R.; Idelsohn, S. R.; Oñate, E.

2010-11-01

Current work presents a monolithic method for the solution of fluid-structure interaction problems involving flexible structures and free-surface flows. The technique presented is based upon the utilization of a Lagrangian description for both the fluid and the structure. A linear displacement-pressure interpolation pair is used for the fluid whereas the structure utilizes a standard displacement-based formulation. A slight fluid compressibility is assumed that allows to relate the mechanical pressure to the local volume variation. The method described features a global pressure condensation which in turn enables the definition of a purely displacement-based linear system of equations. A matrix-free technique is used for the solution of such linear system, leading to an efficient implementation. The result is a robust method which allows dealing with FSI problems involving arbitrary variations in the shape of the fluid domain. The method is completely free of spurious added-mass effects.

Using directed information for influence discovery in interconnected dynamical systems

NASA Astrophysics Data System (ADS)

Rao, Arvind; Hero, Alfred O.; States, David J.; Engel, James Douglas

2008-08-01

Structure discovery in non-linear dynamical systems is an important and challenging problem that arises in various applications such as computational neuroscience, econometrics, and biological network discovery. Each of these systems have multiple interacting variables and the key problem is the inference of the underlying structure of the systems (which variables are connected to which others) based on the output observations (such as multiple time trajectories of the variables). Since such applications demand the inference of directed relationships among variables in these non-linear systems, current methods that have a linear assumption on structure or yield undirected variable dependencies are insufficient. Hence, in this work, we present a methodology for structure discovery using an information-theoretic metric called directed time information (DTI). Using both synthetic dynamical systems as well as true biological datasets (kidney development and T-cell data), we demonstrate the utility of DTI in such problems.

Ultrahigh-Dimensional Multiclass Linear Discriminant Analysis by Pairwise Sure Independence Screening

PubMed Central

Pan, Rui; Wang, Hansheng; Li, Runze

2016-01-01

This paper is concerned with the problem of feature screening for multi-class linear discriminant analysis under ultrahigh dimensional setting. We allow the number of classes to be relatively large. As a result, the total number of relevant features is larger than usual. This makes the related classification problem much more challenging than the conventional one, where the number of classes is small (very often two). To solve the problem, we propose a novel pairwise sure independence screening method for linear discriminant analysis with an ultrahigh dimensional predictor. The proposed procedure is directly applicable to the situation with many classes. We further prove that the proposed method is screening consistent. Simulation studies are conducted to assess the finite sample performance of the new procedure. We also demonstrate the proposed methodology via an empirical analysis of a real life example on handwritten Chinese character recognition. PMID:28127109

Budgeted Interactive Learning

DTIC Science & Technology

2017-06-15

the methodology of reducing the online-algorithm-selecting problem as a contextual bandit problem, which is yet another interactive learning...KH2016a] Kuan-Hao Huang and Hsuan-Tien Lin. Linear upper confidence bound algorithm for contextual bandit problem with piled rewards. In Proceedings

LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

PubMed

Zhang, Huaguang; Feng, Tao; Liang, Hongjing; Luo, Yanhong

2017-03-01

In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.

An efficient variable projection formulation for separable nonlinear least squares problems.

PubMed

Gan, Min; Li, Han-Xiong

2014-05-01

We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time.

A Sparse Reconstruction Approach for Identifying Gene Regulatory Networks Using Steady-State Experiment Data

PubMed Central

Zhang, Wanhong; Zhou, Tong

2015-01-01

Motivation Identifying gene regulatory networks (GRNs) which consist of a large number of interacting units has become a problem of paramount importance in systems biology. Situations exist extensively in which causal interacting relationships among these units are required to be reconstructed from measured expression data and other a priori information. Though numerous classical methods have been developed to unravel the interactions of GRNs, these methods either have higher computing complexities or have lower estimation accuracies. Note that great similarities exist between identification of genes that directly regulate a specific gene and a sparse vector reconstruction, which often relates to the determination of the number, location and magnitude of nonzero entries of an unknown vector by solving an underdetermined system of linear equations y = Φx. Based on these similarities, we propose a novel framework of sparse reconstruction to identify the structure of a GRN, so as to increase accuracy of causal regulation estimations, as well as to reduce their computational complexity. Results In this paper, a sparse reconstruction framework is proposed on basis of steady-state experiment data to identify GRN structure. Different from traditional methods, this approach is adopted which is well suitable for a large-scale underdetermined problem in inferring a sparse vector. We investigate how to combine the noisy steady-state experiment data and a sparse reconstruction algorithm to identify causal relationships. Efficiency of this method is tested by an artificial linear network, a mitogen-activated protein kinase (MAPK) pathway network and the in silico networks of the DREAM challenges. The performance of the suggested approach is compared with two state-of-the-art algorithms, the widely adopted total least-squares (TLS) method and those available results on the DREAM project. Actual results show that, with a lower computational cost, the proposed method can significantly enhance estimation accuracy and greatly reduce false positive and negative errors. Furthermore, numerical calculations demonstrate that the proposed algorithm may have faster convergence speed and smaller fluctuation than other methods when either estimate error or estimate bias is considered. PMID:26207991

A simple attitude control of quadrotor helicopter based on Ziegler-Nichols rules for tuning PD parameters.

PubMed

He, ZeFang; Zhao, Long

2014-01-01

An attitude control strategy based on Ziegler-Nichols rules for tuning PD (proportional-derivative) parameters of quadrotor helicopters is presented to solve the problem that quadrotor tends to be instable. This problem is caused by the narrow definition domain of attitude angles of quadrotor helicopters. The proposed controller is nonlinear and consists of a linear part and a nonlinear part. The linear part is a PD controller with PD parameters tuned by Ziegler-Nichols rules and acts on the quadrotor decoupled linear system after feedback linearization; the nonlinear part is a feedback linearization item which converts a nonlinear system into a linear system. It can be seen from the simulation results that the attitude controller proposed in this paper is highly robust, and its control effect is better than the other two nonlinear controllers. The nonlinear parts of the other two nonlinear controllers are the same as the attitude controller proposed in this paper. The linear part involves a PID (proportional-integral-derivative) controller with the PID controller parameters tuned by Ziegler-Nichols rules and a PD controller with the PD controller parameters tuned by GA (genetic algorithms). Moreover, this attitude controller is simple and easy to implement.

Equating Scores from Adaptive to Linear Tests

ERIC Educational Resources Information Center

van der Linden, Wim J.

2006-01-01

Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test…

Individual Differences in Trajectories of Emotion Regulation Processes: The Effects of Maternal Depressive Symptomatology and Children's Physiological Regulation

ERIC Educational Resources Information Center

Blandon, Alysia Y.; Calkins, Susan D.; Keane, Susan P.; O'Brien, Marion

2008-01-01

Trajectories of emotion regulation processes were examined in a community sample of 269 children across the ages of 4 to 7 using hierarchical linear modeling. Maternal depressive symptomatology (Symptom Checklist-90) and children's physiological reactivity (respiratory sinus arrhythmia [RSA]) and vagal regulation ([delta]RSA) were explored as…

Flipped Classroom with Problem Based Activities: Exploring Self-Regulated Learning in a Programming Language Course

ERIC Educational Resources Information Center

Çakiroglu, Ünal; Öztürk, Mücahit

2017-01-01

This study intended to explore the development of self-regulation in a flipped classroom setting. Problem based learning activities were carried out in flipped classrooms to promote self-regulation. A total of 30 undergraduate students from Mechatronic department participated in the study. Self-regulation skills were discussed through students'…

Guided Discovery, Visualization, and Technology Applied to the New Curriculum for Secondary Mathematics.

ERIC Educational Resources Information Center

Smith, Karan B.

1996-01-01

Presents activities which highlight major concepts of linear programming. Demonstrates how technology allows students to solve linear programming problems using exploration prior to learning algorithmic methods. (DDR)

New Galerkin operational matrices for solving Lane-Emden type equations

NASA Astrophysics Data System (ADS)

Abd-Elhameed, W. M.; Doha, E. H.; Saad, A. S.; Bassuony, M. A.

2016-04-01

Lane-Emden type equations model many phenomena in mathematical physics and astrophysics, such as thermal explosions. This paper is concerned with introducing third and fourth kind Chebyshev-Galerkin operational matrices in order to solve such problems. The principal idea behind the suggested algorithms is based on converting the linear or nonlinear Lane-Emden problem, through the application of suitable spectral methods, into a system of linear or nonlinear equations in the expansion coefficients, which can be efficiently solved. The main advantage of the proposed algorithm in the linear case is that the resulting linear systems are specially structured, and this of course reduces the computational effort required to solve such systems. As an application, we consider the solar model polytrope with n=3 to show that the suggested solutions in this paper are in good agreement with the numerical results.

Hybrid finite element method for describing the electrical response of biological cells to applied fields.

PubMed

Ying, Wenjun; Henriquez, Craig S

2007-04-01

A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.

Summer Proceedings 2016: The Center for Computing Research at Sandia National Laboratories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carleton, James Brian; Parks, Michael L.

Solving sparse linear systems from the discretization of elliptic partial differential equations (PDEs) is an important building block in many engineering applications. Sparse direct solvers can solve general linear systems, but are usually slower and use much more memory than effective iterative solvers. To overcome these two disadvantages, a hierarchical solver (LoRaSp) based on H2-matrices was introduced in [22]. Here, we have developed a parallel version of the algorithm in LoRaSp to solve large sparse matrices on distributed memory machines. On a single processor, the factorization time of our parallel solver scales almost linearly with the problem size for three-dimensionalmore » problems, as opposed to the quadratic scalability of many existing sparse direct solvers. Moreover, our solver leads to almost constant numbers of iterations, when used as a preconditioner for Poisson problems. On more than one processor, our algorithm has significant speedups compared to sequential runs. With this parallel algorithm, we are able to solve large problems much faster than many existing packages as demonstrated by the numerical experiments.« less

Non-linear vibrations of sandwich viscoelastic shells

NASA Astrophysics Data System (ADS)

Benchouaf, Lahcen; Boutyour, El Hassan; Daya, El Mostafa; Potier-Ferry, Michel

2018-04-01

This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring.

Schwarz maps of algebraic linear ordinary differential equations

NASA Astrophysics Data System (ADS)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

The Matrix Pencil and its Applications to Speech Processing

DTIC Science & Technology

2007-03-01

Elementary Linear Algebra ” 8th edition, pp. 278, 2000 John Wiley & Sons, Inc., New York [37] Wai C. Chu, “Speech Coding Algorithms”, New Jeresy: John...Ben; Daniel, James W.; “Applied Linear Algebra ”, pp. 342-345, 1988 Prentice Hall, Englewood Cliffs, NJ [35] Haykin, Simon “Applied Linear Adaptive...ABSTRACT Matrix Pencils facilitate the study of differential equations resulting from oscillating systems. Certain problems in linear ordinary

48 CFR 1329.101 - Resolving tax problems.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Resolving tax problems. 1329.101 Section 1329.101 Federal Acquisition Regulations System DEPARTMENT OF COMMERCE GENERAL CONTRACTING REQUIREMENTS TAXES General 1329.101 Resolving tax problems. Legal questions relating to tax issues...

Spectral-Spatial Shared Linear Regression for Hyperspectral Image Classification.

PubMed

Haoliang Yuan; Yuan Yan Tang

2017-04-01

Classification of the pixels in hyperspectral image (HSI) is an important task and has been popularly applied in many practical applications. Its major challenge is the high-dimensional small-sized problem. To deal with this problem, lots of subspace learning (SL) methods are developed to reduce the dimension of the pixels while preserving the important discriminant information. Motivated by ridge linear regression (RLR) framework for SL, we propose a spectral-spatial shared linear regression method (SSSLR) for extracting the feature representation. Comparing with RLR, our proposed SSSLR has the following two advantages. First, we utilize a convex set to explore the spatial structure for computing the linear projection matrix. Second, we utilize a shared structure learning model, which is formed by original data space and a hidden feature space, to learn a more discriminant linear projection matrix for classification. To optimize our proposed method, an efficient iterative algorithm is proposed. Experimental results on two popular HSI data sets, i.e., Indian Pines and Salinas demonstrate that our proposed methods outperform many SL methods.

Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saad, Yousef

2014-01-16

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners formore » solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.« less

Duality in non-linear programming

NASA Astrophysics Data System (ADS)

Jeyalakshmi, K.

2018-04-01

In this paper we consider duality and converse duality for a programming problem involving convex objective and constraint functions with finite dimensional range. We do not assume any constraint qualification. The dual is presented by reducing the problem to a standard Lagrange multiplier problem.

Comparisons of linear and nonlinear pyramid schemes for signal and image processing

NASA Astrophysics Data System (ADS)

Morales, Aldo W.; Ko, Sung-Jea

1997-04-01

Linear filters banks are being used extensively in image and video applications. New research results in wavelet applications for compression and de-noising are constantly appearing in the technical literature. On the other hand, non-linear filter banks are also being used regularly in image pyramid algorithms. There are some inherent advantages in using non-linear filters instead of linear filters when non-Gaussian processes are present in images. However, a consistent way of comparing performance criteria between these two schemes has not been fully developed yet. In this paper a recently discovered tool, sample selection probabilities, is used to compare the behavior of linear and non-linear filters. In the conversion from weights of order statistics (OS) filters to coefficients of the impulse response is obtained through these probabilities. However, the reverse problem: the conversion from coefficients of the impulse response to the weights of OS filters is not yet fully understood. One of the reasons for this difficulty is the highly non-linear nature of the partitions and generating function used. In the present paper the problem is posed as an optimization of integer linear programming subject to constraints directly obtained from the coefficients of the impulse response. Although the technique to be presented in not completely refined, it certainly appears to be promising. Some results will be shown.

Multivariable control of the Space Shuttle remote manipulator system using H2 and H(infinity) optimization. M.S. Thesis - Massachusetts Inst. of Tech.

NASA Technical Reports Server (NTRS)

Prakash, OM, II

1991-01-01

Three linear controllers are desiged to regulate the end effector of the Space Shuttle Remote Manipulator System (SRMS) operating in Position Hold Mode. In this mode of operation, jet firings of the Orbiter can be treated as disturbances while the controller tries to keep the end effector stationary in an orbiter-fixed reference frame. The three design techniques used include: the Linear Quadratic Regulator (LQR), H2 optimization, and H-infinity optimization. The nonlinear SRMS is linearized by modelling the effects of the significant nonlinearities as uncertain parameters. Each regulator design is evaluated for robust stability in light of the parametric uncertanties using both the small gain theorem with an H-infinity norm and the less conservative micro-analysis test. All three regulator designs offer significant improvement over the current system on the nominal plant. Unfortunately, even after dropping performance requirements and designing exclusively for robust stability, robust stability cannot be achieved. The SRMS suffers from lightly damped poles with real parametric uncertainties. Such a system renders the micro-analysis test, which allows for complex peturbations, too conservative.

An h-p Taylor-Galerkin finite element method for compressible Euler equations

NASA Technical Reports Server (NTRS)

Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

1991-01-01

An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

Solving Two-Level Optimization Problems with Applications to Robust Design and Energy Markets

DTIC Science & Technology

2011-01-01

additional a transportation system operator (TSO) who manages the congestion and 172 flows. The TSO’s linear program is as follows (where other...were tested are shown in Table 5.11 below. Node 1 Node 2 Producer A Producer B Producer C Producer D Transmission System Operator 174... Systems to Solve Problems that are Not Linear. Operational Research Quarterly , 26, 609–618. 9. Beale, E., & Tomlin, J. (1970). Special Facilities

The application of MINIQUASI to thermal program boundary and initial value problems

NASA Technical Reports Server (NTRS)

1974-01-01

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

Boundary-layer stability and airfoil design

NASA Technical Reports Server (NTRS)

Viken, Jeffrey K.

1986-01-01

Several different natural laminar flow (NLF) airfoils have been analyzed for stability of the laminar boundary layer using linear stability codes. The NLF airfoils analyzed come from three different design conditions: incompressible; compressible with no sweep; and compressible with sweep. Some of the design problems are discussed, concentrating on those problems associated with keeping the boundary layer laminar. Also, there is a discussion on how a linear stability analysis was effectively used to improve the design for some of the airfoils.

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1984-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Resource allocation in shared spectrum access communications for operators with diverse service requirements

NASA Astrophysics Data System (ADS)

Kibria, Mirza Golam; Villardi, Gabriel Porto; Ishizu, Kentaro; Kojima, Fumihide; Yano, Hiroyuki

2016-12-01

In this paper, we study inter-operator spectrum sharing and intra-operator resource allocation in shared spectrum access communication systems and propose efficient dynamic solutions to address both inter-operator and intra-operator resource allocation optimization problems. For inter-operator spectrum sharing, we present two competent approaches, namely the subcarrier gain-based sharing and fragmentation-based sharing, which carry out fair and flexible allocation of the available shareable spectrum among the operators subject to certain well-defined sharing rules, traffic demands, and channel propagation characteristics. The subcarrier gain-based spectrum sharing scheme has been found to be more efficient in terms of achieved throughput. However, the fragmentation-based sharing is more attractive in terms of computational complexity. For intra-operator resource allocation, we consider resource allocation problem with users' dissimilar service requirements, where the operator supports users with delay constraint and non-delay constraint service requirements, simultaneously. This optimization problem is a mixed-integer non-linear programming problem and non-convex, which is computationally very expensive, and the complexity grows exponentially with the number of integer variables. We propose less-complex and efficient suboptimal solution based on formulating exact linearization, linear approximation, and convexification techniques for the non-linear and/or non-convex objective functions and constraints. Extensive simulation performance analysis has been carried out that validates the efficiency of the proposed solution.

The paracaspase MALT1 cleaves HOIL1 reducing linear ubiquitination by LUBAC to dampen lymphocyte NF-κB signalling

PubMed Central

Klein, Theo; Fung, Shan-Yu; Renner, Florian; Blank, Michael A.; Dufour, Antoine; Kang, Sohyeong; Bolger-Munro, Madison; Scurll, Joshua M.; Priatel, John J.; Schweigler, Patrick; Melkko, Samu; Gold, Michael R.; Viner, Rosa I.; Régnier, Catherine H.; Turvey, Stuart E.; Overall, Christopher M.

2015-01-01

Antigen receptor signalling activates the canonical NF-κB pathway via the CARD11/BCL10/MALT1 (CBM) signalosome involving key, yet ill-defined roles for linear ubiquitination. The paracaspase MALT1 cleaves and removes negative checkpoint proteins, amplifying lymphocyte responses in NF-κB activation and in B-cell lymphoma subtypes. To identify new human MALT1 substrates, we compare B cells from the only known living MALT1mut/mut patient with healthy MALT1+/mut family members using 10-plex Tandem Mass Tag TAILS N-terminal peptide proteomics. We identify HOIL1 of the linear ubiquitin chain assembly complex as a novel MALT1 substrate. We show linear ubiquitination at B-cell receptor microclusters and signalosomes. Late in the NF-κB activation cycle HOIL1 cleavage transiently reduces linear ubiquitination, including of NEMO and RIP1, dampening NF-κB activation and preventing reactivation. By regulating linear ubiquitination, MALT1 is both a positive and negative pleiotropic regulator of the human canonical NF-κB pathway—first promoting activation via the CBM—then triggering HOIL1-dependent negative-feedback termination, preventing reactivation. PMID:26525107

48 CFR 229.101 - Resolving tax problems.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 48 Federal Acquisition Regulations System 3 2010-10-01 2010-10-01 false Resolving tax problems. 229.101 Section 229.101 Federal Acquisition Regulations System DEFENSE ACQUISITION REGULATIONS SYSTEM...) Within DoD, the agency-designated legal counsels are the defense agency General Counsels, the General...

P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems

NASA Technical Reports Server (NTRS)

Kang, Kab S.

2002-01-01

The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning

Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moryakov, A. V., E-mail: sailor@orc.ru

2016-12-15

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

A robust optimization methodology for preliminary aircraft design

NASA Astrophysics Data System (ADS)

Prigent, S.; Maréchal, P.; Rondepierre, A.; Druot, T.; Belleville, M.

2016-05-01

This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, El Ghaoui, and Nemirovski [Robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented.

Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code

NASA Technical Reports Server (NTRS)

Hou, Gene

2000-01-01

The report documents the recent effort to enhance a transient linear heat transfer code so as to solve nonlinear problems. The linear heat transfer code was originally developed by Dr. Kim Bey of NASA Largely and called the Structure-Compatible Heat Transfer (SCHT) code. The report includes four parts. The first part outlines the formulation of the heat transfer problem of concern. The second and the third parts give detailed procedures to construct the nonlinear finite element equations and the required Jacobian matrices for the nonlinear iterative method, Newton-Raphson method. The final part summarizes the results of the numerical experiments on the newly enhanced SCHT code.

Finite-time H∞ control for linear continuous system with norm-bounded disturbance

NASA Astrophysics Data System (ADS)

Meng, Qingyi; Shen, Yanjun

2009-04-01

In this paper, the definition of finite-time H∞ control is presented. The system under consideration is subject to time-varying norm-bounded exogenous disturbance. The main aim of this paper is focused on the design a state feedback controller which ensures that the closed-loop system is finite-time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. A sufficient condition is presented for the solvability of this problem, which can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

Linear frictional forces cause orbits to neither circularize nor precess

NASA Astrophysics Data System (ADS)

Hamilton, B.; Crescimanno, M.

2008-06-01

For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge-Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure to damped systems suggested recently by Tarasov (2005 J. Phys. A: Math. Gen. 38 2145). In this generalized algebraic structure the orbit-averaged Runge-Lenz vector remains a constant in the linearly damped Kepler problem to leading order in the damping coefficient. Beyond Kepler, we prove that, for any potential proportional to a power of the radius, the orbit shape and precession angle remain constant to leading order in the linear friction coefficient.

Systems of Inhomogeneous Linear Equations

NASA Astrophysics Data System (ADS)

Scherer, Philipp O. J.

Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

[Regulation of Positive and Negative Emotions as Mediator between Maternal Emotion Socialization and Child Problem Behavior].

PubMed

Fäsche, Anika; Gunzenhauser, Catherine; Friedlmeier, Wolfgang; von Suchodoletz, Antje

2015-01-01

The present study investigated five to six year old children's ability to regulate negative and positive emotions in relation to psychosocial problem behavior (N=53). It was explored, whether mothers' supportive and nonsupportive strategies of emotion socialization influence children's problem behavior by shaping their emotion regulation ability. Mothers reported on children's emotion regulation and internalizing and externalizing problem behavior via questionnaire, and were interviewed about their preferences for socialization strategies in response to children's expression of negative affect. Results showed that children with more adaptive expression of adequate positive emotions had less internalizing behavior problems. When children showed more control of inadequate negative emotions, children were less internalizing as well as externalizing in their behavior. Furthermore, results indicated indirect relations of mothers' socialization strategies with children's problem behavior. Control of inadequate negative emotions mediated the link between non-supportive strategies on externalizing problem behavior. Results suggest that emotion regulatory processes should be part of interventions to reduce the development of problematic behavior in young children. Parents should be trained in dealing with children's emotions in a constructive way.

Family poverty and trajectories of children's emotional and behavioural problems: the moderating roles of self-regulation and verbal cognitive ability.

PubMed

Flouri, Eirini; Midouhas, Emily; Joshi, Heather

2014-08-01

Socio-economic disadvantage is strongly associated with children's emotional (internalising) and behavioural (externalising) problems. Self-regulation and verbal cognitive ability have been related to children's emotional and behavioural resilience to socio-economic disadvantage. Despite being inter-related, self-regulation and verbal cognitive ability have not been examined jointly as promoting resilience in young children. This study investigated the roles of self-regulation and verbal cognitive ability in children's emotional and behavioural resilience to family socio-economic disadvantage from early to middle childhood (ages 3, 5, and 7 years; N = 16,916; 49 % girls). Using multivariate response growth curve modelling, we found that the relationship between socio-economic disadvantage and internalising problems was stronger for children with lower verbal cognitive ability. Also, poor children with high and low levels of self-regulation showed a widening gap in both emotional and behavioural problems over time. Poor and non-poor children alike benefited from self-regulation, but poor children appeared to be more vulnerable to low self-regulation. Self-regulation and verbal cognitive ability seem to be important protective factors for young children growing up in poor families.

Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

NASA Technical Reports Server (NTRS)

Ahmad, Shahid

1991-01-01

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

The heterogeneity of attention-deficit/hyperactivity disorder symptoms and conduct problems: Cognitive inhibition, emotion regulation, emotionality, and disorganized attachment.

PubMed

Forslund, Tommie; Brocki, Karin C; Bohlin, Gunilla; Granqvist, Pehr; Eninger, Lilianne

2016-09-01

This study examined the contributions of several important domains of functioning to attention-deficit/hyperactivity disorder (ADHD) symptoms and conduct problems. Specifically, we investigated whether cognitive inhibition, emotion regulation, emotionality, and disorganized attachment made independent and specific contributions to these externalizing behaviour problems from a multiple pathways perspective. The study included laboratory measures of cognitive inhibition and disorganized attachment in 184 typically developing children (M age = 6 years, 10 months, SD = 1.7). Parental ratings provided measures of emotion regulation, emotionality, and externalizing behaviour problems. Results revealed that cognitive inhibition, regulation of positive emotion, and positive emotionality were independently and specifically related to ADHD symptoms. Disorganized attachment and negative emotionality formed independent and specific relations to conduct problems. Our findings support the multiple pathways perspective on ADHD, with poor regulation of positive emotion and high positive emotionality making distinct contributions to ADHD symptoms. More specifically, our results support the proposal of a temperamentally based pathway to ADHD symptoms. The findings also indicate that disorganized attachment and negative emotionality constitute pathways specific to conduct problems rather than to ADHD symptoms. © 2016 The British Psychological Society.

A Linear Theory for Inflatable Plates of Arbitrary Shape

NASA Technical Reports Server (NTRS)

McComb, Harvey G., Jr.

1961-01-01

A linear small-deflection theory is developed for the elastic behavior of inflatable plates of which Airmat is an example. Included in the theory are the effects of a small linear taper in the depth of the plate. Solutions are presented for some simple problems in the lateral deflection and vibration of constant-depth rectangular inflatable plates.

A problem in non-linear Diophantine approximation

NASA Astrophysics Data System (ADS)

Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon

2018-05-01

In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

NASA Technical Reports Server (NTRS)

Sloss, J. M.; Kranzler, S. K.

1972-01-01

The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

Investigating motivational regulations and physical activity over 25 weeks.

PubMed

Sweet, Shane N; Fortier, Michelle S; Blanchard, Chris M

2014-07-01

Because motivation has been deemed a key barrier to physical activity, it is imperative that we know how motivational levels change over time and how that change relates to physical activity. Based in Self-Determination Theory, this study investigated fluctuations in physical activity and motivational regulations over 25 weeks and tested the relationship between these 2 variables. Data from the Physical Activity Counseling trial were examined. Inactive adults recruited from a primary care center (N = 120) answered motivation and physical activity questionnaires during the intervention and postintervention phases. Hierarchical linear modeling was used to test the hypotheses. Quadratic changes were found for external regulation (γ20= 0.02, P < .05) and physical activity (γ20 = -2.64, P < .001), while identified (γ10= 0.04, P = .03) and intrinsic (γ10= 0.04, P = .01) regulations increased linearly over the course of the 25 weeks. Only identified regulation (γ30= 3.15, P = .01) and intrinsic motivation (γ30= 4.68, P < .001) were significantly and positively related with physical activity. Physical activity, external and identified regulations and intrinsic motivation changed over the 25 weeks. Intervention should aim at fostering identified regulation and intrinsic motivation as greater levels of these regulations were related with physical activity.

Discrete Applied Mathematics

DTIC Science & Technology

1993-05-31

program. In paper [28], we give a brief and elementary proof of a result of Hoffman [1952) about approximate solutions to systems, of linear inequalities...UCLA, Vestvood, CA, February 1993. " Linear Problems: Formulation and Solution," International Linear Algebra Society, Pensacola, FL, May 1993. Denise S...thresAold If there is a number h and a linear k-separator w assigning a real number to each vertex so that for any subset S of vertices, the sum of w

Same Old Problem, New Name? Alerting Students to the Nature of the Problem-Solving Process

ERIC Educational Resources Information Center

Yerushalmi, Edit; Magen, Esther

2006-01-01

Students frequently misconceive the process of problem-solving, expecting the linear process required for solving an exercise, rather than the convoluted search process required to solve a genuine problem. In this paper we present an activity designed to foster in students realization and appreciation of the nature of the problem-solving process,…

Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ardema, Mark

2006-01-01

This paper describes a modeling method and a new optimal control approach to investigate a Mach number control problem for the NASA Ames 11-Foot Transonic Wind Tunnel. The flow in the wind tunnel is modeled by the 1-D unsteady Euler equations whose boundary conditions prescribe a controlling action by a compressor. The boundary control inputs to the compressor are in turn controlled by a drive motor system and an inlet guide vane system whose dynamics are modeled by ordinary differential equations. The resulting Euler equations are thus coupled to the ordinary differential equations via the boundary conditions. Optimality conditions are established by an adjoint method and are used to develop a model predictive linear-quadratic optimal control for regulating the Mach number due to a test model disturbance during a continuous pitch

The role of modern control theory in the design of controls for aircraft turbine engines

NASA Technical Reports Server (NTRS)

Zeller, J.; Lehtinen, B.; Merrill, W.

1982-01-01

The development, applications, and current research in modern control theory (MCT) are reviewed, noting the importance for fuel-efficient operation of turbines with variable inlet guide vanes, compressor stators, and exhaust nozzle area. The evolution of multivariable propulsion control design is examined, noting a basis in a matrix formulation of the differential equations defining the process, leading to state space formulations. Reports and papers which appeared from 1970-1982 which dealt with problems in MCT applications to turbine engine control design are outlined, including works on linear quadratic regulator methods, frequency domain methods, identification, estimation, and model reduction, detection, isolation, and accommodation, and state space control, adaptive control, and optimization approaches. Finally, NASA programs in frequency domain design, sensor failure detection, computer-aided control design, and plant modeling are explored

Residential water demand model under block rate pricing: A case study of Beijing, China

NASA Astrophysics Data System (ADS)

Chen, H.; Yang, Z. F.

2009-05-01

In many cities, the inconsistency between water supply and water demand has become a critical problem because of deteriorating water shortage and increasing water demand. Uniform price of residential water cannot promote the efficient water allocation. In China, block water price will be put into practice in the future, but the outcome of such regulation measure is unpredictable without theory support. In this paper, the residential water is classified by the volume of water usage based on economic rules and block water is considered as different kinds of goods. A model based on extended linear expenditure system (ELES) is constructed to simulate the relationship between block water price and water demand, which provide theoretical support for the decision-makers. Finally, the proposed model is used to simulate residential water demand under block rate pricing in Beijing.