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1

Extended Decentralized Linear-Quadratic-Gaussian Control  

NASA Technical Reports Server (NTRS)

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.

Carpenter, J. Russell

2000-01-01

2

A linear-quadratic-Gaussian control problem with innovations-feedthrough solution  

NASA Technical Reports Server (NTRS)

The structure of the separation-theorem solution to the standard linear-quadratic-Gaussian (LQG) control problem does not involve direct output feedback as a consequence of the form of the performance index. It is shown that the performance index may be generalized in a natural fashion so that the optimal control law involves output feedback or, equivalently, innovations feedthrough (IF). Applications where this formulation may be advantageous are indicated through an examination of properties of the IF control law.

Platzman, L. K.; Johnson, T. L.

1976-01-01

3

Design of a linear quadratic Gaussian controller for an adaptive optics system  

Microsoft Academic Search

The authors consider the control of a phase-correcting ground-based adaptive optical telescope. They present the design of a linear quadratic Gaussian controller for generating actuator voltages to a deformable mirror, given a set of slope measurements from a wavefront sensor. A truth model is developed based on theoretical developments and actual test data. The resulting state-space model has as its

Randall N. Paschall; Mark A. Von Bokern; Byron M. Welsh

1991-01-01

4

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

USGS Publications Warehouse

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

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

1997-01-01

5

Active steering control of railway vehicles using linear quadratic Gaussian (LQG)  

NASA Astrophysics Data System (ADS)

In urban transit systems, railway vehicles are often required to negotiate tight curves. During curve negotiation, the wheelsets of conventional vehicles generally misalign radically with the track increasing wheel/rail contact forces and resulting in increased wheel and rail wear, outbreak of squeal noise, fuel consumption, and risk of derailment. This paper presents active steering controller design in the railway systems using Linear Quadratic Gaussian. Simulation results have been shown that the proposed LQG method methodology robustly yields uniform performance with adequate response over the axle weight and wheel conicity variation range.

Kim, Min-Soo; Byun, Yeun-Sub; Park, Joon-Hyuk; You, Won-Hee

2007-12-01

6

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

NASA Technical Reports Server (NTRS)

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.

Gibson, J. S.; Adamian, A.

1988-01-01

7

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

NASA Technical Reports Server (NTRS)

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

Gawronski, W.

2004-01-01

8

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

NASA Technical Reports Server (NTRS)

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

Armstrong, E. S.

1978-01-01

9

Practical gust load alleviation and flutter suppression control laws based on a LQG methodology. [Linear Quadratic Gaussian  

NASA Technical Reports Server (NTRS)

A modified linear quadratic Gaussian (LQG) synthesis procedure has been used to design low-order robust multiloop controllers for a flexible airplane. The introduction of properly constructed fictitious Gauss-Markov processes in the control loops allowed meeting classical frequency-domain stability criteria using the direct synthesis procedures of modern time-domain control theory. Model reduction was used to simplify the control laws to the point where they could be easily implemented on onboard flight computers. These control laws provided excellent gust load and flutter mode control with good stability margins and compared very favorably to other control laws synthesized by the classical root-locus technique.

Gangsaas, D.; Ly, U.; Norman, D. C.

1981-01-01

10

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

NASA Technical Reports Server (NTRS)

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

Jacobson, R. A.

1978-01-01

11

Controller design approaches for large space structures using LQG control theory. [Linear Quadratic Gaussian  

NASA Technical Reports Server (NTRS)

The paper presents several approaches for the design of reduced order controllers for large space structures. These approaches are shown to be based on LQG control theory and include truncation, modified truncation regulators and estimators, use of higher order estimators, selective modal suppression, and use of polynomial estimators. Further, the use of direct sensor feedback, as opposed to a state estimator, is investigated for some of these approaches. Finally, numerical results are given for a long free beam.

Joshi, S. M.; Groom, N. J.

1979-01-01

12

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

PubMed

This paper demonstrates a high-speed spiral imaging technique for an atomic force microscope (AFM). As an alternative to traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFM's piezoelectric tube scanner (PTS). Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoids from the X and Y-PTSs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. As part of the post-processing of the experimental data, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors and a Gaussian image filter is used to filter the images. A comparison of images scanned using the proposed controller (spiral) and the AFM PI controller (raster) shows improvement in the scanning rate using the proposed method. PMID:24689591

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

2014-03-01

13

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

SciTech Connect

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

Habibullah, H., E-mail: h.habib@student.adfa.edu.au; Pota, H. R., E-mail: h.pota@adfa.edu.au; Petersen, I. R., E-mail: i.petersen@adfa.edu.au [School of Engineering and Information Technology, University of New South Wales, Canberra, Australian Capital Territory 2612 (Australia)

2014-03-15

14

Active steering control of railway vehicles using linear quadratic Gaussian (LQG)  

Microsoft Academic Search

In urban transit systems, railway vehicles are often required to negotiate tight curves. During curve negotiation, the wheelsets of conventional vehicles generally misalign radically with the track increasing wheel\\/rail contact forces and resulting in increased wheel and rail wear, outbreak of squeal noise, fuel consumption, and risk of derailment. This paper presents active steering controller design in the railway systems

Min-Soo Kim; Yeun-Sub Byun; Joon-Hyuk Park; Won-Hee You

2007-01-01

15

Active flutter suppression using Linear Quadratic Gaussian theory  

NASA Technical Reports Server (NTRS)

This paper describes the application of Linear Quadratic Gaussian (LQG) methodology to the design of active control systems for suppression of aerodynamic flutter. A full-size wind tunnel model of a supercritical wing with associated sensors and actuators comprises the system to be controlled. Results of a synthesis methodology that provide small values of rms response, insensitivity to flight condition, and robust stability are presented. Results of control surface and sensor position optimization are also presented. Both frequency response matching and residualization are used to obtain practical flutter controllers.

Mahesh, J. K.; Stone, C. R.; Garrard, W. L.; Dunn, H. J.

1980-01-01

16

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing  

NASA Technical Reports Server (NTRS)

Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

Choi, Benjamin B.

2002-01-01

17

Optimal and suboptimal quadratic forms for noncentered Gaussian processes  

NASA Astrophysics Data System (ADS)

Individual random trajectories of stochastic processes are often analyzed by using quadratic forms such as time averaged (TA) mean square displacement (MSD) or velocity auto-correlation function (VACF). The appropriate quadratic form is expected to have a narrow probability distribution in order to reduce statistical uncertainty of a single measurement. We consider the problem of finding the optimal quadratic form that minimizes a chosen cumulant moment (e.g., the variance) of the probability distribution, under the constraint of fixed mean value. For discrete noncentered Gaussian processes, we construct the optimal quadratic form by using the spectral representation of cumulant moments. Moreover, we obtain a simple explicit formula for the smallest achievable cumulant moment that may serve as a quality benchmark for other quadratic forms. We illustrate the optimality issues by comparing the optimal variance with the variances of the TA MSD and TA VACF of fractional Brownian motion superimposed with a constant drift and independent Gaussian noise.

Grebenkov, Denis S.

2013-09-01

18

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

NASA Technical Reports Server (NTRS)

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

Athans, M.

1986-01-01

19

Distributed Control with Integral Quadratic Constraints  

E-print Network

Distributed Control with Integral Quadratic Constraints Hui Fang, Panos J. Antsaklis Department Integral Quadratic Constraints (IQC) on the interconnections are derived. These results take the form in control theory, namely control under communication constraints. In particular, researchers have considered

Antsaklis, Panos

20

Linear?quadratic optimal control with integral quadratic constraints  

Microsoft Academic Search

SUMMARY We derive closed-form solutions for the linear-quadratic (LQ) optimal control problem subject to integral quadratic constraints. The optimal control is a non-linear function of the current state and the initial state. Furthermore, the optimal control is easily calculated by solving an unconstrained LQ control problem together with an optimal parameter selection problem. Gradient formulae for the cost functional of

A. E. B. Lim; Y. Q. Liu; K. L. Teo; J. B. Moore

1999-01-01

21

Distributed Control with Integral Quadratic Constraints  

E-print Network

1 Distributed Control with Integral Quadratic Constraints Hui Fang and Panos J. Antsaklis Abstract, and the multipliers are specified by the underlying integral quadratic constraints to model interconnections between. Antsaklis, "Distributed Control with Integral Quadratic Constraints," ISIS Technical Report ISIS-2007

Antsaklis, Panos

22

Elegant Ince-Gaussian beams in a quadratic-index medium  

NASA Astrophysics Data System (ADS)

Elegant Ince—Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince—Gaussian beams and they display better symmetry between the Ince-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince—Gaussian beams are discussed.

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2011-09-01

23

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

NASA Technical Reports Server (NTRS)

The paper describes a laboratory design facility for digital microprocessor implementation of Linear-Quadratic-Gaussian feedback compensators. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems are conditioned for implementation on a laboratory microcomputer system. The software consists of two parts: (1) an off-line high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains, and (2) a cross compiler/macro assembler which generates object code for the target microprocessor system. Application to the control of a two dimensional inverted pendulum and expanding the design/prototyping system to other target machine architectures are discussed.

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

1979-01-01

24

Nonsmooth Methods for Control Design with Integral Quadratic Constraints  

E-print Network

Nonsmooth Methods for Control Design with Integral Quadratic Constraints Pierre Apkarian to compute local solutions to synthesis problems subject to integral quadratic constraints (IQCs). We use, parametric uncertainty, integral quadratic constraint (IQC), structured controllers, NP-hard problems

Prot, Olivier

25

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

NASA Technical Reports Server (NTRS)

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

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

1978-01-01

26

A quadratically constrained MAP classifier using the mixture of Gaussians models as a weight function.  

PubMed

In this paper, we propose classifiers derived from quadratically constrained maximum a posteriori (QCMAP) estimation. The QCMAP consists of the maximization of the expectation of a cost function, which is derived from the maximum a posteriori probability and a quadratic constraint. This criterion is highly general since its forms include least squares regressions and a support vector machine. Furthermore, the criterion provides a novel classifier, the "Gaussian QCMAP." The QCMAP procedure still has large theoretical interest and its full extensibility has yet to be explored. In this paper, we propose using the mixture of Gaussian distributions as the QCMAP weight function. The mixture of Gaussian distributions has wide-ranging applicability, and encompasses forms, such as a normal distribution model and a kernel density model. We propose four types of mixture of Gaussian functions for QCMAP classifiers, and conduct experiments to demonstrate their advantages. PMID:24808526

Yokota, Tatsuya; Yamashita, Yukihiko

2013-07-01

27

c WISRL, KAIST, APRIL, 2012 1 A Study on the Series Expansion of Gaussian Quadratic Forms  

E-print Network

c WISRL, KAIST, APRIL, 2012 1 A Study on the Series Expansion of Gaussian Quadratic Forms Technical Report WISRL-2012-APR-1 KAIST Juho Park, Youngchul Sung, Donggun Kim, and H. Vincent Poor All rights reserved c WISRL, KAIST Jan. 14, 2010 DRAFT #12;c WISRL, KAIST, APRIL, 2012 2 This report

Sung, Youngchul

28

Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes  

Microsoft Academic Search

Cohen, Guyon, Perrin and Pontier have given assumptions under which the second-order quadratic variations of a Gaussian process converge almost surely to a deterministic limit. In this paper we present two new convergence results about these variations: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we apply these results to identify two-parameter fractional

Arnaud Begyn; Lycee Pierre de Fermat

2007-01-01

29

LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS  

E-print Network

LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ANDREW E. B. LIM AND XUN YU differential equations (BSDEs) with a quadratic cost criteria, or backward linear-quadratic (BLQ) control differential equations (BSDEs), linear-quadratic (LQ) optimal control, Riccati equations, completion of squares

Lim, Andrew

30

Time-averaged quadratic functionals of a Gaussian process  

NASA Astrophysics Data System (ADS)

The characterization of a stochastic process from its single random realization is a challenging problem for most single-particle tracking techniques which survey an individual trajectory of a tracer in a complex or viscoelastic medium. We consider two quadratic functionals of the trajectory: the time-averaged mean-square displacement (MSD) and the time-averaged squared root mean-square displacement (SRMS). For a large class of stochastic processes governed by the generalized Langevin equation with arbitrary frictional memory kernel and harmonic potential, the exact formulas for the mean and covariance of these functionals are derived. The formula for the mean value can be directly used for fitting experimental data, e.g., in optical tweezers microrheology. The formula for the variance (and covariance) allows one to estimate the intrinsic fluctuations of measured (or simulated) time-averaged MSD or SRMS for choosing the experimental setup appropriately. We show that the time-averaged SRMS has smaller fluctuations than the time-averaged MSD, in spite of much broader applications of the latter one. The theoretical results are successfully confirmed by Monte Carlo simulations of the Langevin dynamics. We conclude that the use of the time-averaged SRMS would result in a more accurate statistical analysis of individual trajectories and more reliable interpretation of experimental data.

Grebenkov, Denis S.

2011-06-01

31

Distributed Control with Integral Quadratic Constraints  

Microsoft Academic Search

In this paper, stability conditions for distributed system under general integral quadratic constraints (IQC) for interconnections are derived. These results take the form of coupled linear matrix inequalities (LMIs), and the multipliers are shaped by the underlying IQCs to model these interconnections. It is further shown that these results can be exploited for distributed controllers synthesis similar to the gain-scheduling

Hui Fang; Panos J. Antsaklis

32

Quadratic Programming for Allocating Control Effort  

NASA Technical Reports Server (NTRS)

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

Singh, Gurkirpal

2005-01-01

33

Quadratic  

NSDL National Science Digital Library

Shows how the roots of a quadratic change as the b term in the equation changes. The equation was chosen to illustrate the fact that only real roots are seen as points where the curve crosses the x-axis. This can lead to a useful discussion of what is meant by a physically meaningful solution.

34

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

NASA Technical Reports Server (NTRS)

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

Chen, George T.

1987-01-01

35

Consensus over Ring Networks as a Quadratic Optimal Control Problem  

E-print Network

Consensus over Ring Networks as a Quadratic Optimal Control Problem J. A. Rogge J. A. K. Suykens-mail: {jonathan.rogge,dirk.aeyels}@ugent.be) K. U. Leuven, ESAT-SCD, Kasteelpark Arenberg 10, B-3001 Leuven

36

Nonconvex Problems of Global Optimization: Linear-Quadratic Control Problems with Quadratic Constraints  

Microsoft Academic Search

In this paper, we study a class of optimization problems,which are of certain interest for control theory. These problemsare of global constrained optimization and may be nonconvex ingeneral. A simple approach to their solution is presented. Aspecial attention is paid to the case when the objective andconstraints functions are quadratic functionals on a Hilbertspace. As an example of an application

A. Matveev; V. Yakubovich

1997-01-01

37

Control synthesis with dynamic integral quadratic constraints-LMI approach  

Microsoft Academic Search

In this paper, we consider the control synthesis problem when the disturbance input w is within a set defined by several dynamic integral quadratic constraints (IQC). We show that the condition on the existence of a stabilizing controller can be expressed as a set of linear matrix inequalities (LMI). We also show that the stabilizing controllers, if they exist, have

Chung-Yao Kao; Muralidhar Ravuri; Alexandre Megretski

2000-01-01

38

Analysis of integral controls in linear quadratic regulator design  

NASA Technical Reports Server (NTRS)

The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

Slater, G. L.

1979-01-01

39

Time-Inconsistent Stochastic LinearQuadratic Control Hanqing Jin  

E-print Network

, France. This author is partially supported by the Marie Curie ITN Grant, "Controlled Systems", GA no at the initial time); see, e.g., [20] and all the follow-up works to date on the Markowitz problem, as wellTime-Inconsistent Stochastic Linear­Quadratic Control Ying Hu Hanqing Jin Xun Yu Zhou November 3

40

Finding Optimal Gains In Linear-Quadratic Control Problems  

NASA Technical Reports Server (NTRS)

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.

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

1990-01-01

41

Tuning a fuzzy controller using quadratic response surfaces  

NASA Technical Reports Server (NTRS)

Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

Schott, Brian; Whalen, Thomas

1992-01-01

42

Correlation-preserved non-gaussian statistical timing analysis with quadratic timing model  

Microsoft Academic Search

Recent study shows that the existing first order canonical timing model is not sufficient to represent the dependency of the gate delay on the variation sources when processing and operational variations become more and more significant. Due to the nonlinearity of the mapping from variation sources to the gate\\/wire delay, the distribution of the delay is no longer Gaussian even

Lizheng Zhang; Weijen Chen; Yuhen Hu; John A. Gubner; Charlie Chung-Ping Chen

2005-01-01

43

Optimal Control of Rigid Body Angular Velocity with Quadratic Cost1  

E-print Network

interval with a quadratic integral penalty on the control variables and a terminal constraint on the state. In Section 3 we completely characterize the family of quadratic integrals of the unforced system and weOptimal Control of Rigid Body Angular Velocity with Quadratic Cost1 P. Tsiotras2, M. Corless3 and M

Tsiotras, Panagiotis

44

Application of quadratic optimization to supersonic inlet control  

NASA Technical Reports Server (NTRS)

The application of linear stochastic optimal control theory to the design of the control system for the air intake (inlet) of a supersonic air-breathing propulsion system is discussed. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant control systems are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain the best linear controller that minimizes the nonquadratic performance index. The two systems are compared on the basis of unstart prevention, control effort requirements, and sensitivity to parameter variations.

Lehtinen, B.; Zeller, J. R.

1971-01-01

45

Frequency weighted system identification and linear quadratic controller design  

NASA Technical Reports Server (NTRS)

Application of filters for frequency weighting of Markov parameters (pulse response functions) is described in relation to system/observer identification. The time domain identification approach recovers a model which has a pulse response weighted according to frequency. The identified model is composed of the original system and filters. The augmented system is in a form which can be used directly for frequency weighted linear quadratic controller design. Data from either single or multiple experiments can be used to recover the Markov parameters. Measured acceleration signals from a truss structure are used for system identification and the model obtained is used for frequency weighted controller design. The procedure makes the identification and controler design complementary problems.

Horta, Lucas G.; Phan, Minh; Juang, Jer-Nan; Longman, Richard W.; Sulla, Jeffrey L.

1991-01-01

46

A decentralized linear quadratic control design method for flexible structures  

NASA Technical Reports Server (NTRS)

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

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

1990-01-01

47

Human-Inspired Control of Bipedal Robots via Control Lyapunov Functions and Quadratic Programs  

E-print Network

Human-Inspired Control of Bipedal Robots via Control Lyapunov Functions and Quadratic Programs walking through controller synthesis inspired by human locomotion. Motivated by the hierarchical con- trol present in humans, we begin by viewing the human as a "black box" and describe outputs, or virtual

Ames, Aaron

48

Linear Quadratic and Tumour Control Probability Modelling in External Beam Radiotherapy  

E-print Network

Linear Quadratic and Tumour Control Probability Modelling in External Beam Radiotherapy SFC O, Alberta, T6G 2G1, Canada Abstract The standard Linear-Quadratic (LQ) survival model for external beam development of a cell cycle model within the original Zaider and Minerbo TCP formalism is highlighted

Hillen, Thomas

49

Robust Stability Analysis of Constrained Cross-Directional Control via Integral Quadratic Constraints  

Microsoft Academic Search

A robust stability test for a class of constrained cross-directional controllers is proposed. The cross-directional controller involves a quadratic program embedded within an internal model control structure and achieves optimal steady-state performance when the plant is fully known. Both the non-linearity in the controller and the unmodeled plant dynamics satisfy certain integral quadratic inequalities. This allows us to obtain conditions

R. M. Morales; W. P. Heath

2006-01-01

50

Stochastic optimal LQR control with integral quadratic constraints and indefinite control weights  

Microsoft Academic Search

A standard assumption in traditional (deterministic and stochastic) optimal (minimizing) linear quadratic regulator (LQR) theory is that the control weighting matrix in the cost functional is strictly positive definite. In the deterministic case, this assumption is in fact necessary for the problem to be well-posed because positive definiteness is required to make it a convex optimization problem. However, it has

Andrew E. B. Lim; Xun Yu Zhou

1999-01-01

51

Controllable Gaussian-qubit interface for extremal quantum state engineering  

E-print Network

We study state engineering through bilinear interactions between two remote qubits and two-mode Gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.

G. Adesso; S. Campbell; F. Illuminati; M. Paternostro

2010-07-02

52

Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems  

Microsoft Academic Search

Indexing terms: Time-delay systems, Guaranteed cost control Abstract: The design of robust state feedback controllers for a class of uncertain linear time- delay systems with norm-bounded uncertainty is presented. The state feedback results extend previous results on quadratic guaranteed cost control to the case of uncertain time-delay systems. This is done by the authors' definition of quadratic stability for uncertain

S. O. R. Moheimani; I. R. Petersen

1997-01-01

53

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

NASA Astrophysics Data System (ADS)

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

Khakestari, Marzieh; Ibragimov, Gafurjan; Suleiman, Mohamed

54

Central Control, Sewers and (0,1) quadratic programming  

NASA Astrophysics Data System (ADS)

We consider small sewer systems that combine foul water and storm water sewer functions in flat terrain. These systems are a combination of local gravity flow networks connected by pumps. The pumps are usually fixed speed, so they are on or off. We formulate a (0,1) quadratic programming problem, provide an overview of known solution methods and examine the relative speed of different solution methods.

Kolechkina, Alla; van Nooijen, Ronald

2013-04-01

55

Gain-scheduled Linear Quadratic Control of Wind Turbines Operating at High Wind Speed  

Microsoft Academic Search

This paper addresses state estimation and linear quadratic (LQ) control of variable speed variable pitch wind turbines. On the basis of a nonlinear model of a wind turbine, a set of operating conditions is identified and a LQ controller is designed for each operating point. The controller gains are then interpolated linearly to get a control law for the entire

K. Z. Ostergaard; Per Brath; Jakob Stoustrup

2007-01-01

56

Controlled dephasing of electrons by non-gaussian shot noise  

E-print Network

LETTERS Controlled dephasing of electrons by non-gaussian shot noise IZHAR NEDER1 *, FLORIAN-Maximilians-Universit¨at M¨unchen, 80333 M¨unchen, Germany *e-mail: izhar.neder@weizmann.ac.il Published online: 3 June 2007

Loss, Daniel

57

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

NASA Technical Reports Server (NTRS)

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

Kaidy, J. T.

1986-01-01

58

An adaptive linear quadratic regulator with repetitive controller applied to uninterruptible power supplies  

Microsoft Academic Search

This paper proposes a discrete time adaptive linear quadratic regulator (LQR) with a repetitive controller (RP) for uninterruptible power supplies (UPS). In the controller design, the gains are determined by minimizing a cost function which reduces the tracking error and the control signal. A recursive least squares (RLS) estimator identifies the plant parameters at different load conditions. Then, the LQR

Vinicius Foletto Montagner; Emerson Giovani Carati; H. A. Grundling

2000-01-01

59

Robust Reinforcement Learning Control Using Integral Quadratic Constraints for Recurrent Neural Networks  

Microsoft Academic Search

The applicability of machine learning techniques for feedback control systems is limited by a lack of stability guarantees. Robust control theory offers a framework for analyzing the stability of feedback control loops, but for the integral quadratic constraint (IQC) framework used here, all components are required to be represented as linear, time-invariant systems plus uncertainties with, for IQCs used here,

Charles W. Anderson; Peter Michael Young; Michael R. Buehner; James N. Knight; Keith A. Bush; Douglas C. Hittle

2007-01-01

60

Linear-quadratic model predictive control for urban traffic , Hai L. Vu a  

E-print Network

Linear-quadratic model predictive control for urban traffic networks q Tung Le a, , Hai L. Vu Accepted 30 June 2013 Keywords: Model predictive control Intelligent transport system Congestion control. One key aspect of ITS is the need for efficient and robust integrated network man- agement of urban

Nazarathy, Yoni

61

Gaussian Networks for Direct Adaptive Control  

Microsoft Academic Search

A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gausian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness

Robert M. Sanner; Jean-Jacques E. Slotine

1991-01-01

62

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

NASA Technical Reports Server (NTRS)

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.

Milman, Mark H.

1988-01-01

63

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

NASA Technical Reports Server (NTRS)

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.

Milman, Mark H.

1987-01-01

64

Decentralized state feedback guaranteed cost control of uncertain systems with uncertainty described by integral quadratic constraints  

Microsoft Academic Search

This paper presents a procedure for constructing decentralized state feedback guaranteed cost controllers for a class of uncertain systems in which the uncertainty is described by integral quadratic constraints. The proposed procedure involves solving an algebraic Riccati equation of the Hinfin control type which is dependent on a number of scaling parameters. By treating the off-diagonal elements of the full

Ian R. Petersen

2006-01-01

65

Uncertainty Modeling and Robust Control of LTI Systems Based on Integral Quadratic Constraints  

Microsoft Academic Search

Based on experimental data a joint method for nominal model error modeling and robust control is presented for linear time-invariant (LTI) systems. The goal of the method is to design a controller that attain robust quadratic performance and stability of the closed loop, and simultaneously construct an uncertainty model that is not invalidated by measurement data. The problem is motivated

G. Rodonyi; B. Lantos; J. Bokor

2007-01-01

66

Directional passability and quadratic steering logic for pyramid-type single gimbal control moment gyros  

NASA Astrophysics Data System (ADS)

Singularity analysis and the steering logic of pyramid-type single gimbal control moment gyros are studied. First, a new concept of directional passability in a specified direction is introduced to investigate the structure of an elliptic singular surface. The differences between passability and directional passability are discussed in detail and are visualized for 0H, 2H, and 4H singular surfaces. Second, quadratic steering logic (QSL), a new steering logic for passing the singular surface, is investigated. The algorithm is based on the quadratic constrained quadratic optimization problem and is reduced to the Newton method by using Gröbner bases. The proposed steering logic is demonstrated through numerical simulations for both constant torque maneuvering examples and attitude control examples.

Yamada, Katsuhiko; Jikuya, Ichiro

2014-09-01

67

Integral quadratic constraints-based robust controller two-mass-spring system  

Microsoft Academic Search

We propose the robust controller design for a two-mass-spring system based on integral quadratic constraints (IQCs) and give a design example of multipurpose controllers (state-feedback controller case). The controller design needs to achieve four major constraints: (i) tracking with zero steady-state error, (ii) guaranteed level of H? performance index ? (L2 gain) from the exogenous input w to the output

Chaiwat Jamjareekul; Athikom Roeksabutr; A. Kanchanaharuthai; P. Phokharatkul

2000-01-01

68

Optimal control of a class of linear multivariable systems with integral quadratic energy constraint †  

Microsoft Academic Search

A direct method for the solution of optimal control problems of linear time-invariant systems with integral quadratic energy constraint is developed with the help of functional analysis. It is based on the representation of the state transition matrix of the adjoint system in terms of an orthonormal set of functions in a finite dimensional sub-space of square integrable Hilbert space

B. C. ROY; A. K. CHOUDHURY

1973-01-01

69

On some dynamical and geometrical properties of the Maxwell-Bloch equations with a quadratic control  

E-print Network

In this paper, we analyze the stability of the real-valued Maxwell-Bloch equations with a control that depends on state variables quadratically. We also investigate the topological properties of the energy-Casimir map, as well as the existence of periodic orbits and explicitly construct the heteroclinic orbits.

Tudor Binzar; Cristian Lazureanu

2014-02-24

70

Optimal impulse control for cash management¶with quadratic holding-penalty costs  

Microsoft Academic Search

.   This paper studies optimal control for an infinite horizon cash management problem where the cash fund fluctuates as a Brownian\\u000a motion. Holding-penalty costs are assumed to be a quadratic function of the cash level and there are fixed and proportional\\u000a transaction costs. Using the “impulse technique”, we prove that optimal control exists and takes the form of a control

Stefano Baccarin

2002-01-01

71

The Robustness and Design of Constrained Cross-Directional Control Via Integral Quadratic Constraints  

Microsoft Academic Search

A robust stability test for a class of constrained cross-directional controllers is found. Under special circum- stances, the stability test is executed on a mode-by-mode basis and greatly simplified to a frequency-domain criterion. The test is also exploited to develop tuning algorithms. The control system involves a quadratic program embedded within an internal model control antiwindup structure and achieves optimal

Rafael M. Morales; William P. Heath

2011-01-01

72

Robust adaptive H ? control using integral quadratic constraints  

Microsoft Academic Search

This paper introduces a new approach to robust adaptive H? control. The main idea of the paper is to extend an existing approach to robust H? control to allow for constant or slowly varying unknown parameters in an adaptive way. This is achieved by treating the presence of the unknown parameters as states resulting in a bilinear nonlinearity. A copy

Ian R. Petersen

2008-01-01

73

Domain decomposition methods for advection dominated linear-quadratic elliptic optimal control problems.  

SciTech Connect

We present an optimization-level domain decomposition (DD) preconditioner for the solution of advection dominated elliptic linear-quadratic optimal control problems. The DD preconditioner is based on a decomposition of the optimality conditions for the elliptic linear-quadratic optimal control problem into smaller subdomain optimality conditions with Dirichlet boundary conditions for the states and the adjoints on the subdomain interfaces. These subdomain optimality conditions are coupled through Robin transmission conditions for the states and the adjoints. The parameters in the Robin transmission condition depend on the advection. This decomposition leads to a Schur complement system in which the unknowns are the state and adjoint variables on the subdomain interfaces. The Schur complement operator is the sum of subdomain Schur complement operators, the application of which is shown to correspond to the solution of subdomain optimal control problems, which are essentially smaller copies of the original optimal control problem. We show that, under suitable conditions, the application of the inverse of the subdomain Schur complement operators requires the solution of a subdomain elliptic linear-quadratic optimal control problem with Robin boundary conditions for the state. Numerical tests for problems with distributed and with boundary control show that the dependence of the preconditioners on mesh size and subdomain size is comparable to its counterpart applied to a single advection dominated equation. These tests also show that the preconditioners are insensitive to the size of the control regularization parameter.

Heinkenschloss, Matthias (Rice University, Houston, TX); Bartlett, Roscoe Ainsworth; Van Bloeman Waanders, Paul; Ridzal, Denis (Rice University, Houston, TX)

2005-04-01

74

Multimodel Gain Scheduled Quadratic Controller for Variable-Speed Wind Turbines Performances Improvement  

Microsoft Academic Search

\\u000a This paper deals with the design of a linear quadratic (LQ) control law combined with a multimodel approach for variable-speed,\\u000a variable-pitch wind turbines in order to improve their performances, especially the system global dynamic. The control law\\u000a is based on a linearization of the system around a selected set of operating points. Hence, a set of linear local models (sub-models)

Nadhira Khezami; Xavier Guillaud; Naceur Benhadj Braiek

75

On robust LPV controller synthesis: A dynamic Integral Quadratic Constraint based approach  

Microsoft Academic Search

In this paper the design of robust Linear Parameter Varying (LPV) controllers is addressed. A novel controller\\/scaling algorithm based on dynamic Integral Quadratic Constraints (IQCs) is proposed that completely avoids gridding as well as curve-fitting. Although, in this paper, we restrict our attention to dynamic DG-scalings, the techniques allow for generalization to the use of arbitrary real-rational IQC multipliers with

Joost Veenmanand; Carsten W. Scherer

2010-01-01

76

Searchless tuning of linear controllers for the minimum of quadratic criterion  

NASA Astrophysics Data System (ADS)

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

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

2014-03-01

77

Synthesis of robust controllers for systems with integral and quadratic constraints  

Microsoft Academic Search

The problem of synthesis of fixed-order linear time-invariant controllers which stabilize a system described in terms of multiple integral quadratic constraints is considered. We show that the problem is equivalent to solving a system of bilinear matrix inequalities. In general, this leads to a non-convex optimization with many local minima, which can be searched for by using a suitable method

A. Megretski

1994-01-01

78

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem  

NASA Technical Reports Server (NTRS)

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.

Ito, K.; Teglas, R.

1984-01-01

79

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem  

NASA Technical Reports Server (NTRS)

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.

Ito, Kazufumi; Teglas, Russell

1987-01-01

80

An adaptive Hinfinity controller design for bank-to-turn missiles using ridge Gaussian neural networks.  

PubMed

A new autopilot design for bank-to-turn (BTT) missiles is presented. In the design of autopilot, a ridge Gaussian neural network with local learning capability and fewer tuning parameters than Gaussian neural networks is proposed to model the controlled nonlinear systems. We prove that the proposed ridge Gaussian neural network, which can be a universal approximator, equals the expansions of rotated and scaled Gaussian functions. Although ridge Gaussian neural networks can approximate the nonlinear and complex systems accurately, the small approximation errors may affect the tracking performance significantly. Therefore, by employing the Hinfinity control theory, it is easy to attenuate the effects of the approximation errors of the ridge Gaussian neural networks to a prescribed level. Computer simulation results confirm the effectiveness of the proposed ridge Gaussian neural networks-based autopilot with Hinfinity stabilization. PMID:15565777

Lin, Chuan-Kai; Wang, Sheng-De

2004-11-01

81

Sequencing batch-reactor control using Gaussian-process models.  

PubMed

This paper presents a Gaussian-process (GP) model for the design of sequencing batch-reactor (SBR) control for wastewater treatment. The GP model is a probabilistic, nonparametric model with uncertainty predictions. In the case of SBR control, it is used for the on-line optimisation of the batch-phases duration. The control algorithm follows the course of the indirect process variables (pH, redox potential and dissolved oxygen concentration) and recognises the characteristic patterns in their time profile. The control algorithm uses GP-based regression to smooth the signals and GP-based classification for the pattern recognition. When tested on the signals from an SBR laboratory pilot plant, the control algorithm provided a satisfactory agreement between the proposed completion times and the actual termination times of the biodegradation processes. In a set of tested batches the final ammonia and nitrate concentrations were below 1 and 0.5 mg L(-1), respectively, while the aeration time was shortened considerably. PMID:23597762

Kocijan, Juš; Hvala, Nadja

2013-06-01

82

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

NASA Technical Reports Server (NTRS)

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.

Milman, M. H.

1985-01-01

83

Singular linear-quadratic control problem for systems with linear delay  

SciTech Connect

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

Sesekin, A. N. [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)

2013-12-18

84

Realization theory and quadratic optimal controllers for systems defined over Banach and Frechet algebras  

NASA Technical Reports Server (NTRS)

It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.

Byrnes, C. I.

1980-01-01

85

DOC-DAC: a generator for quadratic Discrete-time Optimal Control problems with options for Degeneracy, Activity and Conditioning  

Microsoft Academic Search

We present a quadratic Discrete-time Optimal Control problem generator, written in C, with options for Degeneracy, Activity and Conditioning (DOC- DAC). We use the generator to investigate badly conditioned and degenerate extended linear-quadratic problems (ELQPs) by solving such problems with primal-dual projected gradient and interior-point methods. The benefit of using second-order information in primal-dual projected gradient methods is also explored.

Anthony Graham; Daniel Ralph

86

Robust reinforcement learning control using integral quadratic constraints for recurrent neural networks.  

PubMed

The applicability of machine learning techniques for feedback control systems is limited by a lack of stability guarantees. Robust control theory offers a framework for analyzing the stability of feedback control loops, but for the integral quadratic constraint (IQC) framework used here, all components are required to be represented as linear, time-invariant systems plus uncertainties with, for IQCs used here, bounded gain. In this paper, the stability of a control loop including a recurrent neural network (NN) is analyzed by replacing the nonlinear and time-varying components of the NN with IQCs on their gain. As a result, a range of the NN's weights is found within which stability is guaranteed. An algorithm is demonstrated for training the recurrent NN using reinforcement learning and guaranteeing stability while learning. PMID:17668656

Anderson, Charles W; Young, Peter Michael; Buehner, Michael R; Knight, James N; Bush, Keith A; Hittle, Douglas C

2007-07-01

87

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

NASA Astrophysics Data System (ADS)

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

Bras, Rafael L.; Seo, Dong-Jun

1987-07-01

88

The International Symposium on Transportation and Traffic Theory 00 (2013) 119 Linear-Quadratic Model Predictive Control  

E-print Network

The International Symposium on Transportation and Traffic Theory 00 (2013) 1­19 Linear-Quadratic Model Predictive Control for Urban Traffic Networks Tung Lea , Hai L. Vua Yoni Nazarathyb , Bao Voa traffic networks. This paper presents a general model predictive control framework for both centralized

Nazarathy, Yoni

89

Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations  

E-print Network

Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations T´erence Bayen J. Fr´ed´eric Bonnans Francisco J. Silva§ September 11, 2013 Abstract In this article we consider an optimal control problem of a semi-linear elliptic equation, with bound constraints

Paris-Sud XI, Université de

90

Application of self-tuning Gaussian networks for control of civil structures equipped with magnetorheological dampers  

E-print Network

This paper proposes an adaptive neural network composed of Gaussian radial functions for mapping the behavior of civil structures controlled with magnetorheological dampers. The online adaptation takes into account the ...

Laflamme, Simon

91

Linear quadratic tracking controller design to improve high frequency power supply system performance  

SciTech Connect

The performance of the High Frequency Power Supply (HFPS) induction heating system is improved by building an optimal controller to achieve optimal closed loop control, using the Linear Quadratic Tracking (LQT) method. The optimal controller is to minimize the difference between the HFPS system output (i{sub SE}) and the desired reference signal (r(t)) while keeping the system input (V{sub d}) minimized. The objective of this research is to improve the performance of a HFPS induction heating system. The utilization of switching devices in such a system result in high power loss, poor line power factor, and harmful harmonics. In this research, first a discrete-time linear system model is developed to simulate the HFPS system with a series-parallel resonant load. Second, in order to improve the system performance, an optimal controller is developed to achieve optimal closed-loop control, by applying LQT method. Third, computer simulation is used to simulate the ideal and real system performance with the optimal controller. The simulation results are compared with the industry test data to confirm the theoretical consideration.

Li, X. [Ajax Magnethermic Corp., Warren, OH (United States); Jalali, J.; Foulkes, R.H. Jr. [Youngstown State Univ., OH (United States). Electrical Engineering Dept.

1999-11-01

92

Multiple Testing and Error Control in Gaussian Graphical Model Selection  

Microsoft Academic Search

Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of conditional independences that is imposed on the variables’ joint distribution. Focusing on Gaussian models, we review

Mathias Drton; Michael D. Perlman

2007-01-01

93

Soliton transmission control by super-Gaussian filters  

NASA Astrophysics Data System (ADS)

Bandwidth-limited filtering has been proven to overcome certain limitations in soliton transmission systems. We propose super-Gaussian filters instead of Butterworth filter response obtained with conventionally used Fabry-Perot etalons as a method to improve soliton stability and reduce dispersion degradation and theoretically demonstrate their practical implementation in the form of holographic fiber gratings.

Peral, E.; Capmany, J.; Marti, J.

1996-12-01

94

Linear-quadratic-regulator pointing control system design for a high-altitude balloon payload  

SciTech Connect

A pointing control system design for the science package of a NASA high-altitude research balloon is described. The balloon assembly consists of a single helium balloon connected to a payload recovery parachute, payload gondola, and ballast hopper. Pointing of the scientific payload is accomplished via an arrangement of drive motors and a flywheel. Linear quadratic regulator (LQR) synthesis techniques are employed to produce the azimuth and elevation controller designs. The use of LQR synthesis is motivated by the azimuthal dynamic coupling encountered between the balloon and gondola. Two control devices are employed in azimuth, one of which is a decoupler motor and the other a flywheel. The decoupler motor is intended to isolate the gondola from the balloon such that the flywheel can be accelerated or decelerated about a steady-state angular velocity to provide precise azimuthal pointing. The multiple-input/multiple-output nature of the azimuth pointing problem is best handled in a matrix synthesis procedure such as LQR. The controller design methodology is explained, and a combination of time responses and singular value analyses are used to analytically evaluate the performance of the control system. 11 refs., 17 figs.

White, J.E.; Etter, J.R.

1987-11-01

95

Optimal PHP control of multiple part-types on a failure-prone machine with quadratic buffer costs  

Microsoft Academic Search

We consider a single, failure-prone machine, producing multiple part-types. The goal is to minimize the expected sum of quadratic buffer costs. In general, the optimal solution to this problem is unknown. However, by restricting the allowable set of control policies to the class of prioritized hedging point policies, we are able to determine simple, analytical expressions for the optimal hedging

Chang Shu; James R. Perkins

1998-01-01

96

Robust stabilization of uncertain linear systems: quadratic stabilizability and H? control theory  

Microsoft Academic Search

The problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency-domain results on H? optimization. A complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given. Relations

PRAMOD P. KHARGONEKAR; IAN R. PETERSEN; KEMIN ZHOU

1990-01-01

97

Lyapunov functions for quadratic differential equations with applications to adaptive control  

Microsoft Academic Search

Conditions are derived for the existence of quadratic Lyapunov functions for vector differential equations with quadratic terms. These conditions are used to establish a set of nonlinear equations for which the null solution is asymptotically stable in the whole. Many of the recent results in the stability of model reference adaptive systems are particular cases of these general conditions.

G. Luders; K. Narendra

1972-01-01

98

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

NASA Astrophysics Data System (ADS)

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

Arimoto, Suguru

99

Sequential Quadratic Programming (SQP) for optimal control in direct numerical simulation of turbulent flow  

NASA Astrophysics Data System (ADS)

The current work focuses on the development and application of an efficient algorithm for optimization of three-dimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or Large-Eddy Simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a damped formulation of the limited-memory BFGS method. The latter is suitable for solving large-scale constrained optimization problems whose Hessian matrices cannot be computed and stored at a reasonable cost. We combine the algorithm with a line-search merit function based on an L1-norm to enforce the convergence from any remote point. It is first shown that the proposed form of the damped L-BFGS algorithm is suitable for solving equality constrained Rosenbrock type functions. Then, we apply the algorithm to an optimal-control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon T. The controls are further subject to a non-linear equality constraint on the total control energy. DNSs are used to resolve all turbulent scales of motion, and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals. We compare the convergence speed of the SQP L-BFGS algorithm to a conventional non-linear conjugate-gradient method (i.e. the current standard in DNS-based optimal control), and find that the SQP algorithm is more than an order of magnitude faster than the conjugate-gradient method.

Badreddine, Hassan; Vandewalle, Stefan; Meyers, Johan

2014-01-01

100

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

SciTech Connect

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

Ayvaz, Muzaffer; Demiralp, Metin [Istanbul Technical University, Informatics Institute, Maslak, 34469, Istanbul (Turkey)

2011-09-14

101

Quadratic formula  

NSDL National Science Digital Library

The quadratic formula is easy to solve, yet sufficiently sophisticated that it provides insight into oscillations of masses connected by springs, as well as insight into chemical bonds between atoms. The purpose of this video is to illustrate what it means to find the "zeros" or "roots" of the quadratic equation, both using a graphical description, as well as by analytically completing the square to obtain the famous quadratic formula.

2013-06-21

102

Robust fuzzy tracking control for nonlinear networked control systems with integral quadratic constraints  

Microsoft Academic Search

This paper investigates the robust tracking control problem for a class of nonlinear networked control systems (NCSs) using\\u000a the Takagi-Sugeno (T-S) fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented\\u000a Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established\\u000a such that the closed-loop systems stability and time-domain integral

Zhi-Sheng Chen; Yong He; Min Wu

2010-01-01

103

Synchronization of Fractional-order Chaotic Systems with Gaussian fluctuation by Sliding Mode Control  

E-print Network

This paper is devoted to the problem of synchronization between fractional-order chaotic systems with Gaussian fluctuation by the method of fractional-order sliding mode control. A fractional integral (FI) sliding surface is proposed for synchronizing the uncertain fractional-order system, and then the sliding mode control technique is carried out to realize the synchronization of the given systems. One theorem about sliding mode controller is presented to prove the proposed controller can make the system synchronize. As a case study, the presented method is applied to the fractional-order Chen-L\\"u system as the drive-response dynamical system. Simulation results show a good performance of the proposed control approach in synchronizing the chaotic systems in presence of Gaussian noise.

Yong Xu; Hua Wang

2013-09-04

104

Model validation for robust control of uncertain systems with an integral quadratic constraint  

Microsoft Academic Search

This paper presents a new approach to the model validation problem for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint. The proposed model validation algorithm is based on the solution to a game-type Riccati differential equation and a set of state equations closely related to a robust Kalman filtering problem.

Andrey V. Savkin; Ian R. Petersen

1996-01-01

105

The Trust Region Sequential Quadratic Programming method applied to two-aircraft acoustic optimal control problem  

E-print Network

more severe constraints on the next generation of aircraft [4]. In sight of reaching one of the 2020The Trust Region Sequential Quadratic Programming method applied to two-aircraft acoustic optimal University of Orléans. CNRS-MAPMO (France) Abstract: This paper aims to reduce noise levels of two-aircraft

Paris-Sud XI, Université de

106

Improved single neuron controller for multivariable stochastic systems with non-Gaussianities and unmodeled dynamics.  

PubMed

In this paper, a new adaptive control approach is presented for multivariate nonlinear non-Gaussian systems with unknown models. A more general and systematic statistical measure, called (h,?)-entropy, is adopted here to characterize the uncertainty of the considered systems. By using the "sliding window" technique, the non-parameter estimate of the (h,?)-entropy is formulated. Then, the improved neuron based controllers are developed for multivariate nonlinear non-Gaussian systems by minimizing the entropies of the tracking errors in closed loops. The condition to guarantee the strictly decreasing entropy of tracking error is presented. Moreover, the convergence in the mean-square sense has been analyzed for all the weights in the neural controllers. Finally, the comparative simulation results are presented to show that the performance of the proposed algorithm is superior to that of PID control strategy. PMID:23910156

Zhang, Jianhua; Jiang, Man; Ren, Mifeng; Hou, Guolian; Xu, Jinliang

2013-11-01

107

Design of robust-stable and quadratic finite-horizon optimal controllers with low trajectory sensitivity for uncertain active suspension systems  

Microsoft Academic Search

This paper presents a design method for designing the robust-stable and quadratic-finite-horizon-optimal controllers of uncertain active suspension systems. The method integrates a robust stabilisability condition, the orthogonal functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA). Using the integrative computational method, a robust-stable and quadratic-finite-horizon-optimal controller with low-trajectory sensitivity can be obtained such that (i) the active suspension system with

Shinn-Horng Chen; Jyh-Horng Chou; Liang-An Zheng; Sheng-Kai Lin

2010-01-01

108

A Rank Constrained LMI Algorithm for Decentralized State Feedback Guaranteed Cost Control of Uncertain Systems with Uncertainty Described by Integral Quadratic Constraints  

Microsoft Academic Search

The paper presents a numerical algorithm for constructing a decentralized state feedback guaranteed cost controller for an uncertain system. The uncertain systems under consideration contain structured uncertainty described by integral quadratic constraints. The decentralized controller is designed to achieve a closed loop system which is absolutely stable and such that a cost function satisfies a given bound for all admissible

Li Li; R. Petersen

2007-01-01

109

Xuping Xu and Panos J. Antsaklis, "An Approach to General Switched Linear Quadratic Optimal Control Problems with State Jumps," Proceedings of the 15th International Symposium on Mathematical Theory of  

E-print Network

Switched Linear Quadratic Optimal Control Problems with State Jumps," Proceedings of the 15th International Control Problems with State Jumps," Proceedings of the 15th International Symposium on Mathematical Theory Switched Linear Quadratic Optimal Control Problems with State Jumps," Proceedings of the 15th International

Antsaklis, Panos

110

POD a-posteriori error estimates for linear-quadratic optimal control problems  

Microsoft Academic Search

The main focus of this paper is on an a-posteriori analysis for the method of proper orthogonal decomposition (POD) applied\\u000a to optimal control problems governed by parabolic and elliptic PDEs. Based on a perturbation method it is deduced how far\\u000a the suboptimal control, computed on the basis of the POD model, is from the (unknown) exact one. Numerical examples illustrate

F. Tröltzsch; S. Volkwein

2009-01-01

111

Application of optimal control theory to the design of the NASA/JPL 70-meter antenna servos  

NASA Technical Reports Server (NTRS)

The application of Linear Quadratic Gaussian (LQG) techniques to the design of the 70-m axis servos is described. Linear quadratic optimal control and Kalman filter theory are reviewed, and model development and verification are discussed. Families of optimal controller and Kalman filter gain vectors were generated by varying weight parameters. Performance specifications were used to select final gain vectors.

Alvarez, L. S.; Nickerson, J.

1989-01-01

112

Solving quadratic Introduction  

E-print Network

Solving quadratic equations 3.2 Introduction A quadratic equation is one which can be written. In this section we describe several ways in which quadratic equations can be solved. ' & $ % Prerequisites Before completing this Section you should be able to . . . recognise a quadratic equation solve a quadratic

Vickers, James

113

Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis  

NASA Technical Reports Server (NTRS)

Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

Jeon, G. J.

1983-01-01

114

Stability analysis for a type of TS fuzzy control systems using integral quadratic constraints  

Microsoft Academic Search

Recently, the well-known circle criterion and Popov criterion are introduced to investigate the stability of a type of T-S fuzzy control systems. Although both the two corresponding stability conditions have elegant graphical interpretations, the relation of them is not well studied. In this paper, we try to explain the two conditions by a new unified stability condition, which is based

Hongqian Lu; Kairui Cao; Xiaojun Ban; Xianlin Huang

2012-01-01

115

Model-based thermoacoustic oscillation control via ?? loop-shaping and Integral Quadratic Constraints  

Microsoft Academic Search

Lean premixed prevaporized (LPP) technology has been widely used in the new generation of gas turbines in which reduced emissions are a priority. However, such combustion systems are susceptible to the damage of self-excited oscillations. Feedback control provide a way of preventing such dynamic stabilities. A flame dynamics assumption is proposed for a recently developed unsteady heat release model, the

Xiaochuan Yuan; Keith Glover

2010-01-01

116

Control of combustion oscillations via Hinfinity loop-shaping, µ-analysis and Integral Quadratic Constraints  

Microsoft Academic Search

Certain combustion processes are inherently unstable due to the coupling of the flame and the acoustic modes of the combustion chamber. Such instabilities lead to oscillating heat release and pressure, which are undesirable. A means to eliminate these oscillations is to design a controller to monitor the fluctuating pressure upstream and modulate the fuel injection accordingly. Making use of a

Yun-Chung Chu; Keith Glover; Ann P. Dowling

2003-01-01

117

On the Dual Decomposition of Linear Quadratic Optimal Control Problems for Vehicular Formations  

E-print Network

systems, owing to its excessive communication requirements. A preferred alternative is to have control that vehicles can iteratively compute their primal and dual variables by only communicating with their immediate of the augmented Lagrangian method, and numerical examples are provided to demonstrate the utility of our results

Fardad, Makan

118

Spatial solitons in a three-level atomic medium supported by a Laguerre-Gaussian control beam  

SciTech Connect

We investigate the existence and stability of various types of spatial solitons in a three-level atomic medium with Laguerre-Gaussian control beam. Radial and azimuthal modulations of the medium properties, introduced by the control beam, provide possibilities for existence of diverse soliton patterns and dynamics. Beam diffraction provides additional soliton controllability. All types of solitons can be generated at very low input energy at a few-photon level.

Hang Chao [Centro de Fisica Teorica e Computacional, Faculdade de Ciencias, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa PT-1649-003 (Portugal); Department of Physics and State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai CN-200062 (China); Konotop, V. V. [Centro de Fisica Teorica e Computacional, Faculdade de Ciencias, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa PT-1649-003 (Portugal); Departamento de Fisica, Faculdade de Ciencias, Universidade de Lisboa, Campo Grande, Ed. C8, Piso 6, Lisboa PT-1749-016 (Portugal)

2011-05-15

119

Separation Theorem for Linearly Constrained LQG Optimal Control -Continuous Time Case 1  

E-print Network

. In this paper, we shall consider linear integral constraints of the form 3.3 for the deterministic problem Distribution Center, Notre Dame, IN 46556 USA. February 1996 Abstract: We solve the linearly constrained linear-quadratic LQ and linear-quadratic-Gaussian LQG optimal control problems. Closed form expressions of the optimal

Moore, John Barratt

120

A line-of-sight performance criterion for controller design of a proposed laboratory model  

NASA Technical Reports Server (NTRS)

A line-of-sight performance criterion is derived for a proposed Controls Structures Interaction model, and its many uses in the control design process for fine pointing control are illustrated. A linearized line-of-sight (LOS) criterion is used for direct controller design and as a performance measure to judge different control methodologies. Numerical simulation results are shown where the three approaches: linear quadratic Gaussian theory, robust eigensystem assignment, and local velocity feedback are used for vibration control. Results indicate that the linear quadratic Gaussian controller, which incorporates a linearized LOS weighting matrix directly, yields good performance without wasting energy to control motions that have no influence on the LOS.

Lim, Kyong B.; Horta, Lucas G.

1990-01-01

121

Comparison of wind turbine LQG controllers using Individual Pitch Control to alleviate fatigue loads  

Microsoft Academic Search

This paper focuses on the design of Linear Quadratic Gaussian (LQG) controllers for variable-speed horizontal axis Wind Turbines (WT). These turbines use blade pitch angle and electromagnetic torque control variables to meet specified objectives for Full Load (FL) zone. The main control objectives are to reduce structural dynamic loads and to regulate the power of the WT. The controllers are

S. Nourdine; H. Camblong; I. Vechiu; G. Tapia

2010-01-01

122

?p-norms of codewords from capacity- and dispersion-achieveing Gaussian codes  

E-print Network

It is demonstrated that codewords of good codes for the additive white Gaussian noise (AWGN) channel become more and more isotropically distributed (in the sense of evaluating quadratic forms) and resemble white Gaussian ...

Polyanskiy, Yury

123

Improved temperature control of a PWR nuclear reactor using an LQG\\/LTR based controller  

Microsoft Academic Search

State feedback assisted classical (SFAC) control has been developed to improve the temperature response performance of nuclear reactors via modifying the embedded classical controller reference signal. This is done by means of an outermost state feedback controller. A linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) at the plant output seems a good candidate for the state feedback loop of

Hussein Arab-Alibeik; Saeed Setayeshi

2003-01-01

124

Graphing Quadratic Equations  

NSDL National Science Digital Library

This is an introductory lesson to graphing quadratic equations. This lesson uses graphing technology to illustrate the differences between quadratic equations and linear equations. In addition, it allows students to identify important parts of the quadratic equation and how each piece changes the look of the graph.

Lengacher, Robert

2012-07-05

125

Lesson 14: Quadratic Formula  

NSDL National Science Digital Library

Completing the square is applied to the general quadratic to derive the quadratic formula. Before an area application example is given there is a quick review of the four methods that have been presented for solving quadratic equations. Complex numbers are introduced before the discriminant is presented.

2011-01-01

126

Self-Replicating Quadratics  

ERIC Educational Resources Information Center

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

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

127

Gaussian Primes  

NSDL National Science Digital Library

This is an introduction to Gaussian primes, complex numbers with integers for real and imaginary parts that are divisible by themselves and 1, but no other complex numbers with integer coefficients. This shows calculations of the first few Gaussian primes.

Loy, Jim

128

Power control for the additive white Gaussian noise channel under channel estimation errors  

Microsoft Academic Search

We investigate the time-varying additive white Gaussian noise channel with imperfect side-information. In practical systems, the channel gain may be estimated from a probing signal and estimation errors cannot be avoided. The goal of this paper is to determine a power allocation that a priori incorporates statistical knowledge of the estimation error. This is in contrast to prior work which

Thierry E. Klein; Robert G. Gallager

2001-01-01

129

Dynamical Gaussian state transfer with quantum-error-correcting architecture  

NASA Astrophysics Data System (ADS)

Transferring a quantum state of a light field to a memory is of particular importance. However, this transfer is usually hampered because the memory system is subjected to some noise and this can limit the performance of the state transfer greatly. In this paper, we consider the transfer of a Gaussian state of light to a linear medium memory such as an optomechanical oscillator and propose a dynamical feedback controller that suppresses the noise in the memory system. To protect an unknown state, the feedback scheme employs the specific configuration of the quantum error correction; that is, a three-mode Gaussian state having appropriate syndromes is taken as the input. Correspondingly, the memory consists of three independent linear systems. The syndrome errors are estimated continuously in time through the measurement of the output field, and the results are then fed back to control the system. Because the input is Gaussian and the systems are all linear, it is possible to formulate the problem using the framework of the celebrated classical Kalman filtering and linear quadratic Gaussian control. A numerical simulation demonstrates the effectiveness of the control scheme.

Tajimi, Go; Yamamoto, Naoki

2012-02-01

130

VTOL controls for shipboard landing. M.S.Thesis  

NASA Technical Reports Server (NTRS)

The problem of landing a VTOL aircraft on a small ship in rough seas using an automatic controller is examined. The controller design uses the linear quadratic Gaussian results of modern control theory. Linear time invariant dynamic models are developed for the aircraft, ship, and wave motions. A hover controller commands the aircraft to track position and orientation of the ship deck using only low levels of control power. Commands for this task are generated by the solution of the steady state linear quadratic gaussian regulator problem. Analytical performance and control requirement tradeoffs are obtained. A landing controller commands the aircraft from stationary hover along a smooth, low control effort trajectory, to a touchdown on a predicted crest of ship motion. The design problem is formulated and solved as an approximate finite-time linear quadratic stochastic regulator. Performance and control results are found by Monte Carlo simulations.

Mcmuldroch, C. G.

1979-01-01

131

Robust control of smart structures using neural network hardware  

Microsoft Academic Search

In this paper, the use of Intel's Electronically Trainable Analog Neural Network (ETANN) chipi80170NX for implementing single-chip robust controllers for smart structures is successfully demonstrated. Robust controllers like the linear quadratic regulator (LQR) and linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) are implemented in various configurations using the ETANN chip on the smart structure test article. The test article

Rajendra Damle; Vittal Rao; Frank Kern

1997-01-01

132

Homotopy approach to optimal, linear quadratic, fixed architecture compensation  

NASA Technical Reports Server (NTRS)

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.

Mercadal, Mathieu

1991-01-01

133

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)

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.

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

1977-01-01

134

Gain scheduling control of variable speed WTG under widely varying turbulence loading  

Microsoft Academic Search

Probabilistic paradigms for wind turbine controller design have been gaining attention. Motivation derives from the need to replace outdated empirical-based designs with more physically relevant models. This paper proposes an adaptive controller in the form of a linear quadratic Gaussian (LQG) for control of a stall-regulated, variable speed wind turbine generator (WTG). In the control scheme, the strategy is twofold:

Endusa Billy Muhando; Tomonobu Senjyu; Naomitsu Urasaki; Atsushi Yona; Hiroshi Kinjo; Toshihisa Funabashi

2007-01-01

135

Design of a candidate flutter suppression control law for DAST ARW-2  

NASA Technical Reports Server (NTRS)

A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQC (Linear Quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

Adams, W. M., Jr.; Tiffany, S. H.

1984-01-01

136

A new eddy current model for magnetic bearing control system design  

NASA Technical Reports Server (NTRS)

This paper describes a new VLSI-based controller for the implementation of a Linear-Quadratic-Gaussian (LQG) theory-based control system. Use of the controller is demonstrated by design of a controller for a magnetic bearing and its performance is evaluated by computer simulation.

Feeley, Joseph J.; Ahlstrom, Daniel J.

1992-01-01

137

A quantum mechanical version of Price's theorem for Gaussian states  

E-print Network

This paper is concerned with integro-differential identities which are known in statistical signal processing as Price's theorem for expectations of nonlinear functions of jointly Gaussian random variables. We revisit these relations for classical variables by using the Frechet differentiation with respect to covariance matrices, and then show that Price's theorem carries over to a quantum mechanical setting. The quantum counterpart of the theorem is established for Gaussian quantum states in the framework of the Weyl functional calculus for quantum variables satisfying the Heisenberg canonical commutation relations. The quantum mechanical version of Price's theorem relates the Frechet derivative of the generalized moment of such variables with respect to the real part of their quantum covariance matrix with other moments. As an illustrative example, we consider these relations for quadratic-exponential moments which are relevant to risk-sensitive quantum control.

Igor G. Vladimirov

2014-09-15

138

Quadratic eigenvalue problems.  

SciTech Connect

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

Walsh, Timothy Francis; Day, David Minot

2007-04-01

139

Direct adaptive control of wind energy conversion systems using Gaussian networks  

Microsoft Academic Search

Grid connected wind energy conversion systems (WECS) present interesting control demands, due to the intrinsic nonlinear characteristics of windmills and electric generators. In this paper a direct adaptive control strategy for WECS control is proposed. It is based on the combination of two control actions: a radial basis function network-based adaptive controller, which drives the tracking error to zero with

Miguel Angel Mayosky; Gustavo I. E. Cancelo

1999-01-01

140

Direct adaptive control of wind energy conversion systems using Gaussian networks.  

PubMed

Grid connected wind energy conversion systems (WECS) present interesting control demands, due to the intrinsic nonlinear characteristics of windmills and electric generators. In this paper a direct adaptive control strategy for WECS control is proposed. It is based on the combination of two control actions: a radial basis zfunction network-based adaptive controller, which drives the tracking error to zero with user specified dynamics, and a supervisory controller, based on crude bounds of the system's nonlinearities. The supervisory controller fires when the finite neural-network approximation properties cannot be guaranteed. The form of the supervisor control and the adaptation law for the neural controller are derived from a Lyapunov analysis of stability. The results are applied to a typical turbine/generator pair, showing the feasibility of the proposed solution. PMID:18252585

Mayosky, M A; Cancelo, I E

1999-01-01

141

Supplementary material for nonparameteric adaptive control of time varying systems using gaussian processes  

E-print Network

Real-world dynamical variations make adaptive control of time-varying systems highly relevant. However, most adaptive control literature focuses on analyzing systems where the uncertainty is represented as a weighted linear ...

Chowdhary, Girish

2013-03-15

142

Quadratic Liénard Equations with Quadratic Damping  

Microsoft Academic Search

In this paper we study the generalized Liénard equations x+f(x)x+g(x)=0 with quadratic polynomialsfandg. We prove that these kind of equations can have at most one limit cycle, and we give the complete bifurcation diagram and classification of the phase portraits. The paper also contains a shorter proof for the result in A. Lins, W. de Melo, and C. C. Pugh,

Freddy Dumortier; Chengzhi Li

1997-01-01

143

Signatures of non-Gaussianity in the curvaton model  

NASA Astrophysics Data System (ADS)

We discuss the signatures of non-Gaussianity in the curvaton model where the potential includes also a non-quadratic term. In such a case the non-linearity parameter fNL can become very small, and we show that non-Gaussianity is then encoded in the non-reducible non-linearity parameter gNL of the trispectrum, which can be very large. Thus the place to look for the non-Gaussianity in the curvaton model may be the trispectrum rather than the bispectrum. We also show that gNL measures directly the deviation of the curvaton potential from the purely quadratic form. While gNL depends on the strength of the non-quadratic terms relative to the quadratic one, we find that for reasonable cases roughly g_{\\mathrm {NL}} \\sim \\mathcal {O}(-10^4) -\\mathcal {O}(-10^5) , which are values that may well be accessible by future observations.

Enqvist, Kari; Takahashi, Tomo

2008-09-01

144

Main graphs: Quadratic equation  

E-print Network

a>0 OR OR OR x x x xxx x x x y y y Quadratic equation: The general solution of a quadratic equation equations: Equation dN dt = kN has the solution: N(t) = N0ekt; N0 is an (arbitrary) initial value of N. Systems of linear differential equations: For system dx dt = ax+by dy dt = cx+dy , the characteristic

Utrecht, Universiteit

145

Gaussian Processes and Reinforcement Learning for Identification and Control of an Autonomous Blimp  

E-print Network

Intel Research Seattle, Seattle, WA Abstract-- Blimps are a promising platform for aerial robotics are mainly based on PID controllers [14], [15], [16] or non- linear dynamic models [1], [2], [3], [5]. System

Washington at SeattleUniversity of

146

A hypothesis-based algorithm for planning and control in non-Gaussian belief spaces  

E-print Network

We consider the partially observable control problem where it is potentially necessary to perform complex information-gathering operations in order to localize state. One approach to solving these problems is to create ...

Platt, Robert, Jr.

2011-08-27

147

Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors  

NASA Technical Reports Server (NTRS)

This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuators and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

Balakrishnan, A. V.

1994-01-01

148

Some results on disturbance rejection control for an adaptive optics system  

NASA Astrophysics Data System (ADS)

Using linear quadratic gaussian (LQG) control theory, we propose a disturbance rejection control for an adaptive optics (AO) system. An a posteriori frequency analysis of the AO multivariable feedback system is carried out to check stability and robustness properties. We present numerical simulations to demonstrate the effectiveness of the proposed approach.

Folcher, J.-P.; Abelli, A.; Ferrari, A.; Carbillet, M.

2010-12-01

149

LQG controller design using GUI: Application to antennas and radio-telescopes  

Microsoft Academic Search

The Linear Quadratic Gaussian (LQG) algorithm has been used to control the JPL's beam wave-guide, and 70-m antennas. This algorithm significantly improves tracking precision in a wind disturbed environment. Based on this algorithm and the implementation experience a Matlab based Graphical User Interface (GUI) was developed to design the LQG controllers applicable to antennas and radiotelescopes. The GUI is described

Erin Maneri; Wodek Gawronski

2000-01-01

150

The quadratic Fock functor  

NASA Astrophysics Data System (ADS)

We construct the quadratic analog of the boson Fock functor. While in the first order (linear) case all contractions on the 1-particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. The encouraging fact is that it contains, as proper subgroups (i.e., the contractions), all the gauge transformations of second kind and all the a.e. invertible maps of Rd into itself leaving the Lebesgue measure quasi-invariant (in particular, all diffeomorphism of Rd). This allows quadratic two-dimensional quantization of gauge theories, of representations of the Witt group (in fact it continuous analog), of the Zamolodchikov hierarchy, and much more. Within this semigroup we characterize the unitary and the isometric elements and we single out a class of natural contractions.

Accardi, Luigi; Dhahri, Ameur

2010-02-01

151

Quadratic exponential vectors  

SciTech Connect

We give a necessary and sufficient condition for the existence of a quadratic exponential vector with test function in L{sup 2}(R{sup d}) intersection L{sup {infinity}}(R{sup d}). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique different from the one used by Accardi et al. [Quantum Probability and Infinite Dimensional Analysis, Vol. 25, p. 262, (2009)], we also extend, to a more general class of test functions, the explicit form of the scalar product between two such vectors.

Accardi, Luigi; Dhahri, Ameur [Volterra Center, University of Roma Tor Vergata, Via Columbia 2, 00133 Roma (Italy)

2009-12-15

152

Active flutter control for flexible vehicles, volume 1  

NASA Technical Reports Server (NTRS)

An active flutter control methodology based on linear quadratic gaussian theory and its application to the control of a super critical wing is presented. Results of control surface and sensor position optimization are discussed. Both frequency response matching and residualization used to obtain practical flutter controllers are examined. The development of algorithms and computer programs for flutter modeling and active control design procedures is reported.

Mahesh, J. K.; Garrard, W. L.; Stones, C. R.; Hausman, P. D.

1979-01-01

153

Why Quadratic Mean Diameter?  

Microsoft Academic Search

Quadratic mean diameter is the measure of average tree diameter conventionally used in forestry, rather than arithmetic mean diameter. The historical and practical reasons for this convention are reviewed. West. J. Appl. For. 15(3):137-139. Average diameter is a widely used stand statistic that appears in virtually all yield tables, simulator outputs, stand summaries, and much inventory data. To most people,

Robert O. Curtis; David D. Marshall

154

Generalized quadratic Liénard equations  

Microsoft Academic Search

In this article we give explicit formulae for the Liapunov quantities of generalized Liénard systems with either quadratic damping or restoring coefficients. These quantities provide necessary conditions in order for the origin to be a centre. Recent results are also presented for these systems.

S. Lynch

1998-01-01

155

Improved perturbation bounds for general quadratic matrix equations  

Microsoft Academic Search

Perturbation analysis of general algebraic quadratic matrix equations is presented, which include as particular cases the standard and descriptor algebraic matrix Riccati equations, arising in the optimal control and filtering of continuous, time-invariant, linear systems. The perturbation bounds derived are superior to the bounds, already available in the literature. They are applicable to the error analysis of general quadratic matrix

M. M. Konstantinov; P. Hr. Petkov; D. W. Gu

1999-01-01

156

A general characteristic equation for a diffusion-controlled gas discharge column of arbitrary shape with electron production and loss rates linear and quadratic in electron density  

Microsoft Academic Search

A simple yet general expression characterizes the electrical properties of a steady-state positive column of arbitrary cross-sectional shape with electron production and loss rates linear or quadratic in electron density in addition to electron loss by diffusion. This equation relates effective ionization and diffusion coefficients (or applied electric field), the total number of electrons per unit column length (or electron

Gerald L. Rogoff

1979-01-01

157

Main graphs: Quadratic equation  

E-print Network

Main graphs: Quadratic equation: Equation A2 +B+C = 0, has solutions given by the following 'abc equations: Equation dN dt = kN has the solution: N(t) = N0ekt; N0 is an (arbitrary) initial value of N. Characteristic time of change is = 1/k. Systems of linear differential equations: For system dx dt = ax+by dy dt

Utrecht, Universiteit

158

Guises and Disguises of Quadratic Divergences  

E-print Network

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

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

2014-10-04

159

Guises and disguises of quadratic divergences  

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

160

Integral quadratic constraint approach vs. multiplier approach  

Microsoft Academic Search

Integral quadratic constraints (IQC) arise in many optimal and\\/or robust control problems. The IQC approach can be viewed as a generalization of the classical multiplier approach in the absolute stability theory. In this paper, we study the relationship between the two approaches for robust stability analysis. The key result shows that for many applications, the existence of an IQC is

Minyue Fu; Soura Dasgupta; Yeng Chai Sohz

2002-01-01

161

Integral quadratic constraint approach vs. multiplier approach  

Microsoft Academic Search

Integral quadratic constraints (IQC) arise in many optimal and\\/or robust control problems. The IQC approach can be viewed as a generalization of the classical multiplier approach in the absolute stability theory. In this paper, we study the relationship between the two approaches for robust stability analysis. Using a slightly modified multiplier approach, we show that the existence of an IQC

Minyue Fu; Soura Dasgupta; Yeng Chai Soh

2005-01-01

162

System analysis via integral quadratic constraints  

Microsoft Academic Search

This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. From an original idea by Yakubovich (1967), the approach has been developed under a combination of influences from the Western and Russian traditions of control theory. It is shown how a complex system can be described, using integral quadratic constraints (IQC) for

Alexandre Megretski; Anders Rantzer

1997-01-01

163

System analysis via integral quadratic constraints  

Microsoft Academic Search

It is demonstrated how a number of widely used tools for stability analysis can be conveniently unified and generalized using integral quadratic constraints (IQCs). The approach has emerged under a combination of influences from the western and Russian traditions of control theory. An IQC based stability theorem is presented, which covers classical small gain conditions with anti-causal multipliers, but gains

A. Rantzer; A. Megretski

1994-01-01

164

LQG\\/LTR robust control of nuclear reactors with improved temperature performance  

Microsoft Academic Search

The authors present the design of a robust controller using the linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) for nuclear reactors with the objective of maintaining a desirable performance for reactor fuel temperature and the temperature of the coolant leaving the reactor for a wide range of reactor powers. The results obtained are compared to those for an observer-based

Adel Ben-Abdennour; Robert M. Edwards; Kwang Y. Lee

1992-01-01

165

Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H? control theory, and linear matrix inequalities  

Microsoft Academic Search

This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems, First, a stability condition for Takagi and Sugeno's fuzzy model is given in terms of Lyapunov stability theory. Next, new stability conditions for a generalized class of uncertain systems are derived from robust control

Kazuo Tanaka; T. Ikeda; H. O. Wang

1996-01-01

166

Lesson 17: Quadratic Inequalities  

NSDL National Science Digital Library

The lesson begins with using graphs to solve quadratic inequalities. AN equation modeling the height of a rocket is graphed along with a second equation that represents the minimum height at which the rocket can legally and safely be exploded. The intersections of the graphs provide the solution interval. A second method is then presented where the inequality is put into standard form and then solved for its x-intercepts. Interval notation and union of sets is reviewed before a purely algebraic procedure for solving the inequalities is presented. The lesson concludes with an application problem.

2011-01-01

167

Properties of quadratic equations and their application to power system analysis  

E-print Network

Properties of quadratic equations and their application to power system analysis Y.V. Makarova,1 and control can be described by algebraic sets of quadratic equations of the form fx y gx 0 1 where x Rn x as a quadratic equations set with the Jacobian matrix Jx being a linear function of unknown variables. In any

Hiskens, Ian A.

168

Event rate and reaction time performance in ADHD: Testing predictions from the state regulation deficit hypothesis using an ex-Gaussian model.  

PubMed

According to the state regulation deficit (SRD) account, ADHD is associated with a problem using effort to maintain an optimal activation state under demanding task settings such as very fast or very slow event rates. This leads to a prediction of disrupted performance at event rate extremes reflected in higher Gaussian response variability that is a putative marker of activation during motor preparation. In the current study, we tested this hypothesis using ex-Gaussian modeling, which distinguishes Gaussian from non-Gaussian variability. Twenty-five children with ADHD and 29 typically developing controls performed a simple Go/No-Go task under four different event-rate conditions. There was an accentuated quadratic relationship between event rate and Gaussian variability in the ADHD group compared to the controls. The children with ADHD had greater Gaussian variability at very fast and very slow event rates but not at moderate event rates. The results provide evidence for the SRD account of ADHD. However, given that this effect did not explain all group differences (some of which were independent of event rate) other cognitive and/or motivational processes are also likely implicated in ADHD performance deficits. PMID:25482092

Metin, Baris; Wiersema, Jan R; Verguts, Tom; Gasthuys, Roos; van Der Meere, Jacob J; Roeyers, Herbert; Sonuga-Barke, Edmund

2014-12-01

169

Solving quadratic equations using reduced unimodular quadratic forms  

Microsoft Academic Search

Let Q be an n × n symmetric matrix with integral entries and with detQ ?= 0, but not necesarily positive definite. We describe a generalized LLL algorithm to reduce this quadratic form. This algorithm either reduces the quadratic form or stops with some isotropic vector. It is proved to run in polynomial time. We also describe an algorithm for

Denis Simon

2005-01-01

170

Anatomy of an experimental two-link flexible manipulator under end-point control  

NASA Technical Reports Server (NTRS)

The design and experimental implementation of an end-point controller for two-link flexible manipulators are presented. The end-point controller is based on linear quadratic Gaussian (LQG) theory and is shown to exhibit significant improvements in trajectory tracking over a conventional controller design. To understand the behavior of the manipulator structure under end-point control, a strobe sequence illustrating the link deflections during a typical slew maneuver is included.

Oakley, Celia M.; Cannon, Robert H., Jr.

1990-01-01

171

A Method for Determining the Nominal Occular Hazard Zone for Gaussian Beam Laser Rangers with a Firmware Controlled Variable Focal Length  

NASA Technical Reports Server (NTRS)

LIDAR systems that maintain a constant beam spot size on a retroreflector in order to increase the accuracy of bearing and ranging data must use a software controlled variable position lens. These systems periodically update the estimated range and set the position of the focusing lens accordingly. In order to precisely calculate the r NOHD for such a system, the software method for setting the variable position lens and gaussian laser propagation can be used to calculate the irradiance at any point given the range estimation. NASA s Space Shuttle LIDAR, called the Trajectory Control Sensor (TCS), uses this configuration. Analytical tools were developed using Excel and VBA to determine the radiant energy to the International Space Station (ISS) crewmembers eyes while viewing the shuttle on approach and departure. Various viewing scenarios are considered including the use of through-the-lens imaging optics and the window transmissivity at the TCS wavelength. The methodology incorporates the TCS system control logic, gaussian laser propagation, potential failure mode end states, and guidance from American National Standard for the Safe Use of Lasers (ANSI Z136.1-2007). This approach can be adapted for laser safety analyses of similar LIDAR systems.

Picco, C. E.; Shavers, M. R.; Victor, J. M.; Duron, J. L.; Bowers, W. h.; Gillis, D. B.; VanBaalen, M.

2009-01-01

172

A long range Spherical model and Exact nonGaussian Solutions of a EnergyEnstrophy  

E-print Network

the energy and enstrophy are both quadratic forms, 2 #12; one can easily integrate the Gaussian partition­Gaussian configurational integral is calculated in closed form. A family of lattice vortex gas models for the Euler that the conservation of enstrophy is mathematically equivalent to Kac's spherical constraint. This Spher­ ical model

Lim, Chjan C.

173

An Isserlis' Theorem for Mixed Gaussian Variables: Application to the Auto-Bispectral Density  

NASA Astrophysics Data System (ADS)

This work derives a version of Isserlis' theorem for the specific case of four mixed-Gaussian random variables. The theorem is then used to derive an expression for the auto-bispectral density for quadratically nonlinear systems driven with mixed-Gaussian iid noise.

Michalowicz, J. V.; Nichols, J. M.; Bucholtz, F.; Olson, C. C.

2009-07-01

174

Mixed-integer quadratic programming  

Microsoft Academic Search

This paper considers mixed-integer quadratic programs in which the objective function is quadratic in the integer and in the continuous variables, and the constraints are linear in the variables of both types. The generalized Benders' decomposition is a suitable approach for solving such programs. However, the program does not become more tractable if this method is used, since Benders' cuts

Rafael Lazimy

1982-01-01

175

Gaussian cloning of coherent states with known phases  

SciTech Connect

The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of 2/3. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of 4/5. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier.

Alexanian, Moorad [Department of Physics and Physical Oceanography, University of North Carolina at Wilmington, Wilmington, North Carolina 28403 (United States)

2006-04-15

176

Gaussian process based recursive system identification  

NASA Astrophysics Data System (ADS)

This paper is concerned with the problem of recursive system identification using nonparametric Gaussian process model. Non-linear stochastic system in consideration is affine in control and given in the input-output form. The use of recursive Gaussian process algorithm for non-linear system identification is proposed to alleviate the computational burden of full Gaussian process. The problem of an online hyper-parameter estimation is handled using proposed ad-hoc procedure. The approach to system identification using recursive Gaussian process is compared with full Gaussian process in terms of model error and uncertainty as well as computational demands. Using Monte Carlo simulations it is shown, that the use of recursive Gaussian process with an ad-hoc learning procedure offers converging estimates of hyper-parameters and constant computational demands.

Prüher, Jakub; Šimandl, Miroslav

2014-12-01

177

Quadratic optimization in ill-posed problems  

NASA Astrophysics Data System (ADS)

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

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

2008-10-01

178

Quadratics, polynomial form in y  

NSDL National Science Digital Library

Explore the graph of a quadratic of the form x = ay2 + by + c. Vary the coefficients of the equation and examine how the graph changes in response. Calculate the location of the vertex and y-intercepts.

ExploreMath.com

2001-01-01

179

An Investigation on Quadratic Equations.  

ERIC Educational Resources Information Center

Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)

Hirst, Keith

1988-01-01

180

An improved Gaussian mixture model  

NASA Astrophysics Data System (ADS)

An improved Gaussian mixture model is presented to substitute the typical method of Chris Stauffer which revealed its weakness in uncontrollability of the background constructing course and foreground mergence time as well as invalidation to the low duty background. By setting appropriate time parameters which meet the monitoring needs, the improved method effectively controls the estimates updating process of each background in Gaussian mixture model via layered attenuating the estimates and intensifying the recurrence events while requires almost the same computation. The simulation of traffic monitoring videos indicates that: this model has no scraps of provisionally staying objects, efficaciously picks up the low duty background.

Gong, Dayong; Wang, Zhihua

2013-03-01

181

A comparison of controller designs for an experimental flexible structure  

NASA Technical Reports Server (NTRS)

Control systems design and hardware testing are addressed for an experimental structure that displays the characteristics of a typical flexible spacecraft. The results of designing and implementing various control design methodologies are described. The design methodologies under investigation include linear quadratic Gaussian control, static and dynamic dissipative controls, and H-infinity optimal control. Among the three controllers considered, it is shown, through computer simulation and laboratory experiments on the evolutionary structure, that the dynamic dissipative controller gave the best results in terms of vibration suppression and robustness with respect to modeling errors.

Lim, K. B.; Maghami, P. G.; Joshi, S. M.

1991-01-01

182

Twisted Gaussian Schell-model beams  

SciTech Connect

The authors introduce a new class of partially coherent axially symmetric Gaussian Schell-model (GSM) beams incorporating a new twist phase quadratic in configuration variables. This phase twists the beam about its axis during propagation and is shown to be bounded in strength because of the positive semidefiniteness of the cross-spectral density. Propagation characteristics and invariants for such beams are derived and interpreted, and two different geometric representations are developed. Direct effects of the twist phase on free propagation as well as in parabolic index fibers are demonstrated. Production of such twisted GSM beams, starting with Li-Wolf anisotropic GSM beams, is described. 34 refs., 3 figs.

Simon, R. (Inst. of Mathematical Sciences, Madras (India)); Mukunda, N. (Indian Inst. of Science, Bangalore (India) Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore (India))

1993-01-01

183

Optimal fine pointing control of a large space telescope using an Annular Momentum Control Device  

NASA Technical Reports Server (NTRS)

This paper discusses the application of an Annular Momentum Control Device (AMCD) to fine pointing control of a large space telescope (LST). The AMCD represents a new development in the field of momentum storage devices. A linearized mathematical model is developed for the AMCD/LST system, including the magnetic suspension actuators. Two approaches to control system design are considered. The first approach uses a stochastic linear-quadratic Gaussian controller which utilizes feedback of all states. The second approach considers a more practical control system design in which the axial and radial loops are designed independently.

Nadkarni, A. A.; Joshi, S. M.; Groom, N. J.

1977-01-01

184

Evolution of massive haloes in non-Gaussian scenarios  

NASA Astrophysics Data System (ADS)

We have performed high-resolution cosmological N-body simulations of a concordance ?CDM model to study the evolution of virialized, dark matter haloes in the presence of primordial non-Gaussianity. Following a standard procedure, departures from Gaussianity are modelled through a quadratic Gaussian term in the primordial gravitational potential, characterized by a dimensionless non-linearity strength parameter fNL. We find that the halo mass function and its redshift evolution closely follow the analytic predictions of Matarrese, Verde & Jimenez. The existence of precise analytic predictions makes the observation of rare, massive objects at large redshift an even more attractive test to detect primordial non-Gaussian features in the large-scale structure of the Universe.

Grossi, M.; Dolag, K.; Branchini, E.; Matarrese, S.; Moscardini, L.

2007-12-01

185

A double integral quadratic cost and tolerance of feedback nonlinearities  

Microsoft Academic Search

A double integral quadratic cost with an associated integral constraint on state trajectories is shown to result in a stable feedback control law for linear time-varying differential systems. The gain matrix for this control is obtained by integrating a Riccati-type matrix differential equation over a finite time interval and is shown to allow for a large class of nonlinearities in

W. Kwon; A. Pearson

1979-01-01

186

First-order approximation in studying beam spreading of cosh-Gaussian and cos-Gaussian beam in Kolmogorov turbulence  

NASA Astrophysics Data System (ADS)

With the help of extended Huygens-Fresnel principle and the expansion of the mutual coherence function in a Taylor series, the analytical expression of the first-order approximation for the average intensity of a cosh-Gaussian and cos-Gaussian beam in Kolmogorov turbulence has been obtained. Based on the analytical expression of the first-order approximation, the variation of average intensity in Kolmogorov turbulence has been examined. Comparing with numerical integration, the relative error due to the quadratic structure function and first-order approximation of the mutual coherence function is studied and discussed. It is shown that the analytical expression of the first-order approximation provides a more precise approach to study the beam spreading of the cosh-Gaussian and cos-Gaussian beam in Kolmogorov turbulence, no matter whether the effect of turbulence is weak or strong.

Chu, X.; Zhou, G.

2010-10-01

187

A Quadratic Closure for Compressible Turbulence  

SciTech Connect

We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.

Futterman, J A

2008-09-16

188

Multiobjective Gaussian Particle Swarm Approach Applied to Multiloop PI Controller Tuning of a Quadruple-Tank System  

Microsoft Academic Search

The use of PI (Proportional-Integral), PD (Proportional-Derivative) and PID (Proportional-Integral-Derivative)controllers\\u000a have a long history in control engineering and are acceptable for most of real applications because of their simplicity in\\u000a architecture and their performances are quite robust for a wide range of operating conditions. Unfortunately, it has been\\u000a quite difficult to tune properly the gains of PI, PD, and PID

Leandro Dos Santos Coelho; Helon Vicente Hultmann Ayala; Nadia Nedjah; Luiza De Macedo Mourelle

2010-01-01

189

Estimation of Clustering Parameters Using Gaussian Process Regression  

PubMed Central

We propose a method for estimating the clustering parameters in a Neyman-Scott Poisson process using Gaussian process regression. It is assumed that the underlying process has been observed within a number of quadrats, and from this sparse information the distribution is modelled as a Gaussian process. The clustering parameters are then estimated numerically by fitting to the covariance structure of the model. It is shown that the proposed method is resilient to any sampling regime. The method is applied to simulated two-dimensional clustered populations and the results are compared to a related method from the literature. PMID:25383766

Rigby, Paul; Pizarro, Oscar; Williams, Stefan B.

2014-01-01

190

Solving Quadratic Equations by Factoring  

NSDL National Science Digital Library

This video explains how to solve quadratic equations with the factoring method. In 4 minutes 23 seconds, the two narrators explain in detail the steps required. Additionally, how these equations relate to objects and events in the real world such as roller coasters is covered.

2012-08-06

191

Learning Accurate Kinematic Control of Cable-Driven Surgical Robots Using Data Cleaning and Gaussian Process Regression  

E-print Network

Assistants (RSAs) are one example of such an automation system, as they are designed for master, as is common for proprietary sys- tems. Semi-autonomous surgery with cable-driven Robotic Surgical AssistantsLearning Accurate Kinematic Control of Cable-Driven Surgical Robots Using Data Cleaning

Abbeel, Pieter

192

Gaussian entanglement of formation  

SciTech Connect

We introduce a Gaussian version of the entanglement of formation adapted to bipartite Gaussian states by considering decompositions into pure Gaussian states only. We show that this quantity is an entanglement monotone under Gaussian operations and provide a simplified computation for states of arbitrary many modes. For the case of one mode per site the remaining variational problem can be solved analytically. If the considered state is in addition symmetric with respect to interchanging the two modes, we prove additivity of the considered entanglement measure. Moreover, in this case and considering only a single copy, our entanglement measure coincides with the true entanglement of formation.

Wolf, M.M. [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748 (Germany); Institut fuer Mathematische Physik, Mendelssohnstrasse. 3, D-38106 Braunschweig (Germany); Giedke, G. [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748 (Germany); Institut fuer Quantenelektronik, ETH Zuerich, Wolfgang-Pauli-Strasse 16, CH-8093 Zurich (Switzerland); Krueger, O.; Werner, R. F. [Institut fuer Mathematische Physik, Mendelssohnstrasse. 3, D-38106 Braunschweig (Germany); Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748 (Germany)

2004-05-01

193

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

NASA Technical Reports Server (NTRS)

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.

Thompson, P. M.

1979-01-01

194

Suppressed non-Gaussianity in the curvaton model  

NASA Astrophysics Data System (ADS)

We show that the local type non-Gaussianity in a class of curvaton models is suppressed, i.e., the nonlinearity parameters fNL and those related with higher order statistics can be at most O(1), even if the curvaton energy density is subdominant at the decay. This situation is naturally realized in a very simple curvaton potential with quadratic term plus quartic term.

Mukaida, Kyohei; Nakayama, Kazunori; Takimoto, Masahiro

2014-06-01

195

Quadratic bosonic and free white noises  

E-print Network

We discuss the meaning of renormalization used for deriving quadratic bosonic commutation relations introduced by Accardi and find a representation of these relations on an interacting Fock space. Also, we investigate classical stochastic processes which can be constructed from noncommutative quadratic white noise. We postulate quadratic free white noise commutation relations and find their representation on an interacting Fock space.

Piotr Sniady

2003-03-20

196

Quadratic Residues a is a quadratic residue mod m if x2  

E-print Network

if the following equation has a solution: x2 = a (mod m) . Otherwise, a is a quadratic nonresidue mod m. Example. 8 a quadratic equation mod p has at most two solutions (Prove it!), there are exactly two. Example. x2 = 8 (mod6-21-2013 Quadratic Residues · a is a quadratic residue mod m if x2 = a (mod m). Otherwise

Ikenaga, Bruce

197

Robust harmonic disturbance rejection for uncertain systems with an integral quadratic constraint  

Microsoft Academic Search

This paper considers a finite-time output feedback control problem for a class of uncertain systems subject to harmonic disturbances of known frequencies. The controller is also required to minimize a quadratic cost functional

Andrey V. Savkin; Ian R. Petersen

1995-01-01

198

OPTICAL SOLITONS: Excitation of two-dimensional soliton matrices by fundamental Gaussian beams  

NASA Astrophysics Data System (ADS)

The excitation of two-dimensional periodic structures of fields of the first and second radiation harmonics due to the modulation instability of fundamental Gaussian beams is studied in a medium with a quadratic nonlinearity. The distances are found at which soliton matrix structures with a specified period are formed and destroyed. Optical gratings formed due to nonlinear aberration of broad Gaussian beams are considered.

Borovkova, O. V.; Chuprakov, D. A.; Sukhorukov, Anatolii P.

2005-01-01

199

Geometrical Solutions of Quadratic Equations.  

ERIC Educational Resources Information Center

Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

Grewal, A. S.; Godloza, L.

1999-01-01

200

Rational quadratic Bézier curve fitting by simulated annealing technique  

NASA Astrophysics Data System (ADS)

A metaheuristic algorithm, which is an approximation method called simulated annealing is implemented in order to have the best rational quadratic Bézier curve from a given data points. This technique is used to minimize sum squared errors in order to improve the middle control point position and the value of weight. As a result, best fitted rational quadratic Bézier curve and its mathematical function that represents all the given data points is obtained. Numerical and graphical examples are also presented to demonstrate the effectiveness and robustness of the proposed method.

Mohamed, Najihah; Abd Majid, Ahmad; Mt Piah, Abd Rahni

2013-04-01

201

Some Remarks for a Decomposition of Linear-Quadratic Optimal ...  

E-print Network

Aug 9, 2013 ... and it is given algorithm for solving Linear-Quadratic optimal Control .... Note2: Since xn+1 is unknown constant (parameter) in the interval [0, 2] (see, .... boundary of the integral of minimizing functional is known as in example ...

202

System Analysis via Integral Quadratic Constraints - Part I  

Microsoft Academic Search

This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time-variations and uncertain parameters. From an original idea by Yakubovich, the approach has been developed under a combination of influences from the western and russian traditions of control theory. It is shown how a complex system can be described by using certain integral quadratic constraints (IQC's), derived

Alexander Megretski; Anders Rantzer

1995-01-01

203

Lower Bounds and Exact Algorithms for the Quadratic Minimum ...  

E-print Network

Dec 16, 2013 ... an algorithm based on artificial bee colony. A local search ...... Once the branching edge is determined, two new nodes are created. For one of them, we ..... Information Technology and Control, 39:257–268, 2010. [28] David ... A swarm intelligence approach to the quadratic minimum spanning tree problem.

2013-12-16

204

Linear quadratic regulators with eigenvalue placement in a horizontal strip  

NASA Technical Reports Server (NTRS)

A method for optimally shifting the imaginary parts of the open-loop poles of a multivariable control system to the desirable closed-loop locations is presented. The optimal solution with respect to a quadratic performance index is obtained by solving a linear matrix Liapunov equation.

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

1987-01-01

205

A Factorization Approach to the Linear Regulator Quadratic Cost Problem  

NASA Technical Reports Server (NTRS)

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

Milman, M. H.

1985-01-01

206

Limits on isocurvature perturbations from non-Gaussianity in WMAP temperature anisotropy  

NASA Astrophysics Data System (ADS)

We study the effect of primordial isocurvature perturbations on non-Gaussian properties of cosmic microwave background (CMB) temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the Gaussian variable ?,S = ?2 - , can give the same signal-to-noise ratio as fNL = 30 even if we impose the current observational limit on the fraction of isocurvature perturbations contained in the primordial power spectrum ?. We give constraints on isocurvature non-Gaussianity from Minkowski Functionals using the Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data. We do not find a significant signal of isocurvature non-Gaussianity. For the quadratic isocurvature model, we obtain a stringent upper limit on the isocurvature fraction ? < 0.070 (95 per cent CL) for a scale-invariant spectrum which is comparable to the limit obtained from the power spectrum.

Hikage, Chiaki; Koyama, Kazuya; Matsubara, Takahiko; Takahashi, Tomo; Yamaguchi, Masahide

2009-10-01

207

Wavelets and WMAP non-Gaussianity  

E-print Network

We study the statistical properties of the 1st year WMAP data on different scales using the spherical mexican hat wavelet transform. Consistent with the results of Vielva et al. (2003) we find a deviation from Gaussianity in the form of kurtosis of wavelet coefficients on $3-4^\\circ$ scales in the southern Galactic hemisphere. This paper extends the work of Vielva et al. as follows. We find that the non-Gaussian signal shows up more strongly in the form of a larger than expected number of cold pixels and also in the form of scale-scale correlations amongst wavelet coefficients. We establish the robustness of the non-Gaussian signal under more wide-ranging assumptions regarding the Galactic mask applied to the data and the noise statistics. This signal is unlikely to be due to the usual quadratic term parametrized by the non-linearity parameter $f_{NL}$. We use the skewness of the spherical mexican hat wavelet coefficients to constrain $f_{NL}$ with the 1st year WMAP data. Our results constrain $f_{NL}$ to be $50\\pm 80$ at 68% confidence, and less than 280 at 99% confidence.

Pia Mukherjee; Yun Wang

2004-02-25

208

Is Gaussian normal?  

NASA Astrophysics Data System (ADS)

For many years, hydraulic conductivity was considered to be lognormal. More so, in stochastic hydrogeology it was postulated that the best multivariate model for logconductivity was the multiGaussian one. However, evidence has proven that in many cases, hydraulic conductivity is not normal and that modeling using a multiGaussian distribution can introduce unwanted spatial patterns. This presentation will discuss some algorithms to address the problem of non Gaussianity of logconductivity in the context of inverse modeling. More precisely, the normal-score ensemble Kalman filter (NS-EnKF), and the ensemble pattern matching (EnPAT) will be commented with its advantages and pitfalls.

Gómez-Hernández, J. Jaime; Xu, Teng

2014-05-01

209

The mass density field in simulated non-Gaussian scenarios  

NASA Astrophysics Data System (ADS)

In this work, we study the properties of the mass density field in the non-Gaussian world models simulated by Grossi et al. In particular, we focus on the one-point density probability distribution function of the mass density field in non-Gaussian models with quadratic non-linearities quantified by the usual parameter fNL. We find that the imprints of primordial non-Gaussianity are well preserved in the negative tail of the probability function during the evolution of the density perturbation. The effect is already notable at redshifts as large as 4 and can be detected out to the present epoch. At z = 0, we find that the fraction of the volume occupied by regions with underdensity ? < -0.9, typical of voids, is about 1.3 per cent in the Gaussian case and increases to ~2.2 per cent if fNL = -1000 while decreases to ~0.5 per cent if fNL = +1000. This result suggests that void-based statistics may provide a powerful method to detect non-Gaussianity even at low redshifts, which is complementary to the measurements of the higher order moments of the probability distribution function like the skewness or the kurtosis for which deviations from the Gaussian case are detected at the 25-50 per cent level.

Grossi, M.; Branchini, E.; Dolag, K.; Matarrese, S.; Moscardini, L.

2008-10-01

210

Gaussian Multipole Model (GMM)  

PubMed Central

An electrostatic model based on charge density is proposed as a model for future force fields. The model is composed of a nucleus and a single Slater-type contracted Gaussian multipole charge density on each atom. The Gaussian multipoles are fit to the electrostatic potential (ESP) calculated at the B3LYP/6-31G* and HF/aug-cc-pVTZ levels of theory and tested by comparing electrostatic dimer energies, inter-molecular density overlap integrals, and permanent molecular multipole moments with their respective ab initio values. For the case of water, the atomic Gaussian multipole moments Qlm are shown to be a smooth function of internal geometry (bond length and bond angle), which can be approximated by a truncated linear Taylor series. In addition, results are given when the Gaussian multipole charge density is applied to a model for exchange-repulsion energy based on the inter-molecular density overlap. PMID:20209077

Elking, Dennis M.; Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.; Pedersen, Lee G.

2009-01-01

211

A long range Spherical model and Exact non-Gaussian Solutions of a Energy-Enstrophy  

E-print Network

that a ex- plicitly non-Gaussian configurational integral is calculated in closed form. A family observation that the conservation of enstrophy is mathematically equivalent to Kac's spherical constraint and micro-canonical in the enstrophy. Since the energy and enstrophy are both quadratic forms

Lim, Chjan C.

212

First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity  

Microsoft Academic Search

We present limits to the amplitude of non-Gaussian primordial fluctuations in the WMAP 1 yr cosmic microwave background sky maps. A nonlinear coupling parameter, fNL, characterizes the amplitude of a quadratic term in the primordial potential. We use two statistics: one is a cubic statistic which measures phase correlations of temperature fluctuations after combining all configurations of the angular bispectrum.

E. Komatsu; A. Kogut; M. R. Nolta; C. L. Bennett; M. Halpern; G. Hinshaw; N. Jarosik; M. Limon; S. S. Meyer; L. Page; D. N. Spergel; G. S. Tucker; L. Verde; E. Wollack; E. L. Wright

2003-01-01

213

Probability distribution of the time-averaged mean-square displacement of a Gaussian process  

NASA Astrophysics Data System (ADS)

We study the probability distribution of the time-averaged mean-square displacement of a discrete Gaussian process. An empirical approximation for the probability density is suggested and numerically validated for fractional Brownian motion. The optimality of quadratic forms for inferring dynamical and microrheological quantities from individual random trajectories is discussed, with emphasis on a reliable interpretation of single-particle tracking experiments.

Grebenkov, Denis S.

2011-09-01

214

Quadratic performance index generation for optimal regular design.  

NASA Technical Reports Server (NTRS)

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

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

1971-01-01

215

Discriminative learning quadratic discriminant function for handwriting recognition.  

PubMed

In character string recognition integrating segmentation and classification, high classification accuracy and resistance to noncharacters are desired to the underlying classifier. In a previous evaluation study, the modified quadratic discriminant function (MQDF) proposed by Kimura et al. was shown to be superior in noncharacter resistance but inferior in classification accuracy to neural networks. This paper proposes a discriminative learning algorithm to optimize the parameters of MQDF with aim to improve the classification accuracy while preserving the superior noncharacter resistance. We refer to the resulting classifier as discriminative learning QDF (DLQDF). The parameters of DLQDF adhere to the structure of MQDF under the Gaussian density assumption and are optimized under the minimum classification error (MCE) criterion. The promise of DLQDF is justified in handwritten digit recognition and numeral string recognition, where the performance of DLQDF is comparable to or superior to that of neural classifiers. The results are also competitive to the best ones reported in the literature. PMID:15384535

Liu, Cheng-Lin; Sako, Hiroshi; Fujisawa, Hiromichi

2004-03-01

216

Atom-laser coherence via multiloop feedback control  

NASA Astrophysics Data System (ADS)

Coherence control is the key to success in the applications of atom-laser beams. A multiloop measurement feedback control scheme is proposed to improve atom-laser coherence. The first loop aims to cancel the decohering effects of the nonlinear atom-atom interactions via direct measurement feedback. However, there are nonlinear interactions with the optical probe field used in the measurement scheme which may also contribute to a degradation in atom-laser performance. Accordingly, a second feedback loop is used to reduce these effects based on linear quadratic Gaussian control. The multiloop design achieves improved atom-laser coherence.

Yanagisawa, M.; James, M. R.

2009-02-01

217

Geometrical and Graphical Solutions of Quadratic Equations.  

ERIC Educational Resources Information Center

Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

Hornsby, E. John, Jr.

1990-01-01

218

Quadratic Equations and Conics A quadratic equation in two variables is an equation that's equivalent to  

E-print Network

Quadratic Equations and Conics A quadratic equation in two variables is an equation that's equivalent to an equation of the form p(x, y) = 0 where p(x, y) is a quadratic polynomial. Examples. · 4x2 - 3xy - 2y2 + x - y + 6 = 0 is a quadratic equation, as are x2 - y2 = 0 and x2 + y2 = 0 and x2 - 1 = 0

Wortman, Kevin

219

Quadratic Isocurvature Cross-Correlation, Ward Identity, and Dark Matter  

E-print Network

Sources of isocurvature perturbations and large non-Gaussianities include field degrees of freedom whose vacuum expectation values are smaller than the expansion rate of inflation. The inhomogeneities in the energy density of such fields are quadratic in the fields to leading order in the inhomogeneity expansion. Although it is often assumed that such isocurvature perturbations and inflaton-driven curvature perturbations are uncorre- lated, this is not obvious from a direct computational point of view due to the form of the minimal gravitational interactions. We thus compute the irreducible gravitational contributions to the quadratic isocurvature-curvature cross-correlation. We find a small but non-decaying cross-correlation, which in principle serves as a consistency prediction of this large class of isocurvature perturbations. We apply our cross-correlation result to two dark matter isocurvature perturbation scenarios: QCD axions and WIMPZILLAs. On the technical side, we utilize a gravita- tional Ward identity in a novel manner to demonstrate the gauge invariance of the computation. Furthermore, the detailed computation is interpreted in terms of a soft-{\\zeta} theorem and a gravitational Ward identity. Finally, we also identify explicitly all the counterterms that are necessary for renormalizing the isocurvature perturbation composite operator in inflationary cosmological backgrounds.

Daniel J. H. Chung; Hojin Yoo; Peng Zhou

2013-03-25

220

Quadratic superconducting cosmic strings revisited  

NASA Astrophysics Data System (ADS)

It has been shown that a 5-dimensional general-relativity action extended by appropriate quadratic terms admits a singular superconducting cosmic string solution. We search for cosmic strings endowed with similar and extended physical properties by directly integrating the non-linear matrix field equations thus avoiding the perturbative approach by which we constructed the above-mentioned exact solution. The most general superconducting cosmic string, subject to some constraints, will be derived and shown to be mathematically unique up to linear coordinate transformations mixing its Killing vectors. The most general solution, however, is not globally equivalent to the old one due to the existence of Killing vectors with closed orbits. Contribution under the title of Exact 5-Dimensional Cosmic String Solutions to the International Conference on Dynamics and Thermodynamics of Black Holes and Naked Singularities II, Milan, Italy, May 2007.

Azreg-Aïnou, M.

2008-03-01

221

Single-photon quadratic optomechanics.  

PubMed

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

Liao, Jie-Qiao; Nori, Franco

2014-01-01

222

Quadratic Equations: From Factored to Standard Form  

NSDL National Science Digital Library

This activity leads students to understand the utility in the factored form of a quadratic equation. Students then express quadratic equations in standard form in the corresponding factored form. The activity is concluded with four critical-thinking questions. website: http://www.mathedpage.org/ copyright information: http://www.mathedpage.org/rights.html

2011-01-01

223

Interval regression analysis by quadratic programming approach  

Microsoft Academic Search

When we use linear programming in possibilistic regression analysis, some coefficients tend to become crisp because of the characteristic of linear programming. On the other hand, a quadratic programming approach gives more diverse spread coefficients than a linear programming one. Therefore, to overcome the crisp characteristic of linear programming, we propose interval regression analysis based on a quadratic programming approach.

Hideo Tanaka; Haekwan Lee

1998-01-01

224

On integral quadratic constraints for linear uncertainty  

Microsoft Academic Search

This paper studies some of the consequences of modelling linear uncertainty with integral quadratic constraints. For such models we give necessary and sufficient conditions for robust stability and introduce the notion of a quantitative stability indicator. To illustrate, we give new examples of uncertainties that admit integral quadratic constraint descriptions

Edgardo G. Eszter; C. V. Hollot

1995-01-01

225

Robust adaptive beamforming under quadratic constraint  

Microsoft Academic Search

In this paper, a adaptive weighted computation algorithm based on quadratic constraint for a robust array antenna is presented to improve the shortcoming of linearly constrained adaptive beamformer's sensitivity to the mismatch between the prescribed and actual direction of arrival (MPDOA). The quadratic constraint is added to the weighted least squared error between the desired and the actual beam patterns

Weihai Zhong; Qun Wan; Zhijiang Shang

2010-01-01

226

An Unexpected Influence on a Quadratic  

ERIC Educational Resources Information Center

Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

Davis, Jon D.

2013-01-01

227

Binary Quadratic Forms: A Historical View  

ERIC Educational Resources Information Center

We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

Khosravani, Azar N.; Beintema, Mark B.

2006-01-01

228

Existence Theorems for Some Quadratic Integral Equations  

Microsoft Academic Search

Using the theory of measures of noncompactness, we prove a few existence theorems for some quadratic integral equations. The class of quadratic integral equations considered below contains as a special case numerous integral equations encountered in the theories of radiative transfer and neutron transport, and in the kinetic theory of gases. In particular, the well-known Chandrasekhar integral equation also belongs

Józef Bana?; Millenia Lecko; Wagdy Gomaa El-Sayed

1998-01-01

229

Non-Gaussian bias: insights from discrete density peaks  

SciTech Connect

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastly simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out that statistics of thresholded regions can be computed using the same formalism. Our results suggest that halo clustering statistics can be modelled consistently (in the sense that the Gaussian and non-Gaussian bias factors agree with peak-background split expectations) from a Lagrangian bias relation only if the latter is specified as a set of constraints imposed on the linear density field. This is clearly not the case of standard Lagrangian local bias. Therefore, one is led to consider additional variables beyond the local mass overdensity.

Desjacques, Vincent; Riotto, Antonio [Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève, CH-1211 Genève (Switzerland); Gong, Jinn-Ouk, E-mail: Vincent.Desjacques@unige.ch, E-mail: jinn-ouk.gong@apctp.org, E-mail: Antonio.Riotto@unige.ch [Theory Division, CERN, CH-1211 Genève 23 (Switzerland)

2013-09-01

230

Large Non-Gaussianity from Multi-Brid Inflation  

NASA Astrophysics Data System (ADS)

A model of multi-component hybrid inflation, dubbed multi-brid inflation, in which various observable quantities including the non-Gaussianity parameter f_{NL} can be analytically calculated was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories, provided that the ratio of the two masses is large. One might question whether the resulting large non-Gaussianity is specific to this particular form of the potential and the condition for the end of inflation. In this paper, we consider a model of multi-brid inflation with a potential given by an exponential function of terms quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation than those studied previously. Then, focusing on the case of two-brid inflation, we find that large non-Gaussianity is possible in the present model even for the equal-mass case. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.

Naruko, A.; Sasaki, M.

2009-01-01

231

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

SciTech Connect

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 MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.

I.R. Goumiri, C.W. Rowley, Z. Ma, D.A. Gates, J.A. Krommes and J.B. Parker

2013-01-28

232

Explicit Solution to a Certain Non-ELQG Risk-sensitive Stochastic Control Problem  

SciTech Connect

A risk-sensitive stochastic control problem with finite/infinite horizon is studied with a 1-dimensional controlled process defined by a linear SDE with a linear control-term in the drift. In the criterion function, a non-linear/quadratic term is introduced by using the solution to a Riccati differential equation, and hence, the problem is not ELQG (Exponential Linear Quadratic Gaussian) in general. For the problem, optimal value and control are calculated in explicit forms and the set of admissible risk-sensitive parameters is given in a concrete form. As applications, two types of large deviations control problems, i.e., maximizing an upside large deviations probability and minimizing a downside large deviations probability, are mentioned.

Hata, Hiroaki, E-mail: hata@math.sinica.edu.t [Academia Sinica, Institute of Mathematics (China); Sekine, Jun, E-mail: sekine@kier.kyoto-u.ac.j [Kyoto University, Institute of Economic Research (Japan)

2010-12-15

233

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

SciTech Connect

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 stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.

Goumiri, I. R.; Rowley, C. W.; Ma, Z. [Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544 (United States); Gates, D. A.; Krommes, J. A.; Parker, J. B. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08544 (United States)

2013-04-15

234

On Gaussian feedback capacity  

NASA Technical Reports Server (NTRS)

Pinsker and Ebert (1970) proved that in channels with additive Gaussian noise, feedback at most doubles the capacity. Cover and Pombra (1989) proved that feedback at most adds half a bit per transmission. Following their approach, the author proves that in the limit as signal power approaches either zero (very low SNR) or infinity (very high SNR), feedback does not increase the finite block-length capacity (which for nonstationary Gaussian channels replaces the standard notion of capacity that may not exist). Tighter upper bounds on the capacity are obtained in the process. Specializing these results to stationary channels, the author recovers some of the bounds recently obtained by Ozarow.

Dembo, Amir

1989-01-01

235

Periodic Continued Fractions A quadratic irrational is an irrational number which is a root of a quadratic equation with integer  

E-print Network

is a root of a quadratic equation with integer coefficients. · Quadratic irrationals can be expressed. Definition. A quadratic irrational is an irrational number which is a root of a quadratic equation ax2 + bx)2 = q, r2 x2 - 2rpx + (p2 - q) = 0. This is a quadratic equation with integer coefficients, and r2

Ikenaga, Bruce

236

Large Deviation Principle for Benedicks-Carleson Quadratic Maps  

NASA Astrophysics Data System (ADS)

Since the pioneering works of Jakobson and Benedicks & Carleson and others, it has been known that a positive measure set of quadratic maps admit invariant probability measures absolutely continuous with respect to Lebesgue. These measures allow one to statistically predict the asymptotic fate of Lebesgue almost every initial condition. Estimating fluctuations of empirical distributions before they settle to equilibrium requires a fairly good control over large parts of the phase space. We use the sub-exponential slow recurrence condition of Benedicks & Carleson to build induced Markov maps of arbitrarily small scale and associated towers, to which the absolutely continuous measures can be lifted. These various lifts together enable us to obtain a control of recurrence that is sufficient to establish a level 2 large deviation principle, for the absolutely continuous measures. This result encompasses dynamics far from equilibrium, and thus significantly extends presently known local large deviations results for quadratic maps.

Chung, Yong Moo; Takahasi, Hiroki

2012-11-01

237

Spinor condensates with a laser-induced quadratic Zeeman effect  

SciTech Connect

We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate {sup 52}Cr gas, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein-de Haas effect for relatively large magnetic fields, and may be employed to create S=1/2 systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exciting new control tool in spinor systems.

Santos, L. [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstr. 2, D-30167 Hannover (Germany); Fattori, M.; Stuhler, J.; Pfau, T. [5. Physikalisches Institut, Universitaet Stuttgart, Pfaffenwaldring 57 V, D-70550 Stuttgart (Germany)

2007-05-15

238

Robust Synchronisation of Heterogeneous Networks via Integral Quadratic Constraints  

E-print Network

Robust Synchronisation of Heterogeneous Networks via Integral Quadratic Constraints Sei Zhen Khong-- Synchronisation, heterogeneous networks, ro- bustness, integral quadratic constraints I. INTRODUCTION quadratic constraints is used to capture the structural uncertainties of the perturbations, and to give

Como, Giacomo

239

Seven Wonders of the Ancient and Modern Quadratic World.  

ERIC Educational Resources Information Center

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

Taylor, Sharon E.; Mittag, Kathleen Cage

2001-01-01

240

Design of Linear Quadratic Regulators and Kalman Filters  

NASA Technical Reports Server (NTRS)

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

Lehtinen, B.; Geyser, L.

1986-01-01

241

Gaussian Processes For Machine Learning  

Microsoft Academic Search

Gaussian processes (GPs) are natural generalisations of multivariate Gaussian ran- dom variables to innite (countably or continuous) index sets. GPs have been applied in a large number of elds to a diverse range of ends, and very many deep theoretical anal- yses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level

Matthias Seeger

2004-01-01

242

A quadratically convergent VBSCF method  

NASA Astrophysics Data System (ADS)

A quadratically convergent valence bond self-consistent field method is described where the simultaneous optimisation of orbitals and the coefficients of the configurations (VB structures) is based on a Newton-Raphson scheme. The applicability of the method is demonstrated in actual calculations. The convergence and efficiency are compared with the Super-CI method. A necessary condition to achieve convergence in the Newton-Raphson method is that the Hessian is positive definite. When this is not the case, a combination of the Super-CI and Newton-Raphson methods is shown to be an optimal choice instead of shifting the eigenvalues of the Hessian to make it positive definite. In the combined method, the first few iterations are performed with the Super-CI method and then the Newton-Raphson scheme is switched on based on an internal indicator. This approach is found computationally a more economical choice than using either the Newton-Raphson or Super-CI method alone to perform a full optimisation of the nonorthogonal orbitals.

Rashid, Zahid; van Lenthe, Joop H.

2013-02-01

243

A quadratically convergent VBSCF method.  

PubMed

A quadratically convergent valence bond self-consistent field method is described where the simultaneous optimisation of orbitals and the coefficients of the configurations (VB structures) is based on a Newton-Raphson scheme. The applicability of the method is demonstrated in actual calculations. The convergence and efficiency are compared with the Super-CI method. A necessary condition to achieve convergence in the Newton-Raphson method is that the Hessian is positive definite. When this is not the case, a combination of the Super-CI and Newton-Raphson methods is shown to be an optimal choice instead of shifting the eigenvalues of the Hessian to make it positive definite. In the combined method, the first few iterations are performed with the Super-CI method and then the Newton-Raphson scheme is switched on based on an internal indicator. This approach is found computationally a more economical choice than using either the Newton-Raphson or Super-CI method alone to perform a full optimisation of the nonorthogonal orbitals. PMID:23406096

Rashid, Zahid; van Lenthe, Joop H

2013-02-01

244

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

Microsoft Academic Search

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

PETER FLEMING

1985-01-01

245

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

NASA Technical Reports Server (NTRS)

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.

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

1989-01-01

246

A separation theorem for the stochastic sampled-data LQG problem. [control of continuous linear plant disturbed by white noise  

NASA Technical Reports Server (NTRS)

This paper considers the control of a continuous linear plant disturbed by white plant noise when the control is constrained to be a piecewise constant function of time; i.e. a stochastic sampled-data system. The cost function is the integral of quadratic error terms in the state and control, thus penalizing errors at every instant of time while the plant noise disturbs the system continuously. The problem is solved by reducing the constrained continuous problem to an unconstrained discrete one. It is shown that the separation principle for estimation and control still holds for this problem when the plant disturbance and measurement noise are Gaussian.

Halyo, N.; Caglayan, A. K.

1976-01-01

247

Decentralized Control of Sound Radiation using a High-Authority/Low-Authority Control Strategy with Anisotropic Actuators  

NASA Technical Reports Server (NTRS)

This paper describes a combined control strategy designed to reduce sound radiation from stiffened aircraft-style panels. The control architecture uses robust active damping in addition to high-authority linear quadratic Gaussian (LQG) control. Active damping is achieved using direct velocity feedback with triangularly shaped anisotropic actuators and point velocity sensors. While active damping is simple and robust, stability is guaranteed at the expense of performance. Therefore the approach is often referred to as low-authority control. In contrast, LQG control strategies can achieve substantial reductions in sound radiation. Unfortunately, the unmodeled interaction between neighboring control units can destabilize decentralized control systems. Numerical simulations show that combining active damping and decentralized LQG control can be beneficial. In particular, augmenting the in-bandwidth damping supplements the performance of the LQG control strategy and reduces the destabilizing interaction between neighboring control units.

Schiller, Noah H.; Cabell, Randolph H.; Fuller, Chris R.

2008-01-01

248

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer  

E-print Network

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.

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

2014-03-20

249

Ensemble Kalman filter method for Gaussian and non-Gaussian priors  

NASA Astrophysics Data System (ADS)

The objective of this work is to find an efficient and robust way to implement the ensemble Kalman filter (EnKF) to assimilate production and seismic data for both Gaussian and truncated pluri-Gaussian geological models. Truncated pluri-Gaussian models have proven to be useful for generating realistic geological models of facies distributions. In this work, we will specifically test a new idea for modeling of a channelized reservoir (fluvial system with two fades, channel facies and non-channel facies). EnKF is used to adjust the facies distribution (e.g. channel and non-channel fades) as well as the porosity and permeability of each fades to match production data and seismic data. For two and three-dimensional pluri-Gaussian models, we present a new procedure to ensure that facies observations at wells are honored at each data assimilation step. As the erroneous saturation distribution obtained with EnKF may result from nonlinearity or the failure of the assumption that the ensemble of predictions is approximately Gaussian, we investigate the application of a global and local normal score transform to transform water saturation to a Gaussian variables before applying the EnKF analysis step. We also apply an iterative EnKF scheme to obtain more plausible saturations distributions. To improve water cut data matches, we consider matching breakthrough times directly before matching watercut data. The integration of seismic data poses problems because of the large number of data that are assimilated. With a global assimilation procedure based on subspace projection, filter divergence becomes severe. On the other hand, our implementation of a local updating method to reduce filter divergence results in an unrealistic rough facies map. We introduce a projection method to obtain a more realistic map of the facies distribution, which retains the inherent smoothness of the underlying geological model. The characterization of measurement error is important if one uses a Bayesian approach to condition reservoir models to dynamic data. We use Savitzky-Golay smoother and wavelet smoother to estimate the measurement error in the production data, and use a modified EM (Expectation-Maximization) algorithm combined with a quadratic fitting to estimate the measurement error in the 4-D seismic data.

Zhao, Yong

250

HYSTERESIS ANALYSIS BASED ON INTEGRAL QUADRATIC CONSTRAINTS  

Microsoft Academic Search

It is shown how the framework of Integral Quadratic Constraints can be applied to analyze systems with hysteresis, in spite of the fact that hysteresis operators are unbounded and that not all system variable can be expected to approach zero.

A. Rantzer; A. Megretski

251

OVERPARTITIONS AND REAL QUADRATIC FIELDS JEREMY LOVEJOY  

E-print Network

OVERPARTITIONS AND REAL QUADRATIC FIELDS JEREMY LOVEJOY Abstract. It is shown that counting certain in Europe". 1 #12;2 JEREMY LOVEJOY families of overpartition theorems which are analogues of some classical

Fondements et Applications, Université Paris 7

252

Quadratic Equations...Origins, Development and Use.  

ERIC Educational Resources Information Center

There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (YP)

McQualter, J. W.

1988-01-01

253

Schur Stability Regions for Complex Quadratic Polynomials  

ERIC Educational Resources Information Center

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

Cheng, Sui Sun; Huang, Shao Yuan

2010-01-01

254

Robust analysis, sectors, and quadratic functionals  

Microsoft Academic Search

Working from a topological separation framework it is shown that integral quadratic constraints useful for robust analysis must have the form ?-??z*S*diag{I,-I}Szd?, for some invertible (possibly frequency dependent) matrix S. It is further shown that many of the integral quadratic constraints used in robustness analysis may be put into a positivity form with a fixed or known generalized sector transform

Keat-Choon Goh; M. G. Safonov

1995-01-01

255

Integral Quadratic Separators for performance analysis  

Microsoft Academic Search

Well-posedness of feedback connected systems is considered in topological separation framework. The case when a known linear descriptor transformation is connected to an uncertain operator is considered. Well-posedness is demonstrated to hold provided an Integral Quadratic Separator satisfying both some Linear Matrix Inequalities and an Integral Quadratic Constraint. The main result is applied to three input-output performance criteria. Keywords: Robustness,

Dimitri Peaucelle; Lucie Baudouin; Fred ´ eric Gouaisbaut

256

Gaussian interferometric power  

NASA Astrophysics Data System (ADS)

The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem only, in the worst-case scenario where a full knowledge of the generator of the dynamics is not available a priori. For finite-dimensional systems, this quantity was proven to be a faithful measure of quantum correlations beyond entanglement. Here we extend the notion of interferometric power to the technologically relevant setting of optical interferometry with continuous-variable probes. By restricting to Gaussian local dynamics, we obtain a closed formula for the interferometric power of all two-mode Gaussian states. We identify separable and entangled Gaussian states which maximize the interferometric power at fixed mean photon number of the probes and discuss the associated metrological scaling. At fixed entanglement of the probes, highly thermalized states can guarantee considerably larger precision than pure two-mode squeezed states.

Adesso, Gerardo

2014-08-01

257

Gaussian interferometric power  

E-print Network

The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem only, in the worst-case scenario where a full knowledge of the generator of the dynamics is not available a priori. For finite-dimensional systems, this quantity was proven to be a faithful measure of quantum correlations beyond entanglement. Here we extend the notion of interferometric power to the technologically relevant setting of optical interferometry with continuous-variable probes. By restricting to Gaussian local dynamics, we obtain a closed formula for the interferometric power of all two-mode Gaussian states. We identify separable and entangled Gaussian states which maximize the interferometric power at fixed mean photon number of the probes, and discuss the associated metrological scaling. At fixed entanglement of the probes, highly thermalized states can guarantee considerably larger precision than pure two-mode squeezed states.

Gerardo Adesso

2014-08-02

258

Resonant non-gaussianity  

NASA Astrophysics Data System (ADS)

We provide a derivation from first principles of the primordial bispectrum of scalar perturbations produced during inflation driven by a canonically normalized scalar field whose potential exhibits small sinusoidal modulations. A potential of this type has been derived in a class of string theory models of inflation based on axion monodromy. We use this model as a concrete example, but we present our derivations and results for a general slow-roll potential with superimposed modulations. We show analytically that a resonance between the oscillations of the background and the oscillations of the fluctuations is responsible for the production of an observably large non-Gaussian signal. We provide an explicit expression for the shape of this resonant non-Gaussianity. We show that there is essentially no overlap between this shape and the local, equilateral, and orthogonal shapes, and we stress that resonant non-Gaussianity is not captured by the simplest version of the effective field theory of inflation. We hope our analytic expression will be useful to further observationally constrain this class of models.

Flauger, Raphael; Pajer, Enrico

2011-01-01

259

Non-Gaussian random vector identification using spherically invariant random processes  

NASA Astrophysics Data System (ADS)

With the modeling of non-Gaussian radar clutter in mind, this paper presents elegant and tractable techniques for characterizing the probability density function (pdf) of a correlated non-Gaussian radar vector. The need for a library of multivariate correlated non-Gaussian pdfs in order to characterize various clutter scenarios is discussed. Specifically, the theory of spherically invariant random processes (SIRP) is examined in detail. Approaches based on the marginal envelope pdf and the marginal characteristic function have been used to obtain several multivariate non-Gaussian pdfs. Finally, an important result providing the pdf of the quadratic form of a spherically invariant random vector (SIRV) is presented. This result enables us to address the problem of distribution identification of a SIRV.

Rangaswamy, Muralidhar; Weiner, Donald; Ozturk, Aydin

1993-01-01

260

The Factorability of Quadratics: Motivation for More Techniques  

ERIC Educational Resources Information Center

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

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

2005-01-01

261

Note on an Additive Characterization of Quadratic Residues Modulo p  

E-print Network

if the quadratic equation x2 = a mod p has a solution. If it has no solution then a is called a quadratic nonNote on an Additive Characterization of Quadratic Residues Modulo p Chris Monico, Michele Elia, . . . , p - 1} of positive residues modulo an odd prime p is the partition into quadratic residues

Monico, Chris

262

Spectral fluctuation properties of constrained unitary ensembles of Gaussian-distributed random matrices  

NASA Astrophysics Data System (ADS)

We investigate the spectral fluctuation properties of constrained ensembles of random matrices (defined by the condition that a number NQ of matrix elements vanish identically; that condition is imposed in unitarily invariant form) in the limit of large matrix dimension. We show that as long as NQ is smaller than a critical value (at which the quadratic level repulsion of the Gaussian unitary ensemble of random matrices may be destroyed) all spectral fluctuation measures have the same form as for the Gaussian unitary ensemble.

Pluha?, Z.; Weidenmüller, H. A.

2009-04-01

263

Truncated Gaussians as tolerance sets  

NASA Technical Reports Server (NTRS)

This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

Cozman, Fabio; Krotkov, Eric

1994-01-01

264

Users manual for flight control design programs  

NASA Technical Reports Server (NTRS)

Computer programs for the design of analog and digital flight control systems are documented. The program DIGADAPT uses linear-quadratic-gaussian synthesis algorithms in the design of command response controllers and state estimators, and it applies covariance propagation analysis to the selection of sampling intervals for digital systems. Program SCHED executes correlation and regression analyses for the development of gain and trim schedules to be used in open-loop explicit-adaptive control laws. A linear-time-varying simulation of aircraft motions is provided by the program TVHIS, which includes guidance and control logic, as well as models for control actuator dynamics. The programs are coded in FORTRAN and are compiled and executed on both IBM and CDC computers.

Nalbandian, J. Y.

1975-01-01

265

7 Quadratic forms in n variables In order to understand quadratic forms in n variables over Z, one is let to study quadratic forms  

E-print Network

7 Quadratic forms in n variables In order to understand quadratic forms in n variables over Z, one is let to study quadratic forms over various rings and fields such as Q, Qp, R and Zp. This is consistent equation in Z, it is useful study the equation over other rings. Definition 7.0.8. Let R be a ring

Martin, Kimball

266

Sharp Quadratic Majorization in One Dimension  

PubMed Central

Majorization methods solve minimization problems by replacing a complicated problem by a sequence of simpler problems. Solving the sequence of simple optimization problems guarantees convergence to a solution of the complicated original problem. Convergence is guaranteed by requiring that the approximating functions majorize the original function at the current solution. The leading examples of majorization are the EM algorithm and the SMACOF algorithm used in Multidimensional Scaling. The simplest possible majorizing subproblems are quadratic, because minimizing a quadratic is easy to do. In this paper quadratic majorizations for real-valued functions of a real variable are analyzed, and the concept of sharp majorization is introduced and studied. Applications to logit, probit, and robust loss functions are discussed. PMID:21738282

de Leeuw, Jan; Lange, Kenneth

2009-01-01

267

Quadratic Integrate-and-Fire Model  

NSDL National Science Digital Library

The Quadratic Integrate-and-Fire model is a slight modification of the integrate-and-fire model. This slight modification has some drastic changes on the dynamics, although the equation is still solvable analytically in order to determine the period of a continuously-spiking neuron. Because of its simplicity, the Quadratic Integrate-and-Fire model and its variations are favorites for mathematical treatments of neural networks. The Quadratic Integrate-and-Fire model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

Thomson, Colin F.

2012-11-06

268

2D Gaussian distributions. Equal height.  

E-print Network

2D Gaussian distributions. Equal height. Noise-free. Well separated. #12;2D Gaussian distributions. Equal height. Noise-free. Well separated. #12;2D Gaussian distributions. Equal height. Noise-free. Somewhat separated. #12;2D Gaussian distributions. Equal height. Noise-free. Overlapping. #12;2D Gaussian

Oakes, Terry

269

Optical power flow with sequential quadratic programming  

NASA Astrophysics Data System (ADS)

Newton's method as an approach to solve the optimal power flow problem in electric power plants is presented. A general formulation of the optimal flow problem is given. Newton's method is applied to solve the nonlinear Kuhn-Tucker conditions by iteration. Every Newton step is calculated by solving a quadratic programming problem. Variations of the sequential quadratic programming method are presented. Byproducts of the optimization, namely the Lagrange multipliers and their interpretation as marginal costs and shadow prices, are outlined. The most important computer programs are enclosed.

Vanamerongen, R. A. M.

1985-01-01

270

Robustness analysis of a nonlinear missile autopilot : an integral quadratic constraint approach  

Microsoft Academic Search

In this paper, integral quadratic constraints (IQC) and linear parameter varying modelling are used to analyse the stability robustness of an uncertain nonlinear control system. A pitch-axis model of a highly maneuverable missile is presented and a nonlinear control based on dynamic inversion is applied. Stability is then analysed in presence of uncertainties on the aerodynamic coefficients via the IQC

I. J. Adounkpe; E. Godoyf; J.-P. Harcaut

2004-01-01

271

On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations  

SciTech Connect

The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula.

Sekine, Jun [Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)], E-mail: sekine@kier.kyoto-u.ac.jp

2006-09-15

272

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals  

NASA Astrophysics Data System (ADS)

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (?H = 2) and eight (?1st = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (? _min^G=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d4 with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step—namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

Przybytek, Michal; Helgaker, Trygve

2013-08-01

273

Combined control-structure optimization  

NASA Technical Reports Server (NTRS)

An approach for combined control-structure optimization keyed to enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and appears to be effective for generating families of designs that can be used in these early trade studies. Analytical results were obtained for classes of structure/control objectives with linear quadratic Gaussian (LQG) and linear quadratic regulator (LQR) costs. For these, researchers demonstrated that global optima can be computed for small values of the homotopy parameter. Conditions for local optima along the homotopy path were also given. Details of two numerical examples employing the LQR control cost were given showing variations of the optimal design variables along the homotopy path. The results of the second example suggest that introducing a second homotopy parameter relating the two parts of the control index in the LQG/LQR formulation might serve to enlarge the family of Pareto optima, but its effect on modifying the optimal structural shapes may be analogous to the original parameter lambda.

Salama, M.; Milman, M.; Bruno, R.; Scheid, R.; Gibson, S.

1989-01-01

274

Competing nonlinearities in quadratic nonlinear waveguide arrays  

E-print Network

Competing nonlinearities in quadratic nonlinear waveguide arrays Frank Setzpfandt,1, * Dragomir N demonstrate experimentally the existence of competing focusing and defocusing nonlinearities in a double- tively. If an optical system, however, exhibits so- called competing nonlinearities a laser beam can ex

275

Quadratic engel curves and consumer demand  

Microsoft Academic Search

This paper presents a model of consumer demand that is consistent with the observed expenditure patterns of individual consumers in a long time series of expenditure surveys and is also able to provide a detailed welfare analysis of shifts in relative prices. A nonparametric analysis of consumer expenditure patterns suggests that Engel curves require quadratic terms in the logarithm of

James Banks; Richard Blundell; Arthur Lewbel

1997-01-01

276

Decision making with fuzzy quadratic programming  

Microsoft Academic Search

Decision making in civil engineering systems necessarily involves imprecise data. Fuzzy linear programming (FLP) has been used to deal with imprecision in parameter definitions. In this paper, it is argued that present methods of FLP can be improved upon by using a new method of fuzzy quadratic programming (FQP) which enables the modelling of independent fuzzy parameters. Several numerical examples

W. Cui; D. I. Blockley

1990-01-01

277

Mapping integral quadratic constraints into parameter space  

Microsoft Academic Search

This paper presents the mapping equations for integral quadratic constraints (IQCs). In particular it is shown that IQCs with bounded rational multipliers can be mapped into parameter space. Using IQCs not only provides a uniform framework to map specifications into parameter space, but provides a unified approach to parameter space based robustness analysis and synthesis with respect to nonlinearities, time

Michael Muhler; Jiirgen Ackermann

2004-01-01

278

Solitons as harmonic oscillators with quadratic constraints  

Microsoft Academic Search

Integrable systems represented by partial differential equations, in particular those having soliton solutions, are different aspects of one and the same system: harmonic oscillators with quadratic constraints. This result is illustrated here by means of one example, the non-linear Schrödinger equation, whose soliton is described by four oscillators with two constraints.

Fernando Lund

1981-01-01

279

Representations of integers by ternary quadratic forms  

Microsoft Academic Search

We investigate the representation of integers by quadratic forms whose theta series lie in Kohnen's plus space M+ 3\\/2(4p), where p is a prime. Conditional upon certain GRH hypotheses, we show eectively that every suciently large discriminant with bounded divisibility by p is represented by the form, up to local conditions. We give an algorithm for explicitly calculating the bounds.

BEN KANE

2010-01-01

280

Block Ciphers and Systems of Quadratic Equations  

Microsoft Academic Search

In this paper we compare systems of multivariate poly- nomials, which completely define the block ciphers Khazad, Misty1, Kasumi, Camellia, Rijndael and Serpent in the view of a potential danger of an algebraic re-linearization attack. Keywords: Block ciphers, multivariate quadratic equations, lineariza- tion, Khazad, Misty, Camellia, Rijndael, Serpent.

Alex Biryukov; Christophe De Cannière

2003-01-01

281

Solving Underdefined Systems of Multivariate Quadratic Equations  

Microsoft Academic Search

The security of several recent digital signature schemes is based on the difficulty of solving large systems of quadratic multivariate polynomial equations over a finite field F. This problem, sometimes called MQ, is known to be NP-hard. When the number m of equations is equal to the number n of variables, and if n< 15, Grobner base algorithms have been

Nicolas Courtois; Louis Goubin; Willi Meier; Jean-daniel Tacier

2002-01-01

282

On quadratic integral equation of fractional orders  

Microsoft Academic Search

We present an existence theorem for a nonlinear quadratic integral equations of fractional orders, arising in the queuing theory and biology, in the Banach space of real functions defined and continuous on a bounded and closed interval. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tool in carrying out our proof.

Mohamed Abdalla Darwish

2005-01-01

283

Quadratic equations and monodromy evolving deformations  

E-print Network

We give a basic theory on monodromy evolving deformations. proposed by Chakravarty and Ablowitz in 1996. We show that Halphen's second quadratic system can be described by monodromy evolving deformations. Our result is a generalization of the work on the DH-V system by Chakravarty and Ablowitz.

Yousuke Ohyama

2007-09-28

284

A Practical Approach to Quadratic Equations.  

ERIC Educational Resources Information Center

The usual methods for solving quadratic equations are noted to require either the use of numerical formula or curve plotting on graph paper. The method described here enables pupils to solve equations using only a 45 degree setsquare, graph paper, and a pencil for those which have both real roots and real coefficients. (Author/MP)

Light, Peter

1983-01-01

285

Theory of the Quadratic Zeeman Effect  

Microsoft Academic Search

The experiments of Jenkins and Segrè, reported in the accompanying paper, are considered theoretically. The quadratic Zeeman effect observed in absorption to large orbits in strong magnetic fields is due to the diamagnetic term in the Hamiltonian, which is proportional to the square of the vector potential and hence to the square of the magnetic field. For the alkalis, the

L. I. Schiff; H. Snyder

1939-01-01

286

Integration of the Quadratic Function and Generalization  

ERIC Educational Resources Information Center

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

Mitsuma, Kunio

2011-01-01

287

A Quadratic Programming Bibliography - Optimization Online  

E-print Network

Feb 27, 2001 ... of the global optimum, computational experience on a number of nonconvex .... Elastic-plastic plane stress finite element analysis of a disk rolling on a .... A decomposition algorithm for a dual angular type quadratic ...... satisfaction of all kinematic boundary conditions and inter-element continuity conditions.

2001-02-27

288

Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements.  

PubMed

We present a formalism to derive entanglement criteria beyond the Gaussian regime that can be readily tested by only homodyne detection. The measured observable is the Einstein-Podolsky-Rosen (EPR) correlation. Its arbitrary functional form enables us to detect non-Gaussian entanglement even when an entanglement test based on second-order moments fails. We illustrate the power of our experimentally friendly criteria for a broad class of non-Gaussian states under realistic conditions. We also show rigorously that quantum teleportation for continuous variables employs a specific functional form of EPR correlation. PMID:22400723

Nha, Hyunchul; Lee, Su-Yong; Ji, Se-Wan; Kim, M S

2012-01-20

289

How many eigenvalues of a Gaussian random matrix are positive?  

NASA Astrophysics Data System (ADS)

We study the probability distribution of the index N+, i.e., the number of positive eigenvalues of an N×N Gaussian random matrix. We show analytically that, for large N and large N+ with the fraction 0?c=N+/N?1 of positive eigenvalues fixed, the index distribution P(N+=cN,N)~exp[-?N2?(c)] where ? is the Dyson index characterizing the Gaussian ensemble. The associated large deviation rate function ?(c) is computed explicitly for all 0?c?1. It is independent of ? and displays a quadratic form modulated by a logarithmic singularity around c=1/2. As a consequence, the distribution of the index has a Gaussian form near the peak, but with a variance ?(N) of index fluctuations growing as ?(N)~lnN/??2 for large N. For ?=2, this result is independently confirmed against an exact finite-N formula, yielding ?(N)=lnN/2?2+C+O(N-1) for large N, where the constant C for even N has the nontrivial value C=(?+1+3ln2)/2?2?0.185248… and ?=0.5772… is the Euler constant. We also determine for large N the probability that the interval [?1,?2] is free of eigenvalues. Some of these results have been announced in a recent letter [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.220603 103, 220603 (2009)].

Majumdar, Satya N.; Nadal, Céline; Scardicchio, Antonello; Vivo, Pierpaolo

2011-04-01

290

OPTIMAL CONTROL APPLICATIONS AND METHODS Optim. Control Appl. Meth., 20, 79}92 (1999)  

E-print Network

OPTIMAL CONTROL WITH INTEGRAL QUADRATIC CONSTRAINTS- A. E. B. LIM, Y. Q. LIU*, K. L. TEO AND J. B. MOORE) optimal control problem subject to integral quadratic constraints. The optimal control is a non & Sons, Ltd. KEY WORDS: LQ optimal control; integral quadratic constraints; feedback 1. INTRODUCTION Many

Moore, John Barratt

291

Coherent controllers for optical-feedback cooling of quantum oscillators  

NASA Astrophysics Data System (ADS)

We study the cooling performance of optical-feedback controllers for open optical and mechanical resonators in the linear quadratic Gaussian setting of stochastic control theory. We utilize analysis and numerical optimization of closed-loop models based on quantum stochastic differential equations to show that coherent control schemes, where we embed the resonator in an interferometer to achieve all-optical feedback, can outperform optimal measurement-based feedback control schemes in the quantum regime of low steady-state excitation number. These performance gains are attributed to the coherent controller's ability to simultaneously process both quadratures of an optical probe field without measurement or loss of fidelity, and may guide the design of coherent feedback schemes for more general problems of robust nonlinear and robust control.

Hamerly, Ryan; Mabuchi, Hideo

2013-01-01

292

Geometric Approaches to Quadratic Equations from Other Times and Places.  

ERIC Educational Resources Information Center

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

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

293

Bound States of the Dirac Equation for a Class of Effective Quadratic Plus Inversely Quadratic Potentials  

E-print Network

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schroedinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.

Antonio S. de Castro

2003-11-10

294

Robust linear quadratic designs with respect to parameter uncertainty  

NASA Technical Reports Server (NTRS)

The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.

Douglas, Joel; Athans, Michael

1992-01-01

295

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulations  

E-print Network

The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of Gaussian variational ansatz applied to the corresponding (1+2D) hyperbolic nonlinear Schr\\"odinger equation, a simplified Lagrangian system of differential equations is derived, which determines the evolution of coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description for the process of nonlinear spatio-temporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system is integrated in quadratures, which fact allows us to understand qualitative differences between the linear and nonlinear regimes of the focusing of wave packet. Comparison of the Gaussian model predictions with results of direct numerical simulation of fully nonlinear long-cres...

Ruban, V P

2015-01-01

296

Effect of primordial non-Gaussianity on halo bias and mass function  

NASA Astrophysics Data System (ADS)

We discuss the effect of quadratic and cubic local non-Gaussianity on the mass function and bias of dark matter halos extracted from cosmological N-body simulations. This type of non-Gaussianity induces a k-dependent bias in the large-scale clustering of rare objects. While we find that at low wavenumbers k<0.03 hMpc-1 the theory and the simulations agree well with each other for biased halos with b(M)>1.5, including a scale independent correction to the non-Gaussian bias improves the agreement on small scales where the k-dependent effect becomes rapidly negligible. Using available large-scale structure data, we obtain a limit on the size of the cubic nonlinear parameter of -3.5×105< gNL<8.2×105. Future observations shall improve this bound by 1-2 orders of magnitude.

Desjacques, Vincent; Seljak, Uroš; Iliev, Ilian T.

2010-06-01

297

Some results on Gaussian mixtures  

NASA Astrophysics Data System (ADS)

We investigate Gaussian mixtures with independent components, whose parameters are numerically estimated. A decomposition of a Gaussian mixture is presented when the components have a common variance. We introduce a shifted and scaled t-Student distribution as an approximation for the distribution of Gaussian mixtures when their components have a common mean and develop a hypothesis test for testing the equality of the components means. Finally, we analyse the fitness of the approximate model to the logarithmic daily returns of the Portuguese stock index PSI-20.

Felgueiras, Miguel; Santos, Rui; Martins, João Paulo

2014-10-01

298

Control-structure interaction  

NASA Technical Reports Server (NTRS)

The feasibility of using conventional proportional-integral-derivative (PID) control and an alternative optimal control to perform the pointing and tracking functions of the Space Station solar dynamic power module is investigated. A very large state model of 6 rigid body modes and 272 flexible modes is used in conjunction with classical linear-quadratic-Gaussian (LQG) optimal control to produce a full-order controller that satisfies the requirements. The results are compared with a classically designed PID controller that was implemented for a much smaller (6 rigid body, 40 flexible modes) model. The conventional control design approach is shown to be very much influenced by the order reduction of the plant model, i.e., the number of retained elastic modes from the full-order model, suggesting that for a complex, large space structure, such as the Space Station Freedom solar dynamic module, application of conventional control system design methods may not be adequate. The use of LQG control is recommended, and method for solving the large matrix. Riccati equation that arises from the optimal formulation is provided.

Cheng, Joseph K.; Ianculescu, George D.; Kenney, Charles S.; Laub, Alan J.; Ly, Jason H. Q.; Papadopoulos, Philip M.

1992-01-01

299

The effect of primordial non-Gaussianity on the topology of large-scale structure  

NASA Astrophysics Data System (ADS)

We study the effect of primordial non-Gaussianity on the development of large-scale cosmic structure using high-resolution N-body simulations. In particular, we focus on the topological properties of the `cosmic web', quantitatively characterized by the Minkowski functionals (MFs), for models with quadratic non-linearities with different values of the usual non-Gaussianity parameter fNL. In the weakly non-linear regime (the amplitude of mass density fluctuations ?0 < 0.1), we find that analytic formulae derived from perturbation theory agree with the numerical results within a few per cent of the amplitude of each MF when |fNL| < 1000. In the non-linear regime, the detailed behaviour of the MFs as functions of threshold density deviates more strongly from the analytical curves, while the overall amplitude of the primordial non-Gaussian effect remains comparable to the perturbative prediction. When smaller-scale information is included, the influence of primordial non-Gaussianity becomes increasingly significant statistically due to decreasing sample variance. We find that the effect of the primordial non-Gaussianity with |fNL| = 50 is comparable to the sample variance of mass density fields with a volume of 0.125(h-1 Gpc)3 when they are smoothed by Gaussian filter at a scale of 5h-1Mpc. The detectability of this effect in actual galaxy surveys will strongly depend on residual uncertainties in cosmological parameters and galaxy biasing.

Hikage, C.; Coles, P.; Grossi, M.; Moscardini, L.; Dolag, K.; Branchini, E.; Matarrese, S.

2008-04-01

300

THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY  

EPA Science Inventory

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

301

Number Theory 2010 Exercise list 3: quadratic forms  

E-print Network

Number Theory 2010 Yuri Bilu Exercise list 3: quadratic forms Unless the contrary is stated f; · "form" means "quadratic form". 1. In this exercise we prove the Theorem of Witt: if f1 and f2 and U2 are called in this case isometric. (a) Let u be an anisotropic vector of a quadratic space U

Bilu, Yuri F.

302

On rational quadratic differential forms H.L. Trentelman  

E-print Network

multipliers or integral quadratic constraints (for the previous works on related topics, see e.g. MegretskiOn rational quadratic differential forms K. Takaba H.L. Trentelman J.C. Willems Department Lyapunov functions, energy storage, performance measures, e.t.c. Such a quadratic functional is called

303

UNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS 1  

E-print Network

definition is closely related to the integral quadratic constraint uncertainty description commonly found as a behavioural generalization of the frequency domain integral quadratic constraint (IQC) 1 This workUNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS 1 Ian R. Petersen Jan C. Willems

304

Constrained Quadratic Minimizations for Signal Processing and Communications  

E-print Network

. The problem is to minimize a quadratic form, under a set of linear or quadratic constraints. We derive) with respect to W, subject to a set of linear or quadratic constraints. WH RW is the covariance matrix of V. Then, the constraint is WH = LH VH , (2) This work is supported by the DARPA Integrated Sensing

Scharf, Louis

305

Linear and quadratic time-frequency signal representations  

Microsoft Academic Search

A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems

F. Hlawatsch; G. F. Boudreaux-Bartels

1992-01-01

306

A Quadratic Gradient Equation for pricing Mortgage-Backed Securities  

E-print Network

A Quadratic Gradient Equation for pricing Mortgage-Backed Securities Marco Papi Institute for Applied Computing - CNR Rome (Italy) A Quadratic Gradient Equation for pricing Mortgage-Backed Securities call option on a corresponding fixed-rate bond. A Quadratic Gradient Equation for pricing Mortgage

Monneau, Régis

307

HOW DO YOU SOLVE A QUADRATIC EQUATION? GEORGE E._ FORSYTHE  

E-print Network

cs40 HOW DO YOU SOLVE A QUADRATIC EQUATION? BY GEORGE E._ FORSYTHE TECHNICAL REPORT NO. CS40 JUNE;1 \\- c. `L L t HOW DO YOU SOLVE A QUADRATIC EQUATION? bY George E. Forsythe Abstract The nature-point computation are illustrated by the formula for solving a quadratic equation. An accurate way of solving

Jiang, Shidong

308

REGULARIZED TOTAL LEAST SQUARES BASED ON QUADRATIC EIGENVALUE PROBLEM SOLVERS  

Microsoft Academic Search

This paper presents a new computational approach for solving the Regularized Total Least Squares problem. The problem is formulated by adding a quadratic constraint to the Total Least Square minimization problem. Starting from the fact that a quadrat- ically constrained Least Squares problem can be solved via a quadratic eigenvalue problem, an iterative procedure for solving the regularized Total Least

DIANA M. SIMA; SABINE VAN HUFFEL; GENE H. GOLUB

2003-01-01

309

INTERFERENCE DETECTION IN GAUSSIAN NOISE  

SciTech Connect

Interference detection in Gaussian noise is proposed. It can be applied for easy detection and editing of interference lines in radio spectral line observations. One does not need to know the position of occurrence or keep track of interference in the band. By using statistical properties of N-channel Gaussian noise it is possible to differentiate interference from normal Gaussian noise. These statistical properties are three quantities which are calculated on the subject spectrum. The first is the expected absolute maximum from the mean level across the spectrum. The second is the expected absolute difference maximum (array of adjacent differences of channel values taken across the spectrum), and the third is the expected absolute added difference maximum. For N-channel Gaussian noise, these quantities have a well-defined value. Any deviation across the spectrum that violates an upper limit formed by these expected maxima is attributed to interference. Results obtained on real data by applying this technique have been displayed.

Baddi, Raju [Raman Research Institute, C.V. Raman Avenue., Bangalore 560 080 (India)

2011-06-15

310

Higgsed Stueckelberg vector and Higgs quadratic divergence  

NASA Astrophysics Data System (ADS)

Here we show that, a hidden vector field whose gauge invariance is ensured by a Stueckelberg scalar and whose mass is spontaneously generated by the Standard Model Higgs field contributes to quadratic divergences in the Higgs boson mass squared, and even leads to its cancellation at one-loop when Higgs coupling to gauge field is fine-tuned. In contrast to mechanisms based on hidden scalars where a complete cancellation cannot be achieved, stabilization here is complete in that the hidden vector and the accompanying Stueckelberg scalar are both free from quadratic divergences at one-loop. This stability, deriving from hidden exact gauge invariance, can have important implications for modeling dark phenomena like dark matter, dark energy, dark photon and neutrino masses. The hidden fields can be produced at the LHC.

Demir, Durmu? Ali; Karahan, Canan Nurhan; Korutlu, Beste

2015-01-01

311

Planar flows and quadratic relations over semirings  

E-print Network

It is well known, due to Lindstr\\"om, that the minors of a matrix can be expressed in terms of weights of flows in a planar directed graph. Another fact is that there are plenty of quadratic relations involving minors, of which Pl\\"ucker ones are most popular. Generalizing and unifying these facts and their tropical counterparts, we consider a wide class of functions which are generated by flows in a planar graph and take values in an arbitrary commutative semiring. We show that the "universal" quadratic relations performed by such functions can be described in terms of certain matchings, and as a consequence, give combinatorial necessary and sufficient conditions for these relations. Also we give applications and discuss related topics.

Danilov, Vladimir I; Koshevoy, Gleb A

2011-01-01

312

Stellar objects in the quadratic regime  

NASA Astrophysics Data System (ADS)

We model a charged anisotropic relativistic star with a quadratic equation of state. Physical features of an exact solution of the Einstein-Maxwell system are studied by incorporating the effect of the nonlinear term from the equation of state. It is possible to regain the masses, radii and central densities for a linear equation of state in our analysis. We generate masses for stellar compact objects and perform a detailed study of PSR J1614-2230 in particular. We also show the influence of the nonlinear equation of state on physical features of the matter distribution. We demonstrate that it is possible to incorporate the effects of charge, anisotropy and a quadratic term in the equation of state in modelling a compact relativistic body.

Mafa Takisa, P.; Maharaj, S. D.; Ray, Subharthi

2014-12-01

313

Stellar objects in the quadratic regime  

E-print Network

We model a charged anisotropic relativistic star with a quadratic equation of state. Physical features of an exact solution of the Einstein-Maxwell system are studied by incorporating the effect of the nonlinear term from the equation of state. It is possible to regain the masses, radii and central densities for a linear equation of state in our analysis. We generate masses for stellar compact objects and perform a detailed study of PSR J1614-2230 in particular. We also show the influence of the nonlinear equation of state on physical features of the matter distribution. We demonstrate that it is possible to incorporate the effects of charge, anisotropy and a quadratic term in the equation of state in modelling a compact relativistic body.

P. Mafa Takisa; S. D. Maharaj; Subharthi Ray

2014-12-28

314

Regular models with quadratic equation of state  

E-print Network

We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein-Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.

S. D. Maharaj; P. Mafa Takisa

2013-01-08

315

Portfolio optimization and mixed integer quadratic programming  

SciTech Connect

We begin with the well-known Markowitz model of risk and return fora portfolio of stocks. This model is used to choose a minimum risk portfolio from a universe of stocks that achieves a specified level of expected return subject to a budget constraint and possibly other (linear) constraints. This model is a convex quadratic programming model over continuous variables. As such, many of the variables may have small and unrealistic values in an optimal solution. In addition, a minimum risk portfolio may contain far too many stocks for an investor to hold. Eliminating these unwanted characteristics of minimum risk solutions can be accomplished using binary decision variables. We discuss an implementation of branch-and-bound for convex quadratic programming using the Optimization Subroutine Library. We then discuss how the structure of these particular types of additional constraints can be used to obtain a more efficient implementation. We present some computational experience with instances from the finance industry.

Jensen, D.

1994-12-31

316

Numerical analysis of a quadratic matrix equation  

Microsoft Academic Search

The quadratic matrix equation AX2+BX +C = 0 in n \\\\Theta n matrices arises inapplications and is of intrinsic interest as one of the simplest nonlinear matrix equations.We give a complete characterization of solutions in terms of the generalizedSchur decomposition and describe and compare various numerical solution techniques.In particular, we give a thorough treatment of functional iteration methodsbased on Bernoulli's

NICHOLAS J. HIGHAM; HYUN-MIN KIM

1999-01-01

317

Characterization of a Quadratic Function in Rn  

ERIC Educational Resources Information Center

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

Xu, Conway

2010-01-01

318

Turbofan engine control system design using the LQG/LTR methodology  

NASA Technical Reports Server (NTRS)

Application of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery methodology to design of a control system for a simplified turbofan engine model is considered. The importance of properly scaling the plant to achieve the desired Target-Feedback-Loop is emphasized. The steps involved in the application of the methodology are discussed via an example, and evaluation results are presented for a reduced-order compensator. The effect of scaling the plant on the stability robustness evaluation of the closed-loop system is studied in detail.

Garg, Sanjay

1989-01-01

319

A wavelet bicoherence-based quadratic nonlinearity feature for translational axis condition monitoring.  

PubMed

The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

2014-01-01

320

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring  

PubMed Central

The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

2014-01-01

321

Linear Quadratic Regulator design for modular matrix converter using Genetic Algorithm  

Microsoft Academic Search

This paper introduces an application of Linear Quadratic Regulator (LQR) based on Genetic Algortihm (GA) for improving the stability of modular matrik converter. GA is used for constructing the weighting matrices Q and R of LQR. To design controller, the converter is analyzed in small signal model and steady state model. Stability performances of converter are presented by the switch

Muldi Yuhendri; Mochammad Ashari; M H Purnomo

2011-01-01

322

The halo bispectrum in N-body simulations with non-Gaussian initial conditions  

NASA Astrophysics Data System (ADS)

We present measurements of the bispectrum of dark matter haloes in numerical simulations with non-Gaussian initial conditions of local type. We show, in the first place, that the overall effect of primordial non-Gaussianity on the halo bispectrum is larger than on the halo power spectrum when all measurable configurations are taken into account. We then compare our measurements with a tree-level perturbative prediction, finding good agreement at large scales when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fitting values of the Gaussian bias factors and their non-Gaussian, scale-independent corrections are in qualitative agreement with the peak-background split expectations. In particular, we show that the effect of non-Gaussian initial conditions on squeezed configurations is fairly large (up to 30 per cent for fNL = 100 at redshift z = 0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum, scale-dependent bias corrections as well as from non-linear matter bispectrum corrections. We show, in addition, that effects at second order in fNL are irrelevant for the range of values allowed by cosmic microwave background and galaxy power spectrum measurements, at least on the scales probed by our simulations (k > 0.01 h Mpc-1). Finally, we present a Fisher matrix analysis to assess the possibility of constraining primordial non-Gaussianity with future measurements of the galaxy bispectrum. We find that a survey with a volume of about 10 h-3 Gpc3 at mean redshift z ? 1 could provide an error on fNL of the order of a few. This shows the relevance of a joint analysis of galaxy power spectrum and bispectrum in future redshift surveys.

Sefusatti, E.; Crocce, M.; Desjacques, V.

2012-10-01

323

Nonperturbative approach to finite-dimensional non-Gaussian integrals  

NASA Astrophysics Data System (ADS)

We study the homogeneous non-Gaussian integral J_{n|r} (S) = int {e^{ - S(x_1 , ldots ,x_n )} } d^n x , where S(x1,…,xn) is a symmetric form of degree r in n variables. This integral is naturally invariant under SL(n) transformations and therefore depends only on the invariants of the form. For example, in the case of quadratic forms, it is equal to the ( -1/2)th power of the determinant of the form. For higher-degree forms, the integral can be calculated in some cases using the so-called Ward identities, which are second-order linear differential equations. We describe the method for calculating the integral and present detailed calculations in the case where n = 2 and r = 5. It is interesting that the answer is a hypergeometric function of the invariants of the form.

Shakirov, Sh. R.

2010-06-01

324

Transformations of symmetric multipartite Gaussian states by Gaussian LOCC  

E-print Network

Multipartite quantum correlations, in spite of years of intensive research, still leave many questions unanswered. While bipartite entanglement is relatively well understood for Gaussian states, the complexity of mere qualitative characterization grows rapidly with increasing number of parties. Here, we present two schemes for transformations of multipartite permutation invariant Gaussian states by Gaussian local operations and classical communication. To this end, we use a scheme for possible experimental realization, making use of the fact, that in this picture, the whole N - partite state can be described using two separable modes. Numerically, we study entanglement transformations of tripartite states. Finally, we look at the effect our protocols have on fidelity of assisted quantum teleportation and find that while adding correlated noise does not affect the fidelity at all, there is strong evidence that partial non-demolition measurement leads to a drop in teleportation fidelity.

Ond?ej ?ernotík; Jaromír Fiurášek

2014-04-30

325

Information geometry of Gaussian channels  

SciTech Connect

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).

Monras, Alex [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); CNR-INFM Coherentia, Napoli (Italy); CNISM Unita di Salerno (Italy) and INFN Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy); Illuminati, Fabrizio [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); CNR-INFM Coherentia, Napoli (Italy) and CNISM Unita di Salerno; and INFN Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy); ISI Foundation for Scientific Interchange, Villa Gualino, Viale Settimio Severo 65, I-10133 Torino (Italy)

2010-06-15

326

Application of IFT and SPSA to servo system control.  

PubMed

This paper treats the application of two data-based model-free gradient-based stochastic optimization techniques, i.e., iterative feedback tuning (IFT) and simultaneous perturbation stochastic approximation (SPSA), to servo system control. The representative case of controlled processes modeled by second-order systems with an integral component is discussed. New IFT and SPSA algorithms are suggested to tune the parameters of the state feedback controllers with an integrator in the linear-quadratic-Gaussian (LQG) problem formulation. An implementation case study concerning the LQG-based design of an angular position controller for a direct current servo system laboratory equipment is included to highlight the pros and cons of IFT and SPSA from an application's point of view. The comparison of IFT and SPSA algorithms is focused on an insight into their implementation. PMID:22086492

R?dac, Mircea-Bogdan; Precup, Radu-Emil; Petriu, Emil M; Preitl, Stefan

2011-12-01

327

Observer-based control of Rijke-type combustion instability  

NASA Astrophysics Data System (ADS)

In this work, observer-based feedback control of combustion instability in a Rijke-type thermoacoustic system is considered. A generalized thermoacoustic model with distributed monopole-like actuators is developed. The model is linearized and formulated in state-space and it is assumed that pressure sensors are the only information available for feedback. It is shown that a system of this form is observable. As a Linear-Quadratic-Gaussian (LQG) controller is implemented to tune the actuators, the system becomes asymptotically stable. The performance of the controller is evaluated with a system involving two modes. The successful demonstration indicates that the observer-based feedback controller can be applied to a real combustion system with multiple modes.

Hervas, Jaime Rubio; Zhao, Dan; Reyhanoglu, Mahmut

2014-12-01

328

Issues in the digital implementation of control compensators. Ph.D. Thesis  

NASA Technical Reports Server (NTRS)

Techniques developed for the finite-precision implementation of digital filters were used, adapted, and extended for digital feedback compensators, with particular emphasis on steady state, linear-quadratic-Gaussian compensators. Topics covered include: (1) the linear-quadratic-Gaussian problem; (2) compensator structures; (3) architectural issues: serialism, parallelism, and pipelining; (4) finite wordlength effects: quantization noise, quantizing the coefficients, and limit cycles; and (5) the optimization of structures.

Moroney, P.

1979-01-01

329

Avoidance of instability of a superluminal Gaussian light pulse via control of nonlinear coherence Kerr effect in a gain-assisted medium  

E-print Network

We investigate nonlinear Kerr-induced coherence effect on a superluminal probing light pulse in a gain-assisted N-type 4-level atomic system via an intense monochromatic laser field. The dispersion exhibits a novel, interesting and useful two-paired double gain lines processes. The system displays lossless characteristics similar to [L. J. Wang, A. Kuzmich, A. Dogariu, Nature \\textbf{406}, 277 (2000)] but with advantages of \\emph{multiple} \\textbf{controllable} anomalous regions, \\emph{significantly enhanced} superluminal behavior and \\textbf{relaxed} temperature, states of matter regardless of its isotropic or anisotropic conditions. Unlike the instability in [A. M. Akulshin, S. Barreiro, and A. Lezama, Phys. Rev. Lett. \\textbf{82}, 4277 (1999)], the present system also \\emph{overcomes the instable-limit} by the Kerr-induced coherence effect in the system. Indeed, the coherence enhances the group velocity remarkably by at least $-30 ms$ more than of an instable Kerr-free system with almost negligible distort...

Bacha, Bakht Amin

2013-01-01

330

Shaping super-Gaussian beam through digital micro-mirror device  

NASA Astrophysics Data System (ADS)

We have set up a novel system for shaping the Gaussian laser beams into super-Gaussian beams. The digital micro-mirror device (DMD) is able to modulate the laser light spatially through binary-amplitude modulation mechanism. With DMD, the irradiance of the laser beam can be redistributed flexibly and various beams with different intensity distribution can be produced. A super-Gaussian beam has been successfully shaped from the Gaussian beam with the use of DMD. This technique will be widely applied in lithography, quantum emulation and holographic optical tweezers which require precise control of beam profile.

Ding, XiangYu; Ren, YuXuan; Lu, RongDe

2014-08-01

331

Shaping super-Gaussian beam through digital micro-mirror device  

NASA Astrophysics Data System (ADS)

We have set up a novel system for shaping the Gaussian laser beams into super-Gaussian beams. The digital micro-mirror device (DMD) is able to modulate the laser light spatially through binary-amplitude modulation mechanism. With DMD, the irradiance of the laser beam can be redistributed flexibly and various beams with different intensity distribution can be produced. A super-Gaussian beam has been successfully shaped from the Gaussian beam with the use of DMD. This technique will be widely applied in lithography, quantum emulation and holographic optical tweezers which require precise control of beam profile.

Ding, XiangYu; Ren, YuXuan; Lu, RongDe

2015-03-01

332

Gaussian Entanglement Distribution via Satellite  

E-print Network

In this work we analyse three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the trade-off between space-based engineering complexity and the rate of ground-station entanglement generation...

Hosseinidehaj, Nedasadat

2014-01-01

333

Gaussian Entanglement Distribution via Satellite  

E-print Network

In this work we analyse three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the trade-off between space-based engineering complexity and the rate of ground-station entanglement generation.

Nedasadat Hosseinidehaj; Robert Malaney

2014-10-06

334

Gaussian Entanglement Distribution via Satellite  

E-print Network

In this work we analyse three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the trade-off between space-based engineering complexity and the rate of ground-station entanglement generation.

Nedasadat Hosseinidehaj; Robert Malaney

2015-02-05

335

Extensions of representations of integral quadratic forms  

Microsoft Academic Search

Let N and M be quadratic ?-lattices, and K be a sublattice of N. A representation ?:K?M is said to be extensible to N if there exists a representation ?:N?M such that ?\\u000a |\\u000a \\u000a K\\u000a =?. We prove in this paper a local–global principle for extensibility of representation, which is a generalization of the main\\u000a theorems on representations by positive definite ?-lattices by Hsia, Kitaoka and

Wai Kiu Chan; Byeong Moon Kim; Myung-Hwan Kim; Byeong-Kweon Oh

2008-01-01

336

Oscillations of a quadratically damped pendulum  

NASA Astrophysics Data System (ADS)

A physical pendulum consisting of a circular disk at the end of a thin metal rod is connected to a low-friction rotary motion sensor, so that its angular position and velocity can be accurately measured. The disk can be oriented either perpendicular or parallel to the plane of swing to give significant or negligible air drag, respectively. The motion is analytically modeled in phase space. A quadratic dependence of the damping torque on the angular velocity fits the results. This laboratory experiment is suitable for undergraduate physics majors taking a first or second course in classical mechanics.

Mungan, Carl E.; Lipscombe, Trevor C.

2013-09-01

337

Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems.  

PubMed

Adaptive optics (AO) systems have to correct tip-tilt (TT) disturbances down to a fraction of the diffraction-limited spot. This becomes a key issue for very or extremely large telescopes affected by mechanical vibration peaks or wind shake effects. Linear quadratic Gaussian (LQG) control achieves optimal TT correction when provided with the temporal model of the disturbance. We propose a nonsupervised identification procedure that does not require any auxiliary system or loop opening and validate it on synthetic profile as well as on experimental data. PMID:21045874

Meimon, Serge; Petit, Cyril; Fusco, Thierry; Kulcsar, Caroline

2010-11-01

338

Restrictions of Quadratic Forms to Lagrangian Planes, Quadratic Matrix Equations, and Gyroscopic Stabilization  

Microsoft Academic Search

We discuss the symplectic geometry of linear Hamiltonian systems with nondegenerate Hamiltonians. These systems can be reduced to linear second-order differential equations characteristic of linear oscillation theory. This reduction is related to the problem on the signatures of restrictions of quadratic forms to Lagrangian planes. We study vortex symplectic planes invariant with respect to linear Hamiltonian systems. These planes are

V. V. Kozlov

2005-01-01

339

A formal approach to the design of multibunch feedback systems: LQG controllers  

SciTech Connect

We formulate the multibunch feedback problem as a standard control-systems design problem and solve it using Linear Quadratic Gaussian (LQG) regulator theory. Use of a specific optimality criterion allows quantitative evaluation of different controllers and leads to the design of optimal LQG controllers. Computer simulations are used to show that, as compared to the existing Finite Impulse Response (FIR) control, LQG control can provide the same closed-loop damping for less peak power, thus making more effective use of limited kicker power. Furthermore, LQG control enables us to use more power to provide better damping without the problem of driving instabilities with higher loop gains. The code for the LQG filters described has been written for the Quick prototype installed at ALS.

Hindi, H.; Fox, J.; Prabhaker, S.; Sapozhnikov, L.; Oxoby, G.; Linscott, I.; Teytelman, D.

1994-06-01

340

Multivariable control of a forward swept wing aircraft. M.S. Thesis  

NASA Technical Reports Server (NTRS)

The impact of independent canard and flaperon control of the longitudinal axis of a generic forward swept wing aircraft is examined. The Linear Quadratic Gaussian (LQG)/Loop Transfer Recovery (LTR) method is used to design three compensators: two single-input-single-output (SISO) systems, one with angle of attack as output and canard as control, the other with pitch attitude as output and canard as control, and a two-input-two-output system with both canard and flaperon controlling both the pitch attitude and angle of attack. The performances of the three systems are compared showing the addition of flaperon control allows the aircraft to perform in the precision control modes with very little loss of command following accuracy.

Quinn, W. W.

1986-01-01

341

Active vibration control of smart hull structure using piezoelectric composite actuators  

NASA Astrophysics Data System (ADS)

In this paper, active vibration control performance of the smart hull structure with macro-fiber composite (MFC) is evaluated. MFC is an advanced piezoelectric composite which has great flexibility and increased actuating performance compared to a monolithic piezoelectric ceramic patch. The governing equations of motion of the hull structure with MFC actuators are derived based on the classical Donnell-Mushtari shell theory. The actuating model for the interaction between hull structure and MFC is included in the governing equations. Subsequently, modal characteristics are investigated and compared with the results obtained from experiment. The governing equations of the vibration control system are then established and expressed in the state space form. A linear quadratic Gaussian (LQG) control algorithm is designed in order to effectively and actively control the imposed vibration. The controller is experimentally realized and vibration control performances are evaluated.

Sohn, Jung Woo; Choi, Seung-Bok; Lee, Chul-Hee

2009-07-01

342

Gaussianity, non-Gaussianity, and photometric redshift surveys  

NASA Astrophysics Data System (ADS)

Many physical properties of galaxies correlate with one another, and these correlations are often used to constrain galaxy formation models. However, the transformation from observable to physical quantity is frequently distance- dependent. Noise in the distance estimate leads to biased estimates of these correlations, thus compromising the ability of photometric redshift surveys to constrain galaxy formation models. Enabling a reliable estimate of these correlations from photometric data, and presenting methods and algorithms for estimating the correlations between distance-dependent observables accurately even if the distance estimate is noisy, is the main focus of the first part of this thesis. Noise properties are also essential in the second part, where we turn our attention to the pursuit of primordial non-Gaussianity in the Cosmic Microwave Background. There are already a number of plausible extensions of the standard inflationary model or alternative early universe models that predict skewed primordial fluctuations, but since the detection of primordial non-Gaussian fluctuations in the CMB would have a profound impact on our understanding of the physics of the early universe, these claims need to be further investigated. Therefore, it is vitally important to test whether the map of the primary temperature anisotropies is indeed Gaussian, as if it is not this fact would indicate a quite different structure formation scenario from the standard inflation model. We investigate the Gaussian hyphothesis using the clustering statistics of pixels and peaks that lie above or below a threshold. It turns out that a careful accounting for the effects of noise is crucial to performing this test. In the case of WMAP, the noise is spatially inhomogeneous; the present work shows how to incorporate this complexity into the analysis. Small differences from the Gaussian-based prediction remain even after this more careful accounting of the noise. While these may indicate primordial non- Gaussianity, we discuss a variety of plausible reasons for these discrepancies. Lastly, in the third part we present a blend of analytic and numerical tools in order to describe the shapes of dark matter halos as seen in the simulations. Shape measurements are useful, as they have important implications for interpretation of gravitational lensing measurements as well as observations of the Sunyaev-Zeldovich effect. In particular, the ellipsoidal collapse model is extended to study halo shapes, and combined with the statistics of Gaussian random fields. By averaging over the correct, mass-dependent distribution of initial shape parameters, each evolved through the ellipsoidal collapse model, we are able to make predictions for how the distribution of final shapes depends on halo mass.

Rossi, Graziano

343

Runge-Kutta methods for quadratic ordinary differential equations  

Microsoft Academic Search

Many systems of ordinary differential equations are quadratic: the derivative can be expressed as a quadratic function of\\u000a the dependent variable. We demonstrate that this feature can be exploited in the numerical solution by Runge-Kutta methods,\\u000a since the quadratic structure serves to decrease the number of order conditions. We discuss issues related to construction\\u000a design and implementation and present a

Arieh Iserles; Geetha Ramaswami; Mark Sofroniou

1998-01-01

344

LARGE TIME SOLUTION FOR QUADRATIC SCHRODINGER EQUATIONS IN HANTAEK BAE  

E-print Network

LARGE TIME SOLUTION FOR QUADRATIC SCHR¨ODINGER EQUATIONS IN 2D AND 3D HANTAEK BAE Abstract. The aim of this paper is to establish the large time well-posedness of the quadratic Schr¨odinger equation in 2D and 3D for the solvability of (1.1), see [5]. In this paper, we consider the Schr¨odinger equation with quadratic

Yorke, James

345

Controlled reshaping of the front surface of the cornea through its full-area ablation outside of the optical zone with a Gaussian ArF excimer laser beam  

NASA Astrophysics Data System (ADS)

We studied in vitro the response of the topography of the cornea to its full-area laser ablation (the laser beam spot diameter is commensurable with the size of the interface) outside of the central zone with an excimer laser having a Gaussian fluence distribution across the beam. Subject to investigation were the topographically controlled surface changes of the anterior cornea in 60 porcine eyes with a 5 ± 1.25-diopter artificially induced astigmatism, the changes being caused by laser ablation of the stromal collagen in two 3.5-mm-dia. circular areas along the weaker astigmatism axis. Experimental relationships are presented between the actual astigmatism correction and the expected correction for the intact optical zones 1, 2, 3, and 4 mm in diameter. The data for each zone were approximated by the least-squares method with the function d = a + bx. The coefficient b is given with the root-mean-square error. The statistical processing of the data yielded the following results: d = (0.14 ± 0.037)x for the 1-mm-dia. optical zone, (1.10 ± 0.036)x for the 2-mm-dia. optical zone, (1.04 ± 0.020)x for the 3-mm-dia. optical zone, and (0.55 ± 0.04)x for the 4-mm-dia. optical zone. Full astigmatism correction was achieved with ablation effected outside of the 3-mm-dia. optical zone. The surface changes of the cornea are shown to be due not only to the removal of the corneal tissue, but also to the biomechanical topographic response of the cornea to its strain caused by the formation of a dense pseudomembrane in the ablation area.

Semchishen, A. V.; Semchishen, V. A.

2014-01-01

346

Measurable metrics and Gaussian concentration  

Microsoft Academic Search

W eintroduce, in the general setting of a measure space endowed with a measurable metric in the sense of N. Weaver, the concentration function. We then extend some results concerning the Gaussian con- centration property. In particular, we study relations between this property and transportation type inequalities or logarithmic Sobolev inequalities.

Francis Hirsch

2006-01-01

347

Non-gaussian shape recognition  

SciTech Connect

A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming cosmic microwave background (CMB) and large-scale structure (LSS) surveys raises a natural question: if a detection given a particular template is made, what does this truly tell us about the underlying theory? Even in the case of non-detections and upper bounds on deviations from Gaussianity, what can we then infer about the viable theories that remain? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high accuracy with between three and seven basis functions. The basis allows shapes to be grouped into broad ''template classes'', satisfying theoretically-relevant priors on their divergence properties in the squeezed limit. We forecast how well a Planck-like CMB survey could not only detect a general non-Gaussian signal but discern more about its shape, using existing templates and new ones we propose. This approach offers an opportunity to tie together minimal theoretical priors with observational constraints on the shape in general, and in the squeezed limit, to gain a deeper insight into what drove inflation.

Byun, Joyce; Bean, Rachel, E-mail: byun@astro.cornell.edu, E-mail: rbean@astro.cornell.edu [Department of Astronomy, Cornell University, Ithaca, NY 14853 (United States)

2013-09-01

348

Quantum Correlations as Correlations of Classical Gaussian Signals: "Entanglement" at the Subquantum Level  

NASA Astrophysics Data System (ADS)

We show that correlations between observables on composite quantum systems can be mathematically represented as correlations of quadratic forms of classical Gaussian signals. The formalism covers correlations for entangled quantum systems; for example, measurements of spin projections for two electrons in the singlet state. In this paper we show that at the subquantum level all quantum systems are correlated including systems in factorizable states. However, in the latter case quadratic forms of the prequantum fields (at the subquantum level these forms represent quantum observables) are uncorrelated. Thus "subquantum entanglement" for prequantum fields representing quantum systems in factorizable states cannot be found by using quantum observables. We have to go beyond quantum mechanics. Coupling with generalized quantum models of Mielnik and Zyczkowski are discussed.

Khrennikov, Andrei

2012-04-01

349

How many eigenvalues of a Gaussian random matrix are positive?  

SciTech Connect

We study the probability distribution of the index N{sub +}, i.e., the number of positive eigenvalues of an NxN Gaussian random matrix. We show analytically that, for large N and large N{sub +} with the fraction 0{<=}c=N{sub +}/N{<=}1 of positive eigenvalues fixed, the index distribution P(N{sub +}=cN,N){approx}exp[-{beta}N{sup 2}{Phi}(c)] where {beta} is the Dyson index characterizing the Gaussian ensemble. The associated large deviation rate function {Phi}(c) is computed explicitly for all 0{<=}c{<=}1. It is independent of {beta} and displays a quadratic form modulated by a logarithmic singularity around c=1/2. As a consequence, the distribution of the index has a Gaussian form near the peak, but with a variance {Delta}(N) of index fluctuations growing as {Delta}(N){approx}lnN/{beta}{pi}{sup 2} for large N. For {beta}=2, this result is independently confirmed against an exact finite-N formula, yielding {Delta}(N)=lnN/2{pi}{sup 2}+C+O(N{sup -1}) for large N, where the constant C for even N has the nontrivial value C=({gamma}+1+3ln2)/2{pi}{sup 2}{approx_equal}0.185 248... and {gamma}=0.5772... is the Euler constant. We also determine for large N the probability that the interval [{zeta}{sub 1},{zeta}{sub 2}] is free of eigenvalues. Some of these results have been announced in a recent letter [Phys. Rev. Lett. 103, 220603 (2009)].

Majumdar, Satya N.; Nadal, Celine [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Scardicchio, Antonello [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy); INFN, Sezione di Trieste, Strada Costiera 11, 34151 Trieste (Italy); Vivo, Pierpaolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)

2011-04-15

350

GAUSSIAN BEAM LASER RESONATOR PROGRAM  

NASA Technical Reports Server (NTRS)

In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.

Cross, P. L.

1994-01-01

351

Monogamy Inequality for Distributed Gaussian Entanglement  

Microsoft Academic Search

We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit

Tohya Hiroshima; Gerardo Adesso; Fabrizio Illuminati

2007-01-01

352

Bipartite and Multipartite Entanglement of Gaussian States  

Microsoft Academic Search

In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect

Gerardo Adesso; Fabrizio Illuminati

2005-01-01

353

Development and modification of a Gaussian and non-Gaussian noise exposure system  

NASA Astrophysics Data System (ADS)

Millions of people across the world currently have noise induced hearing loss, and many are working in conditions with both continuous Gaussian and non-Gaussian noises that could affect their hearing. It was hypothesized that the energy of the noise was the cause of the hearing loss and did not depend on temporal pattern of a noise. This was referred to as the equal energy hypothesis. This hypothesis has been shown to have limitations though. This means that there is a difference in the types of noise a person receives to induce hearing loss and it is necessary to build a system that can easily mimic various conditions to conduct research. This study builds a system that can produce both non-Gaussian impulse/impact noises and continuous Gaussian noise. It was found that the peak sound pressure level of the system could reach well above the needed 120 dB level to represent acoustic trauma and could replicate well above the 85 dB A-weighted sound pressure level to produce conditions of gradual developing hearing loss. The system reached a maximum of 150 dB sound peak pressure level and a maximum of 133 dB A-weighted sound pressure level. Various parameters could easily be adjusted to control the sound, such as the high and low cutoff frequency to center the sound at 4 kHz. The system build can easily be adjusted to create numerous sound conditions and will hopefully be modified and improved in hopes of eventually being used for animal studies to lead to the creation of a method to treat or prevent noise induced hearing loss.

Schlag, Adam W.

354

Dynamic aeroelastic response and active control of composite thin-walled beam structures in compressible flow  

NASA Astrophysics Data System (ADS)

The dynamic aeroelastic response and its active control of composite beam structures in compressible flow and exposed to gust and explosive type loads are examined. Modeling of the structures is based on a refined composite thin-walled beam theory and incorporate a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, and rotatory inertia. The unsteady compressible aerodynamic loads for arbitrary small motion in the time domain are derived based on the concept of indicial functions. The sliding mode control (SMC) and linear-quadratic Gaussian (LQG) control methodology with sliding mode observer are used for the purpose of control. The beam structures are restricted to circumferentially asymmetric lay-up construction and the influence of ply angle, flight speed, and external excitations on the response and its active control are specifically investigated. A number of conclusions are outlined at the end.

Na, Sungsoo; Song, Ji-Seok; Choo, Jeong-Hwan; Qin, Zhanming

2011-10-01

355

Controllable outrigger damping system for high rise building with MR dampers  

NASA Astrophysics Data System (ADS)

A novel energy dissipation system that can achieve the amplified damping ratio for a frame-core tube structures is explored, where vertical dampers are equipped between the outrigger and perimeter columns. The modal characteristics of the structural system with linear viscous dampers are theoretically analyzed from the simplified finite element model by parametric analysis. The result shows that modal damping ratios of the first several modes can increase a lot with this novel damping system. To improve the control performance of system, the semi-active control devices, magnetorheological (MR) dampers, are adopted to develop a controllable outrigger damping system. The clipped optimal control with the linear-quadratic Gaussian (LQG) acceleration feedback is adopted in this paper. The effectiveness of both passive and semi-active control outrigger damping systems is evaluated through the numerical simulation of a representative tall building subjected to two typical earthquake records.

Wang, Zhihao; Chang, Chia-Ming; Spencer, Billie F., Jr.; Chen, Zhengqing

2010-04-01

356

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

PubMed

We present a framework for image segmentation based on quadratic programming, i.e., by minimization of a quadratic regularized energy linearly constrained. In particular, we present a new variational derivation of the quadratic Markov measure field (QMMF) models, which can be understood as a procedure for regularizing model preferences (memberships or likelihoods). We also present efficient optimization algorithms. In the QMMFs, the uncertainty in the computed regularized probability measure field is controlled by penalizing Gini's coefficient, and hence, it affects the convexity of the quadratic programming problem. The convex case is reduced to the solution of a positive definite linear system, and for that case, an efficient Gauss-Seidel (GS) scheme is presented. On the other hand, we present an efficient projected GS with subspace minimization for optimizing the nonconvex case. We demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two-class segmentation, as well as the simultaneous estimation of segmentation and (parametric and nonparametric) generative models. We present extensions to the original formulation for including color and texture clues, as well as imprecise user scribbles in an interactive framework. PMID:21926023

Rivera, Mariano; Dalmau, Oscar

2012-03-01

357

Mammogram enhancement using alpha weighted quadratic filter.  

PubMed

Mammograms are widely used to detect breast cancer in women. The quality of the image may suffer from poor resolution or low contrast due to the limitations of the X-ray hardware systems. Image enhancement is a powerful tool to improve the visual quality of mammograms. This paper introduces a new powerful nonlinear filter called the alpha weighted quadratic filter for mammogram enhancement. The user has the flexibility to design the filter by selecting all of the parameters manually or using an existing quantitative measure to select the optimal enhancement parameters. Computer simulations show that excellent enhancement results can be obtained with no apriori knowledge of the mammogram contents. The filter can also be used for automatic segmentation. PMID:19965002

Zhou, Yicong; Panetta, Karen; Agaian, Sos

2009-01-01

358

Linear stability analysis of dynamical quadratic gravity  

NASA Astrophysics Data System (ADS)

We study the linear stability of dynamical, quadratic gravity, focusing on two particular subclasses (the even-parity sector, exemplified by Einstein-Dilaton-Gauss-Bonnet gravity, and the odd-parity sector, exemplified by dynamical Chern-Simons modified gravity) in the high-frequency, geometric optics approximation. This analysis is carried out by studying gravitational and scalar modes propagating on spherically symmetric and axially symmetric, vacuum solutions of the theory and finding the associated dispersion relations. These relations are solved in two separate cases (the scalar regime and the gravitational wave regime, defined by requiring the ratio of the amplitude of the perturbations to be much greater or smaller than unity) and found in both cases to not lead to exponential growth of the propagating modes, suggesting linearly stability. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.

Ayzenberg, Dimitry; Yagi, Kent; Yunes, Nicolás

2014-02-01

359

Quadratic quantum cosmology with Schutz' perfect fluid  

NASA Astrophysics Data System (ADS)

We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the f(R) gravity. Using Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wavefunction of the universe. In the case of f(R) = R2 (pure quadratic model), for some particular choices of the perfect fluid source, exact solutions to the SWD equation can be obtained and the corresponding results are compared to the usual f(R) = R model.

Vakili, Babak

2010-01-01

360

A general formulation for the efficient evaluation of n-electron integrals over products of Gaussian charge distributions with Gaussian geminal functions  

NASA Astrophysics Data System (ADS)

In this work, we present a general formulation for the evaluation of many-electron integrals which arise when traditional one particle expansions are augmented with explicitly correlated Gaussian geminal functions. The integrand is expressed as a product of charge distributions, one for each electron, multiplied by one or more Gaussian geminal factors. Our formulation begins by focusing on the quadratic form that arises in the general n-electron integral. Using the Rys polynomial method for the evaluation of potential energy integrals, we derive a general formula for the evaluation of any n-electron integral. This general expression contains four parameters ?, ?, v, and h, which can be evaluated by an examination of the general quadratic form. Our analysis contains general expressions for any n-electron integral over s-type functions as well as the recursion needed to build up arbitrary angular momentum. The general recursion relation requires at most n + 1 terms for any n-electron integral. To illustrate the general method, we develop explicit expressions for the evaluation of two, three, and four particle electron repulsion integrals as well as two and three particle overlap and nuclear attraction integrals. We conclude our exposition with a discussion of a preliminary computational implementation as well as general computational requirements. Implementation on parallel computers is briefly discussed.

Komornicki, Andrew; King, Harry F.

2011-06-01

361

Geometric Phases, Squeezed Quantum States and Gaussian Wave Packet States of Relic Gravitons  

NASA Astrophysics Data System (ADS)

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.

Bakke, K.; Pedrosa, I. A.; Furtado, C.

362

Simple formula for a Gaussian beam with general astigmatism in a homogeneous medium  

NASA Astrophysics Data System (ADS)

A simple analytical formula that describes the evolution of a Gaussian beam with general astigmatism in a homogeneous medium is obtained. The quadratic form matrix, which determines the transverse distribution of the field in the beam for an arbitrary value of the longitudinal coordinate, is represented in the form of a linear combination of such matrix in a certain initial cross section and a unit matrix. The coefficients of the linear combination are complex-valued and are expressed via the longitudinal coordinate of the considered cross section, the refractive index of the medium, and the determinant and the trace of the initial matrix.

Plachenov, A. B.; Kudashov, V. N.; Radin, A. M.

2009-06-01

363

Analytically reduced form of multicenter integrals from Gaussian transforms. [in atomic and molecular physics  

NASA Technical Reports Server (NTRS)

The four-dimensional Fourier-Feynman transformations previously used in analytically reducing the general class of integrals containing multicenter products of 1s hydrogenic orbitals, Coulomb or Yukawa potentials, and plane waves, are replaced by the one-dimensional Gaussian transformation. This reduces the previously required double-diagonalization of the quadratic form of the multicenter integrals to only one diagonalization, yielding a simpler reduced form of the integral. The present work also extends the result to include all s states and pairs of states with l not equal to zero summed over the m quantum number.

Straton, Jack C.

1989-01-01

364

Second-order spectra for quadratic nonlinear systems by Volterra functional series: Analytical description and numerical simulation  

NASA Astrophysics Data System (ADS)

Higher-order spectral analysis techniques are often used to identify nonlinearities in complex dynamical systems. More specifically, the auto- and cross-bispectrum have proven to be useful tools in testing for the presence of quadratic nonlinearities based on knowledge of a system's input and output. In this paper, analytical expressions for the auto- and cross-bispectrum are developed using a Volterra functional approach under the assumption of a zero-mean, stationary Gaussian input; proper simplifications are presented when the whiteness of the input signal is also imposed. These formulae show the contributions of the bispectrum in terms of the system frequency response function and elementary physical properties of the system. Simulations based on a stochastic numerical integration technique accompany the analytical solutions for a mechanical mass-spring-damper system possessing quadratic damping and stiffness coefficients and subjected to Gaussian white noise excitation. Subsequent estimates of the bispectrum based on the simulated signals show excellent agreement with theory. These results show how modes may interact nonlinearly producing intermodulation components at the sum and/or difference frequency of the fundamental modes of oscillation. The presence and extent of nonlinear interactions between frequency components are identified. Advantages of using higher-order spectra techniques will be revealed and pertinent conclusions will be outlined.

Marzocca, P.; Nichols, J. M.; Milanese, A.; Seaver, M.; Trickey, S. T.

2008-11-01

365

Nonlinear clustering in models with primordial non-Gaussianity: The halo model approach  

SciTech Connect

We develop the halo model of large-scale structure as an accurate tool for probing primordial non-Gaussianity. In this study we focus on understanding the matter clustering at several redshifts in the context of primordial non-Gaussianity that is a quadratic correction to the local Gaussian potential, characterized by the parameter f{sub NL}. In our formulation of the halo model we pay special attention to the effect of halo exclusion and show that this can potentially solve the long-standing problem of excess power on large scales in this model. The halo model depends on the mass function, clustering of halo centers, and the density profiles. We test these ingredients using a large ensemble of high-resolution Gaussian and non-Gaussian numerical simulations, covering f{sub NL}={l_brace}0,+100,-100{r_brace}. In particular, we provide a first exploration of how halo density profiles change in the presence of primordial non-Gaussianity. We find that for f{sub NL} positive (negative) high-mass haloes have an increased (decreased) core density, so being more (less) concentrated than in the Gaussian case. We also examine the halo bias and show that, if the halo model is correct, then there is a small asymmetry in the scale dependence of the bias on very large scales, which arises because the Gaussian bias must be renormalized. We show that the matter power spectrum is modified by {approx}2.5% and {approx}3.5% on scales k{approx}1.0 h Mpc{sup -1} at z=0 and z=1, respectively. Our halo model calculation reproduces the absolute amplitude to within < or approx. 10% and the ratio of non-Gaussian to Gaussian spectra to within < or approx. 1%. We also measure the matter correlation function and find similarly good levels of agreement between the halo model and the data. We anticipate that this modeling will be useful for constraining f{sub NL} from measurements of the shear correlation function in future weak lensing surveys such as Euclid.

Smith, Robert E. [Institute for Theoretical Physics, University of Zurich, Zurich CH 8037 (Switzerland); Argelander-Institute for Astronomy, Auf dem Huegel 71, D-53121 Bonn (Germany); Desjacques, Vincent [Institute for Theoretical Physics, University of Zurich, Zurich CH 8037 (Switzerland); Marian, Laura [Argelander-Institute for Astronomy, Auf dem Huegel 71, D-53121 Bonn (Germany)

2011-02-15

366

Some Paradoxical Results for the Quadratically Weighted Kappa  

ERIC Educational Resources Information Center

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

Warrens, Matthijs J.

2012-01-01

367

CLOSURES OF QUADRATIC MODULES JAKA CIMPRIC, MURRAY MARSHALL, TIM NETZER  

E-print Network

CLOSURES OF QUADRATIC MODULES JAKA CIMPRIC, MURRAY MARSHALL, TIM NETZER Abstract. We consider the problem of determining the closure M of a quadratic module M in a commutative R-algebra with respect]. The closure of a semiordering is also considered, and it is shown that the space YM consisting of all

Marshall, Murray

368

Estimating species richness from quadrat sampling data: a general approach  

E-print Network

as the asymptote of a cumulative species-area curve). This approach is thus not appropriate to dealEstimating species richness from quadrat sampling data: a general approach J´er^ome Dupuis IMT of species (denoted by S) of a biological community located in a region composed of n quadrats. To address

Paris-Sud XI, Université de

369

Statistical Mechanics of Linear Systems & Quadratic Path Integrals  

E-print Network

Homework 5 Optional Statistical Mechanics of Linear Systems & Quadratic Path Integrals 1. Examine(r) = k 2 x2 . It also represents the imaginary time path integral of an electron in a quadratic potential constraints, the system is free to fluctuate at temperature T. So you can define the partition function with x

Deutsch, Josh

370

1 Statistical Mechanics of Linear Systems and Quadratic Path Integrals  

E-print Network

Homework 6 Due 6/4/08 1 Statistical Mechanics of Linear Systems and Quadratic Path Integrals 1 potential v(r) = k 2 x2 . It also represents the imaginary time path integral of an electron in a quadratic these two constraints, the system is free to fluctuate at temperature T. So you can define the partition

Deutsch, Josh

371

Weaving a Parabola Web with the Quadratic Transformer  

NSDL National Science Digital Library

Investigate how the graph of a quadratic function and its symbolic expression relate to each other. Start with a set of four graphs, which we?ll call a Parabola Web. Experiment with manipulating them with transformations such as shifting and reflection. Learn about quadratic equations in vertex and root form, and explore how changing these equations affect the graphs.

2012-07-19

372

Sketching the General Quadratic Equation Using Dynamic Geometry Software  

ERIC Educational Resources Information Center

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

Stols, G. H.

2005-01-01

373

Effects of Classroom Instruction on Students' Understanding of Quadratic Equations  

ERIC Educational Resources Information Center

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

Vaiyavutjamai, Pongchawee; Clements, M. A.

2006-01-01

374

Tangent Lines without Derivatives for Quadratic and Cubic Equations  

ERIC Educational Resources Information Center

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

Carroll, William J.

2009-01-01

375

Problems in Presenting Quadratics as a Unifying Topic.  

ERIC Educational Resources Information Center

A sequence for teaching quadratic equations is presented. Considered are: multiplying arithmetic binomials, multiplying algebraic polynomials, reversing the process, missing terms, perfect squares, other special forms and diagrams, quadratic equations, completing the square, systematizing the process, the general form, graphing equations, and…

MacDonald, Theodore H.

1986-01-01

376

THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR DIVERSITY: JOURNAL ARTICLE  

EPA Science Inventory

NRMRL-ADA- 98217 Jorgensen*, E.E., and Tunnell, S.J. The Effectiveness of Quadrats for Measuring Vascular Diversity. The Texas Journal of Science 53 (4):365-368 (2001). EPA/600/J-02/027. Quadrats are widely used for measuring characterist...

377

RQL: global placement via relaxed quadratic spreading and linearization  

Microsoft Academic Search

This paper describes a simple and effective quadratic placement algorithm called RQL. We show that a good quadratic placement, followed by local wirelength-driven spreading can produce excellent results on large-scale industrial ASIC designs. As opposed to the current top performing academic placers [4, 7, 11], RQL does not embed a linearization technique within the solver. Instead, it only requires a

Natarajan Viswanathan; Gi-Joon Nam; Charles J. Alpert; Paul Villarrubia; Haoxing Ren; Chris Chu

2007-01-01

378

RQL: Global Placement via Relaxed Quadratic Spreading and Linearization  

E-print Network

RQL: Global Placement via Relaxed Quadratic Spreading and Linearization Natarajan Viswanathan 1}@iastate.edu ABSTRACT This paper describes a simple and effective quadratic place- ment algorithm called RQL. We show,7,11], RQL does not embed a linearization tech- nique within the solver. Instead, it only requires a simpler

Chu, Chris C.-N.

379

AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS  

NASA Technical Reports Server (NTRS)

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.

Lehtinen, B.

1994-01-01

380

Statistically linearized optimal control of an electromagnetic vibratory energy harvester  

NASA Astrophysics Data System (ADS)

In this paper, an extension of linear-quadratic-Gaussian (LQG) control theory is used to determine the optimal state feedback controller for a vibratory energy harvesting system with Coulomb friction. Specifically, the energy harvester is a base-excited single-degree-of-freedom (SDOF) resonant oscillator with an electromagnetic transducer attached between the base and the moving mass. The development of the optimal controller for this system is based on statistical linearization, whereby the Coulomb friction force is replaced by an equivalent linear viscous damping term, which is calculated from the stationary covariance of the closed-loop system. It is shown that the covariance matrix and optimal feedback gain matrix can be computed by implementing an iterative algorithm involving linear matrix inequalities (LMIs). Furthermore, this theory is augmented to account for a non-quadratic dissipation in the electronics used to control the energy conversion. Simulation results are presented for the SDOF energy harvester in which the performance of the optimal state feedback control law is compared to the performance of the optimal static admittance over a range of disturbance bandwidths.

Cassidy, Ian L.; Scruggs, Jeffrey T.

2012-08-01

381

Phase-only shaping algorithm for Gaussian-apodized Bessel beams.  

PubMed

Gaussian-apodized Bessel beams can be used to create a Bessel-like axial line focus at a distance from the focusing lens. For many applications it is desirable to create an axial intensity profile that is uniform along the Bessel zone. In this article, we show that this can be accomplished through phase-only shaping of the wavefront in the far field where the beam has an annular ring structure with a Gaussian cross section. We use a one-dimensional transform to map the radial input field to the axial Bessel field and then optimized the axial intensity with a Gerchberg-Saxton algorithm. By separating out the quadratic portion of the shaping phase the algorithm converges more rapidly. PMID:23842364

Durfee, Charles G; Gemmer, John; Moloney, Jerome V

2013-07-01

382

Quadratic algebras for three-dimensional superintegrable systems  

SciTech Connect

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

Daskaloyannis, C., E-mail: daskalo@math.auth.gr; Tanoudis, Y. [Aristotle University of Thessaloniki, Mathematics Department (Greece)

2010-02-15

383

Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints  

NASA Technical Reports Server (NTRS)

Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

Juang, J.-N.; Turner, J. D.; Chun, H. M.

1984-01-01

384

Non-Gaussianity in the cosmic microwave background induced by dipolar dark matter  

NASA Astrophysics Data System (ADS)

In previous work [L. Blanchet and A. Le Tiec, Phys. Rev. D 80 (2009) 023524], motivated by the phenomenology of dark matter at galactic scales, a model of dipolar dark matter (DDM) was introduced. At linear order in cosmological perturbations, the dynamics of the DDM was shown to be identical to that of standard cold dark matter (CDM). In this paper, the DDM model is investigated at second order in cosmological perturbation theory. We find that the internal energy of the DDM fluid modifies the curvature perturbation generated by CDM with a term quadratic in the dipole field. This correction induces a new type of non-Gaussianity in the bispectrum of the curvature perturbation with respect to standard CDM. Leaving unspecified the primordial amplitude of the dipole field, which could in principle be determined by a more fundamental description of DDM, we find that, in contrast with usual models of primordial non-Gaussianities, the non-Gaussianity induced by DDM increases with time after the radiation-matter equality on super-Hubble scales. This distinctive feature of the DDM model, as compared with standard CDM, could thus provide a specific signature in the CMB and large-scale structure probes of non-Gaussianity.

Blanchet, Luc; Langlois, David; Le Tiec, Alexandre; Marsat, Sylvain

2013-02-01

385

Gaussianity of LISA's confusion backgrounds  

SciTech Connect

Data analysis for the proposed Laser Interferometer Space Antenna (LISA) will be complicated by the huge number of sources in the LISA band. In the frequency band {approx}10{sup -4}-2x10{sup -3} Hz, galactic white dwarf binaries (GWDBs) are sufficiently dense in frequency space that it will be impossible to resolve most of them, and ''confusion noise'' from the unresolved Galactic binaries will dominate over instrumental noise in determining LISA's sensitivity to other sources in that band. Confusion noise from unresolved extreme-mass-ratio inspirals (EMRIs) could also contribute significantly to LISA's total noise curve. To date, estimates of the effect of LISA's confusion noise on matched-filter searches and their detection thresholds have generally approximated the noise as Gaussian, based on the central limit theorem. However in matched-filter searches, the appropriate detection threshold for a given class of signals may be located rather far out on the tail of the signal-to-noise probability distribution, where a priori it is unclear whether the Gaussian approximation is reliable. Using the Edgeworth expansion and the theory of large deviations, we investigate the probability distribution of the usual matched-filter detection statistic, far out on the tail of the distribution. We apply these tools to four somewhat idealized versions of LISA data searches: searches for EMRI signals buried in GWDB confusion noise, and searches for massive black hole binary signals buried in (i) GWDB noise, (ii) EMRI noise, and (iii) a sum of EMRI noise and Gaussian noise. Assuming reasonable short-distance cutoffs in the populations of confusion sources (since the very closest and hence strongest sources will be individually resolvable), modifications to the appropriate detection threshold, due to the non-Gaussianity of the confusion noise, turn out to be quite small for realistic cases. The smallness of the correction is partly due to the fact that these three types of sources evolve on quite different time scales, so no single background source closely resembles any search template. We also briefly discuss other types of LISA searches where the non-Gaussianity of LISA's confusion backgrounds could perhaps have a much greater impact on search reliability and efficacy.

Racine, Etienne [Department of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125 (United States); Cutler, Curt [Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109 (United States)

2007-12-15

386

Modelling geomagnetic reversals as a Gaussian Cox Process  

NASA Astrophysics Data System (ADS)

The mean rate of reversal of the geomagnetic field, as recorded in the Geomagnetic Polarity Time Scale (GPTS), has long been an object of study. The significance of the apparent long-term variations in the mean rate of reversals - including the occurrence of superchrons - has been debated, as has the possible origins of these variations in external control of the geodynamo (e.g. by the time-varying boundary conditions imposed by mantle convection). Here we model the long-term variations in the reversal rate nonparametrically, in terms of an inhomogeneous Poisson process. Specifically, we consider a Gaussian Cox process, a type of doubly-stochastic Poisson process where the mean rate (or intensity) is modelled in terms of a Gaussian process. Such processes are amenable to likelihood-based inference using Bayesian Markov Chain Monte-Carlo (MCMC) methods, which we employ to provide posterior distributions of the model parameters. The specification of a Gaussian process requires a covariance function, relating the intensity at nearby times; crucially, however, the timescale of the covariance function is not prescribed, but appears as a model hyperparameter, whose posterior distribution is an important output of the analysis. For the geodynamo, this hyperparameter should robustly characterise the timescale of long-term variations. Two different types of Gaussian Cox process are considered: a Log Gaussian Cox Process, applied to binned reversal data; and a Sigmoidal Gaussian Cox Process, applied to the discrete reversal data using a technique involving latent variables. Different MCMC algorithms for sampling the posterior distribution of the model parameters are investigated for both types of process, to check (and to optimise) the convergence of the MCMC chains. This analysis is applied to different records of the GPTS, including those of Cande & Kent (1995) and Gradstein & Ogg (1996). The implications of this analysis for the geodynamo, and the possibility of comparable analysis of the output of numerical geodynamo simulations, are discussed.

Sarson, Graeme; Boys, Richard; Golightly, Andrew; Henderson, Daniel

2013-04-01

387

Cooling and squeezing via quadratic optomechanical coupling  

SciTech Connect

We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is nonthermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.

Nunnenkamp, A.; Boerkje, K.; Harris, J. G. E.; Girvin, S. M. [Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520 (United States)

2010-08-15

388

On the optimum ride control of a stochastic model of a tractor-semitrailer vehicle  

NASA Astrophysics Data System (ADS)

A systematic approach based on stochastic optimal control and estimation theories for the optimal design of active suspension systems for a tractor-semitrailer vehicle is presented. The vehicle-road system dynamics combined with the human perception of random vibrations are cast in the standard linear quadratic Gaussian format. The time delays of the stochastic excitation process of the multi-axled vehicle are represented by a first order Padé approximation. The optimal controller/observer is derived which minimizes the mean-squared values of performance variables reflecting the human comfort, cargo safety, suspension working space, roadholding ability and control forces. The advantages of optimally controlled suspension systems over their passive counterparts are indicated.

ElMadany, M. M.; Samaha, M. E.

1992-07-01

389

LQG controller design using GUI: application to antennas and radio-telescopes  

PubMed

The Linear Quadratic Gaussian (LQG) algorithm has been used to control the JPL's beam wave-guide, and 70-m antennas. This algorithm significantly improves tracking precision in a wind disturbed environment. Based on this algorithm and the implementation experience a Matlab based Graphical User Interface (GUI) was developed to design the LQG controllers applicable to antennas and radiotelescopes. The GUI is described in this paper. It consists of two parts the basic LQG design and the fine-tuning of the basic design using a constrained optimization algorithm. The presented GUI was developed to simplify the design process, to make the design process user-friendly, and to enable design of an LQG controller for one with a limited control engineering background. The user is asked to manipulate the GUI sliders and radio buttons to watch the antenna performance. Simple rules are given at the GUI display. PMID:10871218

Maneri; Gawronski

2000-01-01

390

Optofluidic generation of Laguerre-Gaussian beams  

PubMed Central

Laguerre-Gaussian (LG) beams have been extensively studied due to their unique structure, characterized by a phase singularity at the center of the beam. Common methods for generating such beams include the use of diffractive optical elements and spatial light modulators, which although offering excellent versatility, suffers from several drawbacks, including in many cases a low power damage threshold as well as complexity and expense. This paper presents a simple, low cost method for the generation of high-fidelity LG beams using rapid prototyping techniques. Our approach is based on a fluidic-hologram concept, whereby the properties of the LG beam can be finely controlled by varying the refractive-index of the fluid that flows through the hologram. This simple approach, while optimized here for LG beam generation, is also expected to find applications in the production of tunable fluidic optical trains. PMID:19907539

Jeffries, Gavin D. M.; Milne, Graham; Zhao, Yiqiong; Lopez-Mariscal, Carlos; Chiu, Daniel T.

2010-01-01

391

Control and monitoring of sheet and film forming processes  

NASA Astrophysics Data System (ADS)

Sheet and film forming processes refer to a set of processes that have a 2-dimensional sheet or film as their output. They are typically characterized by a scanning sensor which moves between the edges of the sheet in a periodic manner. This work is concerned with control and monitoring of such processes. There are three main contributions in this study. The first and foremost contribution is the reformulation of the Linear Quadratic Gaussian (LQG) objective function to give one the ability to trade-off between control over either dimension of the sheet. The second contribution is a method to derive the LQG trade-off surface between output variability in either dimension and input variance. The third contribution is a set of data driven techniques for performance assessment of these processes. Simulation results using the model used by Bergh and MacGregor (1987) are provided to support the proposed methods.

Ramarathnam, Jaganath

392

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems  

NASA Technical Reports Server (NTRS)

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

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

1986-01-01

393

Robust multivariable controller design for flexible spacecraft  

NASA Technical Reports Server (NTRS)

Large, flexible spacecraft are typically characterized by a large number of significant elastic modes with very small inherent damping, low, closely spaced natural frequencies, and the lack of accurate knowledge of the structural parameters. Summarized here is some recent research on the design of robust controllers for such spacecraft, which will maintain stability, and possible performance, despite these problems. Two types of controllers are considered, the first being the linear-quadratic-Gaussian-(LQG)-type. The second type utilizes output feedback using collocated sensors and actuators. The problem of designing robust LQG-type controllers using the frequency domain loop transfer recovery (LTR) method is considered, and the method is applied to a large antenna model. Analytical results regarding the regions of stability for LQG-type controllers in the presence of actuator nonlinearities are also presented. The results obtained for the large antenna indicate that the LQG/LTR method is a promising approach for control system design for flexible spacecraft. For the second type of controllers (collocated controllers), it is proved that the stability is maintained in the presence of certain commonly encountered nonlinearities and first-order actuator dynamics. These results indicate that collocated controllers are good candidates for robust control in situations where model errors are large.

Joshi, Suresh M.; Armstrong, Ernest S.

1986-01-01

394

Multivariable control of vapor compression systems  

SciTech Connect

This paper presents the results of a study of multi-input multi-output (MIMO) control of vapor compression cycles that have multiple actuators and sensors for regulating multiple outputs, e.g., superheat and evaporating temperature. The conventional single-input single-output (SISO) control was shown to have very limited performance. A low order lumped-parameter model was developed to describe the significant dynamics of vapor compression cycles. Dynamic modes were analyzed based on the low order model to provide physical insight of system dynamic behavior. To synthesize a MIMO control system, the Linear-Quadratic Gaussian (LQG) technique was applied to coordinate compressor speed and expansion valve opening with guaranteed stability robustness in the design. Furthermore, to control a vapor compression cycle over a wide range of operating conditions where system nonlinearities become evident, a gain scheduling scheme was used so that the MIMO controller could adapt to changing operating conditions. Both analytical studies and experimental tests showed that the MIMO control could significantly improve the transient behavior of vapor compression cycles compared to the conventional SISO control scheme. The MIMO control proposed in this paper could be extended to the control of vapor compression cycles in a variety of HVAC and refrigeration applications to improve system performance and energy efficiency.

He, X.D.; Liu, S.; Asada, H.H.; Itoh, Hiroyuki

1999-07-01

395

Shock Wave Admissibility for Quadratic Conservation Laws  

NASA Astrophysics Data System (ADS)

In this work we present a new approach to the study of the stability of admissible shock wave solutions for systems of conservation laws that change type. The systems we treat have quadratic flux functions. We employ the fundamental wave manifold W as a global framework to characterize shock waves that comply with the viscosity admissibility criterion. Points of W parametrize dynamical systems associated with shock wave solutions. The region of W comprising admissible shock waves is bounded by the loci of structurally unstable dynamical systems. Explicit formulae are presented for the loci associated with saddle-node, Hopf, and Bogdanov-Takens bifurcation, and with straight-line heteroclinic connections. Using Melnikov's integral analysis, we calculate the tangent to the homoclinic part of the admissibility boundary at Bogdanov-Takens points of W. Furthermore, using numerical methods, we explore the heteroclinic loci corresponding to curved connecting orbits and the complete homoclinic locus. We find the region of admissible waves for a generic, two-dimensional slice of the fundamental wave manifold, and compare it with the set of shock points that comply with the Lax admissibility criterion, thereby elucidating how this criterion differs from viscous profile admissibility.

Canic, S.; Plohr, B. J.

396

Regular black holes in quadratic gravity  

NASA Astrophysics Data System (ADS)

The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ayón-Beato and Garcí a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration.

Berej, Waldemar; Matyjasek, Jerzy; Tryniecki, Dariusz; Woronowicz, Mariusz

2006-05-01

397

Models for the 3D singular isotropic oscillator quadratic algebra  

SciTech Connect

We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential-differential or differential-difference and difference-difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.

Kalnins, E. G., E-mail: math0236@waikato.ac.n [University of Waikato, Department of Mathematics (New Zealand); Miller, W.; Post, S. [University of Minnesota, School of Mathematics (United States)

2010-02-15

398

Displacement measurement on specimens subjected to non-Gaussian random vibrations in fatigue life tests  

NASA Astrophysics Data System (ADS)

High-cycle fatigue life tests conducted using controlled random vibrations are commonly used to evaluate failure in components and structures. In most cases, a Gaussian distribution of both the input vibration and the stress response is assumed, while real-life loads may be non-Gaussian causing the response to be non-Gaussian as well. Generating non-Gaussian drive signals with high kurtosis and a given power spectral density, however, does not always guarantee that the stress response will actually be non-Gaussian, because this depends on the adherence of the tested system to the Central Limit Theorem. On the other side, suitable measurement methods need to be developed in order to estimate the stress amplitude response at critical failure locations, and therefore to evaluate and select input loads. In this paper, a simple test rig with a notched cantilevered specimen was developed to measure the response and examine the kurtosis values in the case of stationary Gaussian, stationary non-Gaussian, and non-stationary non-Gaussian excitation signals. The Laser Doppler Vibrometry (LDV) technique was used for the first time in this type of test, to estimate the specimen stress amplitude response in terms of differential displacement at the notch section ends. A method based on the use of accelerometers to correct for the occasional signal drops occurring during the experiment is described and the results are discussed with respect to the ability of the test procedure to evaluate the output signal.

Troncossi, M.; Di Sante, R.; Rivola, A.

2014-05-01

399

Gaussian mass optimization for kernel PCA parameters  

NASA Astrophysics Data System (ADS)

This paper proposes a novel kernel parameter optimization method based on Gaussian mass, which aims to overcome the current brute force parameter optimization method in a heuristic way. Generally speaking, the choice of kernel parameter should be tightly related to the target objects while the variance between the samples, the most commonly used kernel parameter, doesn't possess much features of the target, which gives birth to Gaussian mass. Gaussian mass defined in this paper has the property of the invariance of rotation and translation and is capable of depicting the edge, topology and shape information. Simulation results show that Gaussian mass leads a promising heuristic optimization boost up for kernel method. In MNIST handwriting database, the recognition rate improves by 1.6% compared with common kernel method without Gaussian mass optimization. Several promising other directions which Gaussian mass might help are also proposed at the end of the paper.

Liu, Yong; Wang, Zulin

2011-10-01

400

Generation of Gaussian Density Fields  

E-print Network

This document describes analytical and numerical techniques for the generation of Gaussian density fields, which represent cosmological density perturbations. The mathematical techniques involved in the generation of density harmonics in k-space, the filtering of the density fields, and the normalization of the power spectrum to the measured temperature fluctuations of the Cosmic Microwave Background, are presented in details. These techniques are well-known amongst experts, but the current literature lacks a formal description. I hope that this technical report will prove useful to new researchers moving into this field, sparing them the task of reinventing the wheel.

Hugo Martel

2005-07-15

401

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

NASA Technical Reports Server (NTRS)

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.

Fleming, P.

1985-01-01

402

Integrated structural control design of large space structures  

SciTech Connect

Active control of structures has been under intensive development for the last ten years. Reference 2 reviews much of the identification and control technology for structural control developed during this time. The technology was initially focused on space structure and weapon applications; however, recently the technology is also being directed toward applications in manufacturing and transportation. Much of this technology focused on multiple-input/multiple-output (MIMO) identification and control methodology because many of the applications require a coordinated control involving multiple disturbances and control objectives where multiple actuators and sensors are necessary for high performance. There have been many optimal robust control methods developed for the design of MIMO robust control laws; however, there appears to be a significant gap between the theoretical development and experimental evaluation of control and identification methods to address structural control applications. Many methods have been developed for MIMO identification and control of structures, such as the Eigensystem Realization Algorithm (ERA), Q-Markov Covariance Equivalent Realization (Q-Markov COVER) for identification; and, Linear Quadratic Gaussian (LQG), Frequency Weighted LQG and H-/ii-synthesis methods for control. Upon implementation, many of the identification and control methods have shown limitations such as the excitation of unmodelled dynamics and sensitivity to system parameter variations. As a result, research on methods which address these problems have been conducted.

Allen, J.J.; Lauffer, J.P.

1995-01-01

403

Optimal PHP production of multiple part-types on a failure-prone machine with quadratic buffer costs  

Microsoft Academic Search

We consider a single, failure-prone machine, producing multiple part-types The objective is to minimize the expected sum of quadratic buffer costs. In general, the optimal solution to this problem is unknown. However, by restricting the allowable set of control policies to the class of prioritized hedging point (PHP) policies, we are able to determine simple, analytical expressions for the optimal

Chang Shu; James R. Perkins

2001-01-01

404

Monogamy inequality for distributed Gaussian entanglement  

E-print Network

We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.

Tohya Hiroshima; Gerardo Adesso; Fabrizio Illuminati

2006-11-08

405

Strongly scale-dependent non-Gaussianity  

SciTech Connect

We discuss models of primordial density perturbations where the non-Gaussianity is strongly scale dependent. In particular, the non-Gaussianity may have a sharp cutoff and be very suppressed on large cosmological scales, but sizable on small scales. This may have an impact on probes of non-Gaussianity in the large-scale structure and in the cosmic microwave background radiation anisotropies.

Riotto, Antonio [INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padua (Italy); CERN, PH-TH Division, CH-1211, Geneve 23 (Switzerland); Sloth, Martin S. [CERN, PH-TH Division, CH-1211, Geneve 23 (Switzerland)

2011-02-15

406

Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems  

NASA Astrophysics Data System (ADS)

This paper presents two new lemmas related to the Caputo fractional derivatives, when ? ?(0, 1 ] , for the case of general quadratic forms and for the case where the trace of the product of a rectangular matrix and its transpose appear. Those two lemmas allow using general quadratic Lyapunov functions and the trace of a matrix inside a Lyapunov function respectively, in order to apply the fractional-order extension of Lyapunov direct method, to analyze the stability of fractional order systems (FOS). Besides, the paper presents a theorem for proving uniform stability in the sense of Lyapunov for fractional order systems. The theorem can be seen as a complement of other methods already available in the literature. The two lemmas and the theorem are applied to the stability analysis of two Fractional Order Model Reference Adaptive Control (FOMRAC) schemes, in order to prove the usefulness of the results.

Duarte-Mermoud, Manuel A.; Aguila-Camacho, Norelys; Gallegos, Javier A.; Castro-Linares, Rafael

2015-05-01

407

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

NASA Technical Reports Server (NTRS)

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.

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

1990-01-01

408

A Parallel Quadratic Programming Method for Dynamic Optimization ...  

E-print Network

A Parallel Quadratic Programming Method for Dynamic. Optimization ..... finite number of disjoint active sets further induces a subdivision of the dual ? space: ..... Cholesky factorization, the latter only regularizes those diagonal elements for.

2013-11-29

409

Regular zeros of quadratic maps and their application  

SciTech Connect

Sufficient conditions for the existence of regular zeros of quadratic maps are obtained. Their applications are indicated to certain problems of analysis related to the inverse function theorem in a neighbourhood of an abnormal point. Bibliography: 13 titles.

Arutyunov, Aram V; Karamzin, Dmitry Yu

2011-06-30

410

Integrable Hamiltonian systems and interactions through quadratic constraints  

Microsoft Academic Search

On-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems.

K. Pohlmeyer

1976-01-01

411

Geometric Procedures for Graphing the General Quadratic Equation.  

ERIC Educational Resources Information Center

How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)

DeTemple, Duane W.

1984-01-01

412

AdS waves as exact solutions to quadratic gravity  

SciTech Connect

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

Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram [Department of Physics, Middle East Technical University, 06531 Ankara (Turkey); Guerses, Metin [Department of Mathematics, Faculty of Sciences Bilkent University, 06800 Ankara (Turkey)

2011-04-15

413

RQL: Global Placement via Relaxed Quadratic Spreading and Linearization  

Microsoft Academic Search

This paper describes a simple and effective quadratic place- ment algorithm called RQL. We show that a good quadratic placement, followed by local wirelength-driven spreading can produce excellent results on large-scale industrial ASIC de- signs. As opposed to the current top performing academic placers (4,7,11), RQL does not embed a linearization tech- nique within the solver. Instead, it only requires

Natarajan Viswanathan; Gi-joon Nam; Charles J. Alpert; Paul Villarrubia; Haoxing Ren; Chris C. N. Chu

2007-01-01

414

Fast algorithms for convex quadratic programming and multicommodity flows  

Microsoft Academic Search

In the first part of the paper, we extend Karmarkar's interior point method to give an algorithm for Convex Quadratic Programming which requires O(Na'~7(logL)(logN)L) arithmetic operations. At each iteration, Karmarkar's method locally minimizes the linear (convex) numerator of a transformed objective function in the transformed domain. However, in the case of Convex Quadratic Programming the numerator of the transformed objective

Sanjiv Kapoor; Pravin M. Vaidya

1986-01-01

415

Reliable fusion of control and sensing in intelligent machines. Thesis  

NASA Technical Reports Server (NTRS)

Although robotics research has produced a wealth of sophisticated control and sensing algorithms, very little research has been aimed at reliably combining these control and sensing strategies so that a specific task can be executed. To improve the reliability of robotic systems, analytic techniques are developed for calculating the probability that a particular combination of control and sensing algorithms will satisfy the required specifications. The probability can then be used to assess the reliability of the design. An entropy formulation is first used to quickly eliminate designs not capable of meeting the specifications. Next, a framework for analyzing reliability based on the first order second moment methods of structural engineering is proposed. To ensure performance over an interval of time, lower bounds on the reliability of meeting a set of quadratic specifications with a Gaussian discrete time invariant control system are derived. A case study analyzing visual positioning in robotic system is considered. The reliability of meeting timing and positioning specifications in the presence of camera pixel truncation, forward and inverse kinematic errors, and Gaussian joint measurement noise is determined. This information is used to select a visual sensing strategy, a kinematic algorithm, and a discrete compensator capable of accomplishing the desired task. Simulation results using PUMA 560 kinematic and dynamic characteristics are presented.

Mcinroy, John E.

1991-01-01

416

Analytic solution of flat-top Gaussian and Laguerre-Gaussian laser field components.  

PubMed

We generalized the nonparaxial field components of Laguerre-Gaussian and flattened Gaussian beams obtained using the angular spectrum method to include symmetric radial and angular expansions and simplified them using an approximate evaluation of the integral equations for the field components. These field components possess series expressions in orders of a natural expansion parameter, which clarifies the physical interpretation of the series expansion. A connection between Laguerre-Gaussian and flat-top Gaussian profiles is obtained. PMID:20967101

Cerjan, Alexander; Cerjan, Charles

2010-10-15

417

Information bounds for Gaussian copulas  

PubMed Central

Often of primary interest in the analysis of multivariate data are the copula parameters describing the dependence among the variables, rather than the univariate marginal distributions. Since the ranks of a multivariate dataset are invariant to changes in the univariate marginal distributions, rank-based estimators are natural candidates for semiparametric copula estimation. Asymptotic information bounds for such estimators can be obtained from an asymptotic analysis of the rank likelihood, i.e. the probability of the multivariate ranks. In this article, we obtain limiting normal distributions of the rank likelihood for Gaussian copula models. Our results cover models with structured correlation matrices, such as exchangeable or circular correlation models, as well as unstructured correlation matrices. For all Gaussian copula models, the limiting distribution of the rank likelihood ratio is shown to be equal to that of a parametric likelihood ratio for an appropriately chosen multivariate normal model. This implies that the semiparametric information bounds for rank-based estimators are the same as the information bounds for estimators based on the full data, and that the multivariate normal distributions are least favorable. PMID:25313292

Hoff, Peter D.; Niu, Xiaoyue; Wellner, Jon A.

2013-01-01

418

Refraction of a Gaussian Seaway  

E-print Network

Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations in average energy and wave action. These variations take the form of lumps or streaks, and they explicitly survive dispersion over wavelength and incoming wave propagation direction. Thus, the uniform sampling assumed in the venerable Longuet-Higgins theory does not apply following refraction by random currents. Proper handling of the non-uniform sampling results in greatly increased probability of freak wave formation. The present theory represents a synthesis of Longuet-Higgins Gaussian seas and the refraction model of White and Fornberg, which considered the effect of currents on a plane wave incident seaway. Using the linearized equations for deep ocean waves, we obtain quantitative predictions for the increased probability of freak wave formation when the refractive effects are taken into account. The crest height or wave height distribution depends primarily on the ``freak index", gamma, which measures the strength of refraction relative to the angular spread of the incoming sea. Dramatic effects are obtained in the tail of this distribution even for the modest values of the freak index that are expected to occur commonly in nature. Extensive comparisons are made between the analytical description and numerical simulations.

E. J. Heller; L. Kaplan; A. Dahlen

2008-01-04

419

A Comparison of Multivariable Control Design Techniques for a Turbofan Engine Control  

NASA Technical Reports Server (NTRS)

This paper compares two previously published design procedures for two different multivariable control design techniques for application to a linear engine model of a jet engine. The two multivariable control design techniques compared were the Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) and the H-Infinity synthesis. The two control design techniques were used with specific previously published design procedures to synthesize controls which would provide equivalent closed loop frequency response for the primary control loops while assuring adequate loop decoupling. The resulting controllers were then reduced in order to minimize the programming and data storage requirements for a typical implementation. The reduced order linear controllers designed by each method were combined with the linear model of an advanced turbofan engine and the system performance was evaluated for the continuous linear system. Included in the performance analysis are the resulting frequency and transient responses as well as actuator usage and rate capability for each design method. The controls were also analyzed for robustness with respect to structured uncertainties in the unmodeled system dynamics. The two controls were then compared for performance capability and hardware implementation issues.

Garg, Sanjay; Watts, Stephen R.

1995-01-01

420

A new adaptive control approach for aerospace vehicles with parameter uncertainties  

NASA Technical Reports Server (NTRS)

A new stochastic adaptive control structure is developed for the problem of combined parameter estimation and control of aerospace vehicles with changing parameters. Parameter uncertainties are modeled as first-order Gauss-Markov processes, and are introduced to the system dynamics through a small parameter. It is assumed that an accurate inertial measurement unit gives perfect measurements of the state variables. Since the stochastic system is assumed to be Gauss-Markov, the density function of the parameters given these measurements is conditionally Gaussian. Based on this conditionally Gaussian density, the problem of minimizing a quadratic cost over an infinite time horizon can be set up within the framework of stochastic optimal control theory. The optimal feedback control law is derived from a straightforward expansion of the Hamilton-Jacobi-Bellman equation, based on the LQG solution. The resulting nonlinear controller is applied to the pitch axis control of a space platform with uncertain moments of inertia and is shown to produce marked improvement over a fixed controller.

Hahn, Yungsun; Speyer, Jason L.

1989-01-01

421

A Numerical-Integration Perspective on Gaussian Filters  

Microsoft Academic Search

This paper proposes a numerical-integration perspective on the Gaussian filters. A Gaussian filter is approximation of the Bayesian inference with the Gaussian posterior probability density assumption being valid. There exists a variation of Gaussian filters in the literature that derived themselves from very different backgrounds. From the numerical-integration viewpoint, various versions of Gaussian filters are only distinctive from each other

Yuanxin Wu; Dewen Hu; Meiping Wu; Xiaoping Hu

2006-01-01

422

Control Law Synthesis for Vertical Fin Buffeting Alleviation Using Strain Actuation  

NASA Technical Reports Server (NTRS)

In the present investigation, the results obtained during the ground test of a closed-loop control system conducted on a full-scale fighter to attenuate vertical fin buffeting response using strain actuation are presented. Two groups of actuators consisting of piezoelectric elements distributed over the structure were designed to achieve authority over the first and second modes of the vertical fin. The control laws were synthesized using the Linear Quadratic Gaussian (LQG) method for a time-invariant control system. Three different pairs of sensors including strain gauges and accelerometers at different locations were used to close the feedback loop. The results demonstrated that measurable reductions in the root-mean-square (RMS) values of the fin dynamic response identified by the strain transducer at the critical point for fatigue at the root were achieved under the most severe buffet condition. For less severe buffet conditions, reductions of up to 58% were achieved.

Nitzsche, F.; Zimcik, D. G.; Ryall, T. G.; Moses, R. W.; Henderson, D. A.

1999-01-01

423

First on-sky SCAO validation of full LQG control with vibration mitigation on the CANARY pathfinder.  

PubMed

Adaptive optics provides real time correction of wavefront disturbances on ground based telescopes. Optimizing control and performance is a key issue for ever more demanding instruments on ever larger telescopes affected not only by atmospheric turbulence, but also by vibrations, windshake and tracking errors. Linear Quadratic Gaussian control achieves optimal correction when provided with a temporal model of the disturbance. We present in this paper the first on-sky results of a Kalman filter based LQG control with vibration mitigation on the CANARY instrument at the Nasmyth platform of the 4.2-m William Herschel Telescope. The results demonstrate a clear improvement of performance for full LQG compared with standard integrator control, and assess the additional improvement brought by vibration filtering with a tip-tilt model identified from on-sky data, thus validating the strategy retained on the instrument SPHERE at the VLT. PMID:25321824

Sivo, Gaetano; Kulcsár, Caroline; Conan, Jean-Marc; Raynaud, Henri-François; Gendron, Eric; Basden, Alastair; Vidal, Fabrice; Morris, Tim; Meimon, Serge; Petit, Cyril; Gratadour, Damien; Martin, Olivier; Hubert, Zoltan; Sevin, Arnaud; Perret, Denis; Chemla, Fanny; Rousset, Gérard; Dipper, Nigel; Talbot, Gordon; Younger, Eddy; Myers, Richard; Henry, David; Todd, Stephen; Atkinson, David; Dickson, Colin; Longmore, Andy

2014-09-22

424

Quantum Filtering and Optimal Control  

NASA Astrophysics Data System (ADS)

Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability case. Quantum theory of time continuous measurements and quantum filtering developed by VPB on the basis of semi-Markov independent increment models for quantum noise and quantum nondemolition (QND) observability is generalized for demolition indirect measurements of quantum unstable systems satisfying the microcausality principle. The reduced quantum feedback-controlled dynamics is described both by linear semi-Markov and nonlinear conditionally-Markov stochastic master equations. Using this scheme for diffusive and counting measurement to describe the stochastic evolution of the open quantum system under the continuous indirect observation and working in parallel with classical indeterministic control theory, we show the conditionally-Markov Bellman equations for optimal feedback control of the a posteriori stochastic quantum states conditioned upon these measurements. The resulting Bellman equation for the diffusive observation is then applied to the explicitly solvable quantum linear-quadratic-Gaussian (LQG) problem which emphasizes many similarities with the corresponding classical control problem.

Belavkin, Viacheslav P.; Edwards, Simon

2008-08-01

425

Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method  

NASA Astrophysics Data System (ADS)

By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.

Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

2014-11-01

426

A Balanced Model Reduction for TS Fuzzy Systems with Integral Quadratic Constraints  

Microsoft Academic Search

\\u000a This paper deals with a balanced model reduction for a class of nonlinear systems with integral quadratic constraints(IQC’s)\\u000a using a T-S(Takagi-Sugeno) fuzzy approach. We define a generalized controllability Gramian and a generalized observability\\u000a Gramian for a stable T-S fuzzy systems with IQC’s. We obtain a balanced state space realization using the generalized controllability\\u000a and observability Gramians and obtain a reduced

Seog-hwan Yoo; Byung-jae Choi

2005-01-01

427

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

NASA Technical Reports Server (NTRS)

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.

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

1989-01-01

428

Escape through an unstable limit cycle driven by multiplicative colored non-Gaussian and additive white Gaussian noises  

E-print Network

white Gaussian noises Bidhan Chandra Bag1, * and Chin-Kun Hu1,2, 1 Institute of Physics, Academia Sinica by multiplicative colored Gaussian and additive Gaussian white noises and found resonant activation RA behavior mentioned above driven by multiplicative colored Gaussian and addi- tive Gaussian white noises and found

429

Gaussian process emulation of dynamic computer codes  

E-print Network

Gaussian process emulation of dynamic computer codes By Stefano Conti, Centre for Health Economics simulators; Emulation; Gaussian process; Recursive modelling 1 Introduction Complex computer codes are used on emulation of the simulator's output has been developed that offers substantial efficiency gains over

Oakley, Jeremy

430

Distributed Kalman Filter via Gaussian Belief Propagation  

E-print Network

Distributed Kalman Filter via Gaussian Belief Propagation Danny Bickson IBM Haifa Research Lab interpretations. First, we show equivalence to computing one iteration of the Kalman filter. Second, we show that the Kalman filter is a special case of the Gaussian information bottleneck algorithm, when the weight

Dolev, Danny

431

Geostatistics for Power Models of Gaussian Fields  

Microsoft Academic Search

This paper introduces geostatistical approaches (i.e., kriging estimation and simulation) for a group of non-Gaussian random fields that are power algebraic transformations of Gaussian and lognormal random fields. These are power random fields (PRFs) that allow the construction of stochastic polynomial series. They were derived from the exponential random field, which is expressed as Taylor series expansion with PRF terms.

J. A. Vargas-Guzmán

2004-01-01

432

Quadratic 0-1 programming: Geometric methods and duality analysis  

NASA Astrophysics Data System (ADS)

The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems.

Liu, Chunli

433

On Gaussian Beams Described by Jacobi's Equation  

E-print Network

Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the \\v{C}erven\\'y equations for the amplitude and phase of Gaussian beams is developed by applying the equivalence of Hamilton-Jacobi theory with Jacobi's equation that connects Riemannian curvature to geodesic flow. Thus the paper makes a fundamental connection between Gaussian beams and an acoustic channel's so-called intrinsic Gaussian curvature from differential geometry. (2) A new formula $\\pi(c/c")^{1/2}$ for the distance between convergence zones is derived and applied to several well-known profiles. (3) A class of "model spaces" are introduced that connect the acoustics of ducting/divergence zones with the channel's Gaussian curvature $K=cc"-(c')^2$. The "model" SSPs yield constant Gaussian curvature in which the geometry of ducts corresponds to great circles on a sphere and convergence zones correspond to antipodes. The distance between caustics $\\pi(c/c")^{1/2}$ is equated with an ideal hyperbolic cosine SSP duct. (4) An "intrinsic" version of \\v{C}erven\\'y's formulae for the amplitude and phase of Gaussian beams is derived that does not depend on an "extrinsic" arbitrary choice of coordinates such as range and depth. Direct comparisons are made between the computational frameworks used by the three different approaches to Gaussian beams: Snell's law, the extrinsic Frenet-Serret formulae, and the intrinsic Jacobi methods presented here. The relationship of Gaussian beams to Riemannian curvature is explained with an overview of the modern covariant geometric methods that provide a general framework for application to other special cases.

Steven Thomas Smith

2014-04-18

434

Energy management of a power-split plug-in hybrid electric vehicle based on genetic algorithm and quadratic programming  

NASA Astrophysics Data System (ADS)

This paper introduces an online and intelligent energy management controller to improve the fuel economy of a power-split plug-in hybrid electric vehicle (PHEV). Based on analytic analysis between fuel-rate and battery current at different driveline power and vehicle speed, quadratic equations are applied to simulate the relationship between battery current and vehicle fuel-rate. The power threshold at which engine is turned on is optimized by genetic algorithm (GA) based on vehicle fuel-rate, battery state of charge (SOC) and driveline power demand. The optimal battery current when the engine is on is calculated using quadratic programming (QP) method. The proposed algorithm can control the battery current effectively, which makes the engine work more efficiently and thus reduce the fuel-consumption. Moreover, the controller is still applicable when the battery is unhealthy. Numerical simulations validated the feasibility of the proposed controller.

Chen, Zheng; Mi, Chris Chunting; Xiong, Rui; Xu, Jun; You, Chenwen

2014-02-01

435

Primordial black holes as a tool for constraining non-Gaussianity  

NASA Astrophysics Data System (ADS)

Primordial black holes (PBHs) can form in the early Universe from the collapse of large density fluctuations. Tight observational limits on their abundance constrain the amplitude of the primordial fluctuations on very small scales which cannot otherwise be constrained, with PBHs only forming from the extremely rare large fluctuations. The number of PBHs formed is therefore sensitive to small changes in the shape of the tail of the fluctuation distribution, which itself depends on the amount of non-Gaussianity present. We study, for the first time, how quadratic and cubic local non-Gaussianity of arbitrary size (parametrized by fNL and gNL respectively) affects the PBH abundance and the resulting constraints on the amplitude of the fluctuations on very small scales. Intriguingly we find that even nonlinearity parameters of order unity have a significant impact on the PBH abundance. The sign of the non-Gaussianity is particularly important, with the constraint on the allowed fluctuation amplitude tightening by an order of magnitude as fNL changes from just -0.5 to 0.5. We find that if PBHs are observed in the future, then regardless of the amplitude of the fluctuations, non-negligible negative fNL would be ruled out. Finally we show that gNL can have an even larger effect on the number of PBHs formed than fNL.

Byrnes, Christian T.; Copeland, Edmund J.; Green, Anne M.

2012-08-01

436

Optimal output feedback vibration control of rotor-bearing systems  

NASA Astrophysics Data System (ADS)

A procedure for the lateral vibration control of general high-order asymmetric discrete rotor-bearing systems is presented. It is found that the complex mode and balanced realization methods can be successively applied to a general linear high-order asymmetric system to obtain a further reduced-order model without loss of model accuracy. However, the balanced realization method, by itself, is not a good choice for such systems. The matrix transformations between the original high-order system and the reduced-order system are derived for the design of the Linear Quadratic Regulator (LQR). An LQR-based least-squares output feedback control procedure is introduced for the LQR control of high-order asymmetric discrete systems, and takes advantage of the fact that an 'almost' LQR control is possible without using an observer. Furthermore, the number of measured states can be much less than the number of eigenvectors retained in the reduced-order model while acceptable performance and robustness of the controller are still maintained. The simulation result on a 52-degree-of-freedom rotor model shows that the lateral vibration can be effectively reduced by monitoring a single location along the shaft with the control inputs at horizontal and vertical directions at a single location for a certain spin speed. The spill-over problem of the LQR control system is also investigated for both collocated and non-collocated cases based on the same reduced-order model. Furthermore, the discussion of the robustness of the closed-loop control system against system parameters when including the actuator dynamics is also addressed by means of root-locus plots. The application of the well-known Linear Quadratic Gaussian (LQG) and LQG with Loop Transfer Recovery (LQC/LTR) techniques on two typical low-order rotor dynamic systems is discussed so that a comparison with an LQR-based least-squares output feedback controller can be made.

Fan, Guangwuu William

437

Hollow sinh-Gaussian beams and their paraxial properties.  

PubMed

A new mathematical model of dark-hollow beams, described as hollow sinh-Gaussian (HsG) beams, has been introduced. The intensity distributions of HsG beams are characterized by a single bright ring along the propagation whose size is determined by the order of beams; the shape of the ring can be controlled by beam width and this leads to the elliptical HsG beams. Propagation characteristics of HsG beams through an ABCD optical system have been researched, they can be regarded as superposition of a series of Hypergeometric-Gaussian (HyGG) beams. As a numerical example, the propagation characteristics of HsG beams in free space have been demonstrated graphically. PMID:22535059

Sun, Qiongge; Zhou, Keya; Fang, Guangyu; Zhang, Guoqiang; Liu, Zhengjun; Liu, Shutian

2012-04-23

438

Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states  

SciTech Connect

We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they are as well bounded from above.

Adesso, Gerardo; Illuminati, Fabrizio [Dipartimento di Fisica 'E. R. Caianiello', Universita di Salerno, CNR-Coherentia, Gruppo di Salerno (Italy); INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi, SA (Italy)

2005-09-15

439

A class of quadratic deformations of Lie superalgebras  

E-print Network

We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. We derive the equivalent of the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate in detail one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.

Peter Jarvis; Gerd Rudolph; Luke Yates

2010-10-19

440

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems  

SciTech Connect

There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

Marquette, Ian [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)

2011-04-15

441

H2, fixed architecture, control design for large scale systems. Ph.D. Thesis  

NASA Technical Reports Server (NTRS)

The H2, fixed architecture, control problem is a classic linear quadratic Gaussian (LQG) problem whose solution is constrained to be a linear time invariant compensator with a decentralized processing structure. The compensator can be made of p independent subcontrollers, each of which has a fixed order and connects selected sensors to selected actuators. The H2, fixed architecture, control problem allows the design of simplified feedback systems needed to control large scale systems. Its solution becomes more complicated, however, as more constraints are introduced. This work derives the necessary conditions for optimality for the problem and studies their properties. It is found that the filter and control problems couple when the architecture constraints are introduced, and that the different subcontrollers must be coordinated in order to achieve global system performance. The problem requires the simultaneous solution of highly coupled matrix equations. The use of homotopy is investigated as a numerical tool, and its convergence properties studied. It is found that the general constrained problem may have multiple stabilizing solutions, and that these solutions may be local minima or saddle points for the quadratic cost. The nature of the solution is not invariant when the parameters of the system are changed. Bifurcations occur, and a solution may continuously transform into a nonstabilizing compensator. Using a modified homotopy procedure, fixed architecture compensators are derived for models of large flexible structures to help understand the properties of the constrained solutions and compare them to the corresponding unconstrained ones.

Mercadal, Mathieu

1990-01-01

442

Gaussian Mixture Model of Heart Rate Variability  

PubMed Central

Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

443

Cloning of Gaussian states by linear optics  

SciTech Connect

We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of nonunit quantum efficiency and unbalanced mode mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and the number of thermal photons being only partially known.

Olivares, Stefano; Paris, Matteo G. A.; Andersen, Ulrik L. [Dipartimento di Fisica dell'Universita degli Studi di Milano (Italy); Institut fuer Optik, Information und Photonik, Max-Planck Forschungsgruppe, Universitaet Erlangen-Nuernberg, Guenther-Scharowsky strasse 1, 91058, Erlangen (Germany)

2006-06-15

444

Quantum bit commitment under Gaussian constraints  

NASA Astrophysics Data System (ADS)

Quantum bit commitment has long been known to be impossible. Nevertheless, just as in the classical case, imposing certain constraints on the power of the parties may enable the construction of asymptotically secure protocols. Here, we introduce a quantum bit commitment protocol and prove that it is asymptotically secure if cheating is restricted to Gaussian operations. This protocol exploits continuous-variable quantum optical carriers, for which such a Gaussian constraint is experimentally relevant as the high optical nonlinearity needed to effect deterministic non-Gaussian cheating is inaccessible.

Mandilara, Aikaterini; Cerf, Nicolas J.

2012-06-01

445

Wide field adaptive optics laboratory demonstration with closed-loop tomographic control.  

PubMed

HOMER, the new bench developed at ONERA devoted to wide field adaptive optics (WFAO) laboratory research, has allowed the first experimental validations of multi-conjugate adaptive optics (MCAO) and laser tomography adaptive optics (LTAO) concepts with a linear quadratic Gaussian (LQG) control approach. Results obtained in LTAO in closed loop show the significant gain in performance brought by LQG control, which allows tomographic reconstruction. We present a calibration and model identification strategy. Experimental results are shown to be consistent with end-to-end simulations. These results are very encouraging and demonstrate robustness of performance with respect to inevitable experimental uncertainties. They represent a first step for the study of very large telescope (VLT) and extremely large telescopes (ELT) instruments. PMID:20208937

Costille, Anne; Petit, Cyril; Conan, Jean-Marc; Kulcsár, Caroline; Raynaud, Henri-François; Fusco, Thierry

2010-03-01

446

Application of piezoelectric devices to vibration suppression - From modeling and controller designs to implementation  

NASA Technical Reports Server (NTRS)

Embedded piezoelectric devices may be ideally suited for vibration control of space structures, which lack an inertial ground. When subjected to an input voltage, an embedded piezoelectric actuator changes its dimensions, which in turn generates a pair of forces exerted on adjacent structural members. From the direct piezoelectric effect, an embedded piezoelectric transducer generates an electric charge proportional to the structural dynamic response. In this paper, the implementation, testing and modeling of an active truss structure consisting of piezoelectric sensors and actuators are described. Linear quadratic Gaussian (LQG), second-order, and direct rate feedback control schemes are designed to suppress the vibrations of the active structure. Simulation and test results are presented. It is shown that special model reduction considerations are required to achieve good correlation between test and analysis.

Won, Chin C.; Sparks, Dean; Belvin, Keith; Sulla, Jeff

1992-01-01

447

Engineering extremal two-qubit entangled states with maximally entangled Gaussian light  

E-print Network

We study state engineering induced by bilinear interactions between two remote qubits and light fields prepared in two-mode Gaussian states. The attainable two-qubit states span the entire physically allowed region in the entanglement-vs-global-purity plane. We show that two-mode Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. The target two-qubit entanglement is determined quantitatively only by the purities of the two-mode Gaussian resource. Thus, a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control completely the engineering of extremally entangled two-qubit states, which can be realized in realistic scenarios of cavity and circuit quantum electrodynamics.

Adesso, G; Illuminati, F; Paternostro, M

2010-01-01

448

Generation of radially polarized Bessel-Gaussian beams from c-cut Nd:YVO? laser.  

PubMed

We experimentally demonstrate the generation of radially polarized Bessel-Gaussian beams from a c-cut Nd:YVO? laser with a hemispherical cavity configuration by proper mode control. The output beam has an annular-shaped intensity distribution with radial polarization. When the beam is focused, the intensity pattern changes to a multi-ring, which is a typical characteristic of the lowest transverse mode of vector Bessel-Gaussian beam. Higher-order modes of vector Bessel-Gaussian beam are also observed from the same cavity by slightly changing the cavity alignment. The experimental results show a good agreement with the simulation results for both focal and far fields. The present method is a simple and direct way for generating vector Bessel-Gaussian beams. PMID:24562288

Vyas, Sunil; Kozawa, Yuichi; Sato, Shunichi

2014-02-15

449

Stability of the Quadratic Equation of Pexider Type  

Microsoft Academic Search

We will investigate the stability problem of the quadratic equation (1) and extend the results of Borelli and Forti, Czerwik,\\u000a and Rassias. By applying this result and an improved theorem of the author, we will also prove the stability of the quadratic\\u000a functional equation of Pexider type,f\\u000a 1 (x +y) + f2(x -y) =f\\u000a 3(x) +f\\u000a 4(y), for a large

Soon-Mo Jung

2000-01-01

450

A discontinuity capturing SUPG formulation using quadratic element  

NASA Astrophysics Data System (ADS)

The purpose of the present study is to add the discontinuity capturing term into the quadratic streamline upwind Petrov-Galerkin (SUPG) finite element formulation for predicting high resolution solution in a flowfield containing possible discontinuities. Both good stability and high-order accuracy can be achieved in solving the linear one-dimensional Burgers' equation containing three profiles of different characters and nonlinear Burgers' equation. The extension to the two dimensional analysis is also attempted in this study in the context of quadratic element formulation.

Sheu, Tony W. H.; Husang, Philip G. Y.; Wang, Morten M. T.

1992-12-01

451

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

NASA Technical Reports Server (NTRS)

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

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

1986-01-01

452

Modification on static responses of a nano-oscillator by quadratic optomechanical couplings  

NASA Astrophysics Data System (ADS)

A quadratic coupling enabled parametric oscillation in an optomechanical system is used to modify the nonlinear static responses of a mechanical oscillator with a normal linear coupling. The mean value study showed that the modification of the static response on a mechanical oscillator is extremely sensitive and useful, which can readily enhance or suppress the nonlinear displacement response from a bistability case to singlet or triplet well case, freely bifurcating the equilibrium position from one to two or three. The static equilibria structure and the stability regions for mean-value controls on nano-oscillator were analyzed under the possible modification parameters.

Zhang, Lin; Song, ZhangDai

2014-05-01

453

Friction analysis based on integral quadratic constraints  

Microsoft Academic Search

One of the most important nonlinearities in mechanical control systems is friction. Friction may cause steady state errors, as well as unwanted oscillations. The purpose of this paper is to demonstrate how recently developed tools for nonlinear system analysis can give us a better understanding of these effects. One of the most common approaches to analysis friction systems is passivity

A. Rantzer

1996-01-01

454

A contribution to matrix quadratic equations  

Microsoft Academic Search

The well-known matrix algebraic equation of the optimal control and filtering theory is considered. A necessary and sufficient condition for its solution to yield an optimal as well as asymptotically stable closed-loop system is given. The condition involves the concepts of stabilizability and detectability.

V. Kucera

1972-01-01

455

Approximate inference in Gaussian graphical models  

E-print Network

The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a ...

Malioutov, Dmitry M., 1981-

2008-01-01

456

Improved Gaussian Beam-Scattering Algorithm  

NASA Technical Reports Server (NTRS)

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

Lock, James A.

1995-01-01

457

String Gas Cosmology and Non-Gaussianities  

E-print Network

Recently it has been shown that string gas cosmology, an alternative model of the very early universe which does not involve a period of cosmological inflation, can give rise to an almost scale invariant spectrum of metric perturbations. Here we calculate the non-Gaussianities of the spectrum of cosmological fluctuations in string gas cosmology, and find that these non-Gaussianities depend linearly on the wave number and that their amplitude depends sensitively on the string scale. If the string scale is at the TeV scale, string gas cosmology could lead to observable non-Gaussianities, if it is close to the Planck scale, then the non-Gaussianities on current cosmological scales are negligible.

Chen, Bin; Xue, Wei; Brandenberger, Robert

2007-01-01

458

Generalized competitive learning of gaussian mixture models.  

PubMed

When fitting Gaussian mixtures to multivariate data, it is crucial to select the appropriate number of Gaussians, which is generally referred to as the model selection problem. Under regularization theory, we aim to solve this model selection problem through developing an entropy regularized likelihood (ERL) learning on Gaussian mixtures. We further present a gradient algorithm for this ERL learning. Through some theoretic analysis, we have shown a mechanism of generalized competitive learning that is inherent in the ERL learning, which can lead to automatic model selection on Gaussian mixtures and also make our ERL learning algorithm less sensitive to the initialization as compared to the standard expectation-maximization algorithm. The experiments on simulated data using our algorithm verified our theoretic analysis. Moreover, our ERL learning algorithm has been shown to outperform other competitive learning algorithms in the application of unsupervised image segmentation. PMID:19362913

Lu, Zhiwu; Ip, Horace H S

2009-08-01

459

Optimal cloning of mixed Gaussian states  

SciTech Connect

We construct the optimal one to two cloning transformation for the family of displaced thermal equilibrium states of a harmonic oscillator, with a fixed and known temperature. The transformation is Gaussian and it is optimal with respect to the figure of merit based on the joint output state and norm distance. The proof of the result is based on the equivalence between the optimal cloning problem and that of optimal amplification of Gaussian states which is then reduced to an optimization problem for diagonal states of a quantum oscillator. A key concept in finding the optimum is that of stochastic ordering which plays a similar role in the purely classical problem of Gaussian cloning. The result is then extended to the case of n to m cloning of mixed Gaussian states.

Guta, Madalin [University of Nijmegen, Toernooiveld 1, Postbus 9010, 6500 GL Nijmegen (Netherlands); Matsumoto, Keiji [National Inatitute of Informatics, 2-1-2, Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430 (Japan); Quantum Computation and Information Project, JST, Hongo 5-28-3, Bunkyo-ku, Tokyo 113-0033 (Japan)

2006-09-15

460

Modeling and control of flexible structures  

NASA Technical Reports Server (NTRS)

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Gibson, J. S.; Mingori, D. L.

1988-01-01

461

Unitarily localizable entanglement of Gaussian states  

Microsoft Academic Search

We consider generic (m×n) -mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as (m+n) -mode Gaussian states invariant under local mode permutations on the m -mode and n -mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of m+n-2

Alessio Serafini; Gerardo Adesso; Fabrizio Illuminati

2005-01-01

462

Gaussian Polynomials and Content Ideal in Pullbacks  

Microsoft Academic Search

This article deals mainly with rings (with zerodivisors) in which regular Gaussian polynomials have locally principal contents. Precisely, we show that if (T,M) is a local ring which is not a field, D is a subring of T\\/M such that qf(D) = T\\/M, h: T ? T\\/M is the canonical surjection and R = h (D), then if T satisfies the property “every regular Gaussian polynomial

Chahrazade Bakkari; Najib Mahdou

2006-01-01

463

Speaker Verification Using Adapted Gaussian Mixture Models  

Microsoft Academic Search

Reynolds, Douglas A., Quatieri, Thomas F., and Dunn, Robert B., Speaker Verification Using Adapted Gaussian Mixture Models, Digital Signal Processing10(2000), 19–41.In this paper we describe the major elements of MIT Lincoln Laboratory's Gaussian mixture model (GMM)-based speaker verification system used successfully in several NIST Speaker Recognition Evaluations (SREs). The system is built around the likelihood ratio test for verification, using

Douglas A. Reynolds; Thomas F. Quatieri; Robert B. Dunn

2000-01-01

464

Gaussian-Beam Laser-Resonator Program  

NASA Technical Reports Server (NTRS)

Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).

Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman

1989-01-01

465

Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition  

NASA Astrophysics Data System (ADS)

In target recognition applications of discriminant of classification analysis, each 'feature' is a result of a convolution of an imagery with a filter, which may be derived from a feature vector. It is important to use relatively few features. We analyze an optimal reduced-rank classifier under the two-class situation. Assuming each population is Gaussian and has zero mean, and the classes differ through the covariance matrices: ?1 and ?2. The following matrix is considered: ?=(?1+?2)-1/2?1(?1+?2)-1/2. We show that the k eigenvectors of this matrix whose eigenvalues are most different from 1/2 offer the best rank k approximation to the maximum likelihood classifier. The matrix ? and its eigenvectors have been introduced by Fukunaga and Koontz; hence this analysis gives a new interpretation of the well known Fukunaga-Koontz transform. The optimality that is promised in this method hold if the two populations are exactly Guassian with the same means. To check the applicability of this approach to real data, an experiment is performed, in which several 'modern' classifiers were used on an Infrared ATR data. In these experiments, a reduced-rank classifier-Tuned Basis Functions-outperforms others. The competitive performance of the optimal reduced-rank quadratic classifier suggests that, at least for classification purposes, the imagery data behaves in a nearly-Gaussian fashion.

Huo, Xiaoming; Elad, Michael; Flesia, Ana G.; Muise, Robert R.; Stanfill, S. Robert; Friedman, Jerome; Popescu, Bogdan; Chen, Jihong; Mahalanobis, Abhijit; Donoho, David L.

2003-09-01

466

FIVE SQUARES IN ARITHMETIC PROGRESSION OVER QUADRATIC FIELDS  

E-print Network

FIVE SQUARES IN ARITHMETIC PROGRESSION OVER QUADRATIC FIELDS ENRIQUE GONZ´ALEZ-JIM´ENEZ AND XAVIER) there is a non-constant arithmetic progression of five squares. This is carried out by translating the problem that the only non-constant arithmetic progression of five squares over Q( 409), up to equivalence, is 72 , 132

González, Enrique

467

The Ant System Applied to the Quadratic Assignment Problem  

Microsoft Academic Search

In recent years, there has been growing interest in algorithms inspired by the observation of natural phenomena to define computational procedures that can solve complex problems. We describe a distributed heuristic algorithm that was inspired by the observation of the behavior of ant colonies, and we propose its use for the quadratic assignment problem. The results obtained in solving several

Vittorio Maniezzo; Alberto Colorni

1999-01-01

468

Supercritical ordered trajectories with quadratically irrational winding number  

Microsoft Academic Search

The dynamics of the circle map is studied in the supercritical regime where the map is not invertible and thus the trajectory elements are clustered on the circle. Existence of a simple ordering structure is established for trajectories with arbitrary irrational winding number. A previously developed formalism is then generalized to predict the trajectories when the winding number is quadratically

Subir Kumar Sarkar

1984-01-01

469

Unravelling Student Challenges with Quadratics: A Cognitive Approach  

ERIC Educational Resources Information Center

The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

Kotsopoulos, Donna

2007-01-01

470

Cosmological Vorticity in a Gravity with Quadratic Order Curvature Couplings  

E-print Network

We analyse the evolution of the rotational type cosmological perturbation in a gravity with general quadratic order gravitational coupling terms. The result is expressed independently of the generalized nature of the gravity theory, and is simply interpreted as a conservation of the angular momentum.

J. Hwang; H. Noh

1997-10-07

471

DIMACS Technical Report 9940 Camel Sequences and Quadratic Residues  

E-print Network

DIMACS Technical Report 99­40 Camel Sequences and Quadratic Residues by V. Gurvich 1 DIMACS generate them, will be called the camel distributions and camel sequences, respectively up­camel and down­camel. For example, the first sequence above is down­camel, and the second one is up­camel. Camel sequences have

472

Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions  

ERIC Educational Resources Information Center

An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

Leyendekkers, J. V.; Shannon, A. G.

2004-01-01

473

Number theoretic transforms over the golden section quadratic field  

Microsoft Academic Search

A new number theoretic transform (NTT) over the real quadratic field Q(?5) is suggested and analyzed. Conventional NTTs are used for fast convolution of integer sequences. A new approach for computing number theoretic transforms (NTTs) is proposed, allowing real signals to be processed as well. The method is based on a Diophantine approximation of the input real signal before the

Vassil S. Dimitrov; T. V. Cosklev; B. Bonevsky

1995-01-01

474

Parallel Interior Point Solver for Structured Quadratic Programs ...  

E-print Network

Parallel Interior-Point Solver for Structured Quadratic Programs: Application to ... ?1 and X and S are diagonal matrices in Rn×n with elements of vectors x and ..... at times t = 0,... ,T; each of the ?t has only a finite number of possible outcomes.

1910-30-82

475

Discriminative learning quadratic discriminant function for handwriting recognition  

Microsoft Academic Search

In character string recognition integrating segmentation and classification, high classification accuracy and resistance to noncharacters are desired to the underlying classifier. In a previous evaluation study, the modified quadratic discriminant function (MQDF) proposed by Kimura et al. was shown to be superior in noncharacter resistance but inferior in classification accuracy to neural networks. This paper proposes a discriminative learning algorithm

Cheng-Lin Liu; Hiroshi Sako; Hiromichi Fujisawa

2004-01-01

476

Quadratic algebra contractions and 2nd order superintegrable systems  

E-print Network

Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces we show that the free quadratic algebras generated by the 1st and 2nd order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.

Ernest G. Kalnins; Willard Miller Jr

2014-01-04

477

Characterization of local quadratic growth for strong minima in the ...  

E-print Network

Oct 14, 2011 ... Our aim is to characterize local quadratic growth for the cost function J in .... there exists a constant Cs depending only on s, such that yu ? + yu 2,s ..... u ? K is a Pontryagin extremal in integral form with respect to U if. ?. ?.

2011-10-14

478

Sobolev seminorm of quadratic functions with applications to ...  

E-print Network

36,14]. The following quadratic interpolation plays an important role in Conn and Toint ... remaining freedom is to minimize some functional subject to the interpolation constraints, that is to .... Because of symmetry, the integral of xTGg is zero.

2012-01-18

479

Mixed-integer Quadratic Programming is in NP  

E-print Network

Jul 17, 2014 ... showing that if the decision version of mixed-integer quadratic ... where the minimal binary encoding length of any feasible integral ..... for every S ? {1,...,n}; note that the complexity of the additional constraints is O(n) and.

2014-07-17

480

A Rigorous Global Filtering Algorithm for Quadratic Constraints  

Microsoft Academic Search

Abstract: This paper introduces a new filtering algorithm for handling systems of quadratic equations and inequations. Such constraints are widely used to model distance relations in numerous application areas ranging from robotics to chemistry. Classical filtering algorithms are based upon local consistencies and thus, are often unable to achieve a significant pruning of the domains of the variables occurring in

Yahia Lebbah; Claude Michel; Michel Rueher

2005-01-01

481

Holomorphic quantum mechanics with a quadratic Hamiltonian constraint  

Microsoft Academic Search

A finite-dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic, and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator algebra. The different representations yield drastically different Hilbert spaces. In particular, all the spaces obtained in the antiholomorphic representation violate classical expectations for the spectra of certain operators, whereas

Jorma Louko

1993-01-01

482

System Analysis via Integral Quadratic Constraints Part IIa: Abstract theory  

Microsoft Academic Search

In this second report on system analysis via integral quadratic con- straints, the theory is refined compared to Part I (6), to cover a number of additional cases. The report is split into two halfs, denoted Part IIa and Part IIb. Unbounded operators are treated by encapsulating them in a feedback loop,thathasboundedclosedloopgain.Ageneraltheoremforwell-posedness of suchfeedback loops is given. A concept of

A. Rantzer; A. Megretski

483

Integral quadratic constraints for monotonic and slope restricted diagonal operators  

Microsoft Academic Search

Studies the description, by means of integral quadratic constraints (IQCs), of a class of static diagonal operators with equal diagonal entries. In particular, the diagonal entries considered are monotonic and slope-restricted nonlinearities. First, we give new IQCs for this type of operators which exploit the equality among nonlinearities. Then we show how these results can be used to derive new

F. J. D'Amato; U. T. Jonson; A. Megretski; M. A. Rotea

1999-01-01

484

Stability analysis with Popov multipliers and integral quadratic constraints  

Microsoft Academic Search

It is shown that a general form of Popov multipliers can be used in stability analysis based on integral quadratic constraints (IQC). The Popov multiplier is nonproper and a condition that the nominal plant is strictly proper will be imposed in order to ensure boundedness of the IQC corresponding to the Popov multiplier. A consequence of our main result is

Ulf Jönsson

1997-01-01

485

A Unified Approach to Teaching Quadratic and Cubic Equations.  

ERIC Educational Resources Information Center

Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

Ward, A. J. B.

2003-01-01

486

Finding the Best Quadratic Approximation of a Function  

ERIC Educational Resources Information Center

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

487

Quadratic function fields with exponent two ideal class group  

Microsoft Academic Search

It has been shown by Madden that there are only finitely many quadratic extensions of k(x), k a finite field, in which the ideal class group has exponent two and the infinity place of k(x) ramifies. We give a characterization of such fields that allow us to find a full list of all such field extensions for future reference. In

Victor Bautista-Ancona; Javier Diaz-Vargas

2006-01-01

488

Quadratic Function Fields with Exponent Two Ideal Class Group  

Microsoft Academic Search

It has been shown by Madden that there are only finitely many quadratic extensions of k(x), k a finite field, in which the ideal class group has exponent two and the infinity place of k(x) ramifies. We give a characterization of such fields that allow us to find a full list of all such field extensions for future reference. In

Victor Bautista-Ancona; Javier Diaz-Vargas

2005-01-01

489

An Improved Algorithm for the Generalized Quadratic Assignment ...  

E-print Network

This paper is concerned with solving GQAPs (generalized quadratic .... Even though the GQAP was formulated only recently, special cases have been studied extensively. Related problems, other than the QAP and the GAP, include the ...... Department of Mechanical and Industrial Engineering, University of Toronto, Toronto ...

artur

2008-05-15

490

Semidefinite-Based Branch-and-Bound for Nonconvex Quadratic ...  

E-print Network

Jun 27, 2005 ... This paper presents a branch-and-bound algorithm for nonconvex quadratic pro- ... †Department of Mechanical and Industrial Engineering, University of ... Recent work by Bomze and de Klerk (2002) has studied ... Such SDPs—including the related ones introduced in this paper—are too large to be solved.

2005-06-27

491

A Generalized Method for Constructing Sub-quadratic Complexity ) Multipliers  

E-print Network

-parallel multipliers, finite fields, Winograd convolution 1 Introduction Finite fields have numerous applications representation of the field elements (and hence the operands). It is customary to view a finite field as a vectorA Generalized Method for Constructing Sub-quadratic Complexity GF(2k ) Multipliers Draft Copy B

492

On the Number of Representation of Integers into Quadratic Forms  

E-print Network

We give formulas for the number of representations of non negative integers into quadratic forms. We also consider the case cubic and quintic forms. Finally we give a mean value asymptotic formula, for the behavior of the function that counts the number of representations of an integer as sum of two squares, known also as Gauss circle problem.

Nikos Bagis; M. L Glasser

2014-12-18

493

Feasibility testing for systems of real quadratic equations  

Microsoft Academic Search

We consider the problem of deciding whether a given system of quadratic homogeneous equations over the reals has non-trivial solution. We design an approximative algorithm whose complexity is polynomial in the number of variables and exponential in the number of equations. Some applications to general systems of polynomial equations and inequalities over the reals are discussed.

Alexander I. Barvinok

1992-01-01

494

Monotonic solutions of a quadratic integral equation of fractional order  

Microsoft Academic Search

In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112–119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with

Józef Bana?; Beata Rzepka

2007-01-01

495

Visualising the Complex Roots of Quadratic Equations with Real Coefficients  

ERIC Educational Resources Information Center

The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

Bardell, Nicholas S.

2012-01-01

496

Feasibility Testing for Systems of Real Quadratic Equations  

Microsoft Academic Search

We consider the problem of deciding whether a given system of quadratic homogeneous equations over the reals has nontrivial\\u000a solution. We design an algorithm which, for a fixed number of equations, uses a number of arithmetic operations bounded by\\u000a a polynomial in the number of variables only.

Alexander I. Barvinok

1993-01-01

497

Quadratic Expressions by Means of "Summing All the Matchsticks"  

ERIC Educational Resources Information Center

This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such "matchstick" problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are…

Gierdien, M. Faaiz

2012-01-01

498

On a bi-quadratic functional equation and its stability  

Microsoft Academic Search

In this paper, we obtain the general solution and the generalized Hyers–Ulam stability of the bi-quadratic functional equation f(x+y,z+w)+f(x+y,z-w)+f(x-y,z+w)+f(x-y,z-w)=4[f(x,z)+f(x,w)+f(y,z)+f(y,w)].

Won-Gil Park; Jae-Hyeong Bae

2005-01-01

499

Monotonic solutions of a quadratic integral equation of Volterra type  

Microsoft Academic Search

We study a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval. With the help of a suitable measure of noncompactness, we show that the mentioned integral equation has monotonic solutions.

A. Martinon

2004-01-01

500

Neural net solutions to fuzzy problems: The quadratic equation  

Microsoft Academic Search

This paper continues our research on using neural nets to solve fuzzy equations. After outlining our general method of employing neural nets to solve fuzzy problems we concentrate on solving the fuzzy quadratic equation. We show how neural nets can produce both real, and complex, fuzzy number solutions.

J. J. Buckley; E. Eslami

1997-01-01