Download or read book Approximation in the Solution of the Optimal Linear Quadratic Regulator Problem for Infinite Dimensional Systems written by Carl Stewart Cressler and published by . This book was released on 1991 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Approximation for the Infinite dimensional Discrete time Optimal Linear quadratic Regulator Problem written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1986 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Theory for LQG Linear Quadratic Gaussian Optimal Control of Flexible Structures written by and published by . This book was released on 1988 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents approximation theory for the 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 separates into an optimal linear-quadratic control problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme in the paper 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 of stability of the closed-loop systems produced with the finite dimensional compensators are discussed. (JHD).
Download or read book Computational Methods for Optimal Linear quadratic Compensators for Infinite Dimensional Discrete time Systems written by J. S. Gibson and published by . This book was released on 1986 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Approximation for the Infinite dimensional Discrete time Optimal Linear quadratic Regulator Problem written by John Sevier Gibson and published by . This book was released on 1986 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Methods for Optimal Linear quadratic Compensators for Infinite Dimensional Discrete time Systems written by John Sevier Gibson and published by . This book was released on 1986 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Feedback Control Infinite Dimensional Parabolic Evolution Systems Approximation Techniques written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1989 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Numerical Algorithm for Optimal Feedback Gains in High Dimensional LQR Problems written by H. T. Banks and published by . This book was released on 1986 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors a hybrid method for computing the feedback gains in linear quadratic regulator (LQR) problems. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of our proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented. (Author).
Download or read book Numerical Solution of the Infinite Dimensional LQR Problem and the Associated Differential Riccati Equations written by Hermann Mena and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The numerical analysis of linear quadratic regulator design problems for parabolic partial differential equations requires solving large-scale Riccati equations. In the finite time horizon case, the differential Riccati equation (DRE) arises. Typically, the coefficient matrices of the resulting DRE have a given structure, e.g., sparse, symmetric or low rank. Moreover, in most control problems, fast and slow modes arepresent. This implies that the associated DRE will be fairly stiff. Therefore, implicit schemes have to be used to solve such DREs numerically. In this paper we derive efficient numerical methods for solving DREs capable of exploiting this structure, which are based on a matrix-valued implementation of the BDF and Rosenbrock methods. We show that these methods are particularly suitable for large-scale problems by working only on low-rank factors of the solutions. Step size and order control strategies can also be implemented based only on information contained in the solution factors. Finally, we briefly show that within a Galerkin projection framework the solutions of the finite-dimensional DREs converge in the strong operator topology to the solutions of the infinite-dimensional DREs. The performance of each of these methods is tested in numerical experiments.
Download or read book Linear Quadratic Regulator Problem for Infinite Dimensional Linear Systems with Delays in Control written by Kazufumi Ito and published by . This book was released on 1988 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book solution approximation in infinite horizon linear quadratic control written by irwin e. schochetman and published by . This book was released on 1991 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Discrete time LQR Problems for Parabolic Systems with Unbounded Input Approximation and Convergence written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1988 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Strong Convergence and Convergence Rates of Approximating Solutions for Algebraic Riccati Equations in Hilbert Spaces written by Kazufumi Ito and published by . This book was released on 1987 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the linear quadratic optimal control problem on infinite time interval for linear time-invariant systems define on Hilbert spaces. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sub n of finite dimensional approximations of the solution to ARE. A sufficient condition that shows N sub n converges strongly to pi is obtained. Under this condition, we derive a formula which can be used to obtain rate of convergence of N sub n to pi. We demonstrate and apply the results for the Galerkin approximation for parabolic systems and the averaging approximation for heredity differential systems. (Author).
Download or read book On the Continuous Dependence with Respect to Sampling of the Linear Quadratic Regulator Problem for Distributed Parameter Systems written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1990 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: The convergence of solutions to the discrete or sampled time linear quadratic regulator problem and associated Riccati equation for infinite dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite and infinite time horizon problems are studied. In the finite time horizon case, strong continuity of the operators which define the control system and performance index together with a stability and consistency condition on the sampling scheme are required. For the infinite time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary of delay system, and a flexible beam are presented and discussed. (kr).
Download or read book Control and Boundary Analysis written by John Cagnol and published by CRC Press. This book was released on 2005-03-04 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises selected papers from the 21st Conference on System Modeling and Optimization in Sophia Antipolis, France. It covers over three decades of studies involving partial differential systems and equations. Topics include: the modeling of continuous mechanics involving fixed boundary, control theory, shape optimization and moving bou
Download or read book Shifting the Closed loop Spectrum in the Optimal Linear Quadratic Regulator Problem for Hereditary Systems written by J. S. Gibson and published by . This book was released on 1985 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hankel Norm Approximation for Infinite Dimensional Systems written by A. Sasane and published by Springer Science & Business Media. This book was released on 2002-05-14 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model reduction is an important engineering problem in which one aims to replace an elaborate model by a simpler model without undue loss of accuracy. The accuracy can be mathematically measured in several possible norms and the Hankel norm is one such. The Hankel norm gives a meaningful notion of distance between two linear systems: roughly speaking, it is the induced norm of the operator that maps past inputs to future outputs. It turns out that the engineering problem of model reduction in the Hankel norm is closely related to the mathematical problem of finding solutions to the sub-optimal Nehari-Takagi problem, which is called "the sub-optimal Hankel norm approximation problem" in this book. Although the existence of a solution to the sub-optimal Hankel norm approximation problem has been known since the 1970's, this book presents explicit solutions and, in particular, new formulae for several large classes of infinite-dimensional systems for the first time.
