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Extensions of Linear-Quadratic Control, Optimization and Matrix Theory

Extensions of Linear-Quadratic Control, Optimization and Matrix Theory
Author:
Publisher: Academic Press
Total Pages: 229
Release: 2000-04-01
Genre: Mathematics
ISBN: 0080956424

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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering


Optimal Control

Optimal Control
Author: Brian D. O. Anderson
Publisher: Courier Corporation
Total Pages: 465
Release: 2007-02-27
Genre: Technology & Engineering
ISBN: 0486457664

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Numerous examples highlight this treatment of the use of linear quadratic Gaussian methods for control system design. It explores linear optimal control theory from an engineering viewpoint, with illustrations of practical applications. Key topics include loop-recovery techniques, frequency shaping, and controller reduction. Numerous examples and complete solutions. 1990 edition.


Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions

Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions
Author: Jingrui Sun
Publisher: Springer Nature
Total Pages: 129
Release: 2020-06-29
Genre: Mathematics
ISBN: 3030209229

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This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.


Linear Quadratic Control

Linear Quadratic Control
Author: Peter Dorato
Publisher:
Total Pages: 0
Release: 2000
Genre: Control theory
ISBN: 9781575241562

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Presents an introduction to Linear-Quadratic (LQ) Control theory. The theory is augmented with practical design problems using MATLAB software for numerical solutions, thus the text should also be of interest to practicing engineers. There are homework problems at the end of each chapter.


Linear Control Theory

Linear Control Theory
Author: Shankar P. Bhattacharyya
Publisher: CRC Press
Total Pages: 924
Release: 2018-10-03
Genre: Technology & Engineering
ISBN: 1420019619

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Successfully classroom-tested at the graduate level, Linear Control Theory: Structure, Robustness, and Optimization covers three major areas of control engineering (PID control, robust control, and optimal control). It provides balanced coverage of elegant mathematical theory and useful engineering-oriented results. The first part of the book develops results relating to the design of PID and first-order controllers for continuous and discrete-time linear systems with possible delays. The second section deals with the robust stability and performance of systems under parametric and unstructured uncertainty. This section describes several elegant and sharp results, such as Kharitonov’s theorem and its extensions, the edge theorem, and the mapping theorem. Focusing on the optimal control of linear systems, the third part discusses the standard theories of the linear quadratic regulator, Hinfinity and l1 optimal control, and associated results. Written by recognized leaders in the field, this book explains how control theory can be applied to the design of real-world systems. It shows that the techniques of three term controllers, along with the results on robust and optimal control, are invaluable to developing and solving research problems in many areas of engineering.


Linear Dynamical Systems

Linear Dynamical Systems
Author: Casti
Publisher: Academic Press
Total Pages: 350
Release: 1987-03-19
Genre: Computers
ISBN: 0080956440

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Linear Dynamical Systems


Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems

Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems
Author: Jingrui Sun
Publisher: Springer Nature
Total Pages: 138
Release: 2020-06-29
Genre: Mathematics
ISBN: 3030483061

Download Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems Book in PDF, ePub and Kindle

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.