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Max Plus Methods for Nonlinear Control

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Synopses & Reviews

Publisher Comments:

The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. Well-known dynamic programming arguments show there is a direct relationship between the solution of a control problem and the solution of a corresponding Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). The max-plus-based methods examined in this monograph belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated HJB PDEs; they are not equivalent to either of the more commonly used finite element or characteristic approaches. The potential advantages of the max-plus-based approaches lie in the fact that solution operators for nonlinear HJB problems are linear over the max-plus algebra, and this linearity is exploited in the construction of algorithms. The book will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods. Researchers and practitioners tangentially interested in this area will also find a readable, concise discussion of the subject through a careful selection of specific chapters and sections. Basic knowledge of control theory for systems with dynamics governed by differential equations is required.

Synopsis:

The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality.

The max-plus-based methods examined in this work belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated Hamilton-Jacobi-Bellman (HJB) PDEs; these methods are not equivalent to either of the more commonly used finite element or characteristic approaches.

Max-Plus Methods for Nonlinear Control and Estimation will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods.

Table of Contents

Preface.- Introduction.- Max-Plus Analysis.- Dynamic Programming and Viscosity Solutions.- Max-Plus Eigenvector Method for the Infinite Horizon Problem.- Max-Plus Eigenvector Method Error Analysis.- A Semigroup Construction Method.- Curse-of-Dimensionality-Free Method.- Finite Time-Horizon Application: Nonlinear Filtering.- Mixed L-infinity/L2 Criteria.- Miscellaneous Proofs.- References.-  Index

Product Details

ISBN:
9780817635343
Author:
Mceneaney, William
Publisher:
Birkhauser
Author:
McEneaney, William
Author:
McEneaney, William M.
Author:
McEneaney, W. M.
Subject:
Differential Equations
Subject:
Applied
Subject:
Matrices
Subject:
Nonlinear control theory
Subject:
Number Systems
Subject:
Systems Theory, Control
Subject:
Control, Robotics, Mechatronics
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Computational Mathematics and Numerical Analysis
Subject:
Mathematics-Applied
Subject:
System Theory
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Systems & Control: Foundations & Applications
Publication Date:
December 2005
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
260
Dimensions:
235 x 155 mm 1200 gr

Related Subjects

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Science and Mathematics » Mathematics » Systems Theory
Science and Mathematics » Physics » Nuclear

Max Plus Methods for Nonlinear Control New Hardcover
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Product details 260 pages Birkhauser - English 9780817635343 Reviews:
"Synopsis" by , The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality.

The max-plus-based methods examined in this work belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated Hamilton-Jacobi-Bellman (HJB) PDEs; these methods are not equivalent to either of the more commonly used finite element or characteristic approaches.

Max-Plus Methods for Nonlinear Control and Estimation will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods.

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