Max-Plus Methods for Nonlinear Control and Estimation

AvWilliam M. McEneaney

Inbunden, Engelska, 2005

Del i serien Systems & Control: Foundations & Applications

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Beskrivning

The control and estimation of continuous-time/continuous-space nonlinear systems continues to be a challenging problem, and this is one of the c- tral foci of this book. A common approach is to use dynamic programming; this typically leads to solution of the control or estimation problem via the solution of a corresponding Hamilton–Jacobi (HJ) partial di?erential eq- tion (PDE). This approach has the advantage of producing the “optimal” control. (The term “optimal” has a somewhat more complex meaning in the class of H problems. However, we will freely use the term for such controllers ? throughout, and this meaning will be made more precise when it is not ob- ous. )Thus,insolvingthecontrol/estimationproblem,wewillbesolvingsome nonlinear HJ PDEs. One might note that a second focus of the book is the solution of a class of HJ PDEs whose viscosity solutions have interpretations as value functions of associated control problems. Note that we will brie?y discuss the notion of viscosity solution of a nonlinear HJ PDE, and indicate that this solution has the property that it is the correct weak solution of the PDE. By correct weak solution in this context, we mean that it is the solution that is the value function of the associated control (or estimation) problem. The viscosity solution is also the correct weak solution in many PDE classes not considered here, and references to further literature on this subject will be given.

Produktinformation

Utgivningsdatum:2005-12-13
Mått:156 x 235 x 22 mm
Vikt:452 g
Format:Inbunden
Språk:Engelska
Serie:Systems & Control: Foundations & Applications
Antal sidor:246
Upplaga:2006
Förlag:Birkhauser Boston Inc
ISBN:9780817635343

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

"As is well known, control and estimation of continuous time and continuous space nonlinear systems are difficult to handle. One frequently uses dynamic programming methods to treat such problems. Central to this approach are solutions of the associated Hamilton-Jacobi-Bellman (HJB) equations. The book under review is motivated by solutions of such problems... The entire book is divided into nine chapters and an appendix. Chapter 1 provides an introduction, and states why the problem to be studied and methods are needed. Concepts of max-plus methods are also provided... All in all, this is a nicely written book that introduces important topics." -Mathematical Reviews "This outstanding book discusses new theoretical approaches to the study of the control and estimation of continuous-time/continuous-space nonlinear systems to be a challenging problem...This book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of the max-plus algebra and some basics of functional analysis over the max-plus algebra...The volume is primarily addressed to applied mathematicians...However, the book will also be useful for scientists from the application areas, in particular, applied scientists from engineering and physics." (Jan Lovisek, Zentralblatt MATH, Vol. 1103 (5), 2007)

Innehållsförteckning

Max-Plus Analysis.- Dynamic Programming and Viscosity Solutions.- Max-Plus Eigenvector Method for the Infinite Time-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?/L2 Criteria.