Max-Plus Methods for Nonlinear Control and Estimation

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Dezember 2005



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.


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.


"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)
EAN: 9780817635343
ISBN: 0817635343
Untertitel: 'Systems & Control: Foundations'. Auflage 2006. Sprache: Englisch.
Erscheinungsdatum: Dezember 2005
Seitenanzahl: 241 Seiten
Format: gebunden
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