McEneaney, William M. creator author. SpringerLink (Online service) text xxu 2006 monographic eng

electronic

electronic resource

access XIII, 241 p. 17 illus. online resource. 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. 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. by William M. McEneaney. MATHEMATICS DIFFERENTIAL EQUATIONS, PARTIAL SYSTEMS THEORY COMPUTER SCIENCE MATHEMATICS ENGINEERING MATHEMATICS MATHEMATICS SYSTEMS THEORY, CONTROL CONTROL ENGINEERING PARTIAL DIFFERENTIAL EQUATIONS APPL.MATHEMATICS/COMPUTATIONAL METHODS OF ENGINEERING COMPUTATIONAL MATHEMATICS AND NUMERICAL ANALYSIS 519 9780817644536 99780817644536 http://dx.doi.org/10.1007/0-8176-4453-9 http://dx.doi.org/10.1007/0-8176-4453-9 100301 20260521092026.0 978-0-8176-4453-6