Mathematics
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Synopsis
Product Description This book concerns existence and necessary conditions, such as Potryagin's maximum principle, for optimal control problems described by ordinary and partial differential equations. The author obtains these necessary conditions from Kuhn-Tucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints, state constraints and target conditions. Fattorini studies evolution partial differential equations using semigroup theory, abstract differential equations in linear spaces, integral equations and interpolation theory. The author establishes existence of optimal controls for arbitrary control sets by means of a general theory of relaxed controls. Applications include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls. Review "Fattorini's extensive monograph is a fundamental contribution to optimal control theory of evolution finite- or infinite-dimensional systems, and summarizes and extends his many decades of intensive research in this area...This outstanding monograph should be on the desk of every expert in optimal control theory...it will be a great source for graduate students interested in calculus of variations, nonlinear programming, optimization theory and optimal control." Mathematical Reviews Book Description This book treats optimal problems for systems described by ordinary and partial differential equations, using an approach that unifies finite dimensional and infinite dimensional nonlinear programming. Problems include control and state constraints and target conditions. Applications of the theory include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls.Although written at a level suitable for beginning graduate students in applied mathematics this comprehensive treatment will also be a valuable reference for researchers in control theory. About the Author Hector O. Fattorini graduated from the Licenciado en Matemática, Universidad de Buenos Aires in 1960 and gained a Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences, New York University, in 1965. Since 1967, he has been a member of the Department of Mathematics at the University of California, Los Angeles.Book Details
Published
April 1, 2013
Publisher
Cambridge University Press
ISBN
9780511574795