Infinite dimensional optimization and control theory - Fattorini, H. O., (Hector O.) (Cambridge University Press, 1999)
Includes bibliographical references (p. 773-793) and index
Pt. I. - Finite Dimensional Control Problems - 1 - Calculus of Variations and Control Theory - 2 - Optimal Control Problems Without Target Conditions - 3 - Abstract Minimization Problems: The Minimum Principle for the Time Optimal Problem - 4 - The Minimum Principle for General Optimal Control Problems -- - Pt. II. - Infinite Dimensional Control Problems - 5 - Differential Equations in Banach Spaces and Semigroup Theory - 6 - Abstract Minimization Problems in Hilbert Spaces - 7 - Abstract Minimization Problems in Banach Spaces - 8 - Interpolation and Domains of Fractional Powers - 9 - Linear Control Systems - 10 - Optimal Control Problems with State Constraints - 11 - Optimal Control Problems with State Constraints -- - Pt. III. - Relaxed Controls
This book is on existence and necessary conditions, such as Potryagin's maximum principle, for optimal control problems described by ordinary and partial differential equations. These necessary conditions are obtained from Kuhn-Tucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints, state constraints and target conditions. Evolution partial differential equations are studied using semigroup theory, abstract differential equations in linear spaces, integral equations and interpolation theory. Existence of optimal controls is established for arbitrary control sets by means of a general theory of relaxed controls