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. Applications include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls.

Review of the hardback:‘This outstanding monograph will be a great source both for experts and for graduate students interested in calculus of variations, non-linear programming, optimisation theory, optimal control and relaxation theory.’

Source: European Mathematical Society

Review of the hardback:‘… an impressive monograph on infinite dimensional optimal control theory. This is an original and extensive contribution which is not covered by other recent books in the control theory.’

J. P. Raymond Source: Zentralblatt für Mathematik