Infinite Dimensional Optimization and Control Theory

Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.

Hector O. Fattorini (Author)

9780521154543, Cambridge University Press

Paperback, published 24 June 2010

816 pages
22.9 x 15.2 x 4.1 cm, 1.07 kg

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, Zentralblatt für Mathematik

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.

Part 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. Abstract minimization problems: the minimum principle for general optimal control problems
Part II. Infinite Dimensional Control Problems: 5. Differential equations in Banach spaces and semigroup theory
6. Abstract minimization problems in Hilbert spaces: applications to hyperbolic control systems
7. Abstract minimization problems in Banach spaces: abstract parabolic linear and semilinear equations
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: The abstract parabolic case
Part III. Relaxed Controls: 12. Spaces of relaxed controls: topology and measure theory
13. Relaxed controls in finite dimensional systems: existence theory
14. Relaxed controls in infinite dimensional spaces: existence theory.

Subject Areas: Optimization [PBU]