Infinite Dimensional Optimization and Control Theory: 62 (Encyclopedia of Mathematics and its Applications, Series Number 62)
Cambridge University Press, 6/3/1999
EAN 9780521451253, ISBN10: 0521451256
Hardcover, 816 pages, 23.4 x 15.5 x 4.3 cm
Language: English
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.