Infinite Dimensional Optimization and Control Theory
Infinite Dimensional Optimization and Control Theory
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.
- Unifies finite and infinite dimensional control problems
- Deals with the important problems of target conditions and state constraints
Reviews & endorsements
"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
Product details
June 2010Paperback
9780521154543
816 pages
229 × 152 × 41 mm
1.07kg
Available
Table of Contents
- 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.
