Infinite Dimensional Optimization and Control Theory
Series: Encyclopedia of Mathematics and its Applications; 62;
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97 171 Ft
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Product details:
- Publisher Cambridge University Press
- Date of Publication 28 March 1999
- ISBN 9780521451253
- Binding Hardback
- No. of pages816 pages
- Size 242x165x29 mm
- Weight 1007 g
- Language English 0
Categories
Short description:
Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.
MoreLong description:
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.' European Mathematical Society
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.
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