02507aam a2200181 4500008004500000020001800045082001600063100002500079245005700104260004800161300006300209440005700272504090100329520101901230650003002249650002702279650001902306200316b 1999 ||||| |||| 00| 0 eng d a9780521154543 a003.5bF2I6 aFattorini, Hector O. aInfinite dimensional optimization and control theory bCambridge University Pressc1999aCambridge axv, 798 p. bIncludes bibliographical references and index aEncyclopedia of mathematics and its applications; 62 aTable 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. 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
7. Abstract minimization problems in Banach spaces
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
Part III. Relaxed controls
12. Spaces of relaxed controls. Topology and measure theory
13. Relaxed controls in finite dimensional systems
14. Relaxed controls in infinite dimensional systems. aThis 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 Kuhnâ€“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.
https://www.cambridge.org/core/books/infinite-dimensional-optimization-and-control-theory/01A8F63A952B118229FB4BCE5BD01FD6#fndtn-information aMathematical optimization aCalculus of variations aControl theory