Existence Theory and the Maximum Principle for Relaxed Infinite-Dimensional Optimal Control Problems

Abstract

Existence theorems are considered for relaxed optimal control problems described by semilinear systems in Banach spaces. Relaxed controls are used whose values are finitely additive probability measures; this class of relaxed controls does not require special assumptions (such as compactness) on the control set. Under suitable conditions, relaxed trajectories coincide with those obtained from differential inclusions. Existence theorems for relaxed controls are obtained that apply to distributed parameter systems described by semilinear parabolic and wave equations, as well as a version of Pontryagin's maximum principle for relaxed optimal control problems.

Keywords

This publication has 18 references indexed in Scilit:

Relaxation Theorems, Differential Inclusions, and Filippov′s Theorem for Relaxed Controls in Semilinear Infinite Dimensional Systems
Journal of Differential Equations, 1994
Optimal control problems for distributed parameter systems in Banach spaces
Applied Mathematics & Optimization, 1993
Necessary conditions for infinite-dimensional control problems
Mathematics of Control, Signals, and Systems, 1991
Relaxed controls in infinite dimensional systems
Published by Springer Nature ,1991
A unified theory of necessary conditions for nonlinear nonconvex control systems
Applied Mathematics & Optimization, 1987
Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space
Journal of Optimization Theory and Applications, 1986
Properties of Relaxed Trajectories for a Class of Nonlinear Evolution Equations on a Banach Space
SIAM Journal on Control and Optimization, 1983
Nonconvex minimization problems
Bulletin of the American Mathematical Society, 1979
The time-optimal control problem in Banach spaces
Applied Mathematics & Optimization, 1974
Linear operations on summable functions
Transactions of the American Mathematical Society, 1940