The Banach method and the monotone mapping method for finding optimal controls in reflexive (B)-spaces

Abstract

Control and observation problems for operator equations of the first kind in reflexive strictly convex Banach spaces are considered. A BUME (Banach uniqueness and existence) method and a method of monotone nonlinear mappings for finding optimal (i.e., norm-minimal) controls are proposed, and an abstract maximum principle is stated. Under the additional assumption of separability and smoothness on (B)-spaces, an optimal control is found by the Galerkin method. As applications, ODE systems and partial differential equations are considered.