Optimal Control and Maximum Principle in (B)-Spaces. Examples for PDE in (H)-Spaces and ODE in\({{\mathbb{R}}^{n}}\)

Abstract

Observation and control problems in Banach (B)-spaces are investigated. A criterion for controllability and optimal controllability is formulated on the basis of the BUME method and the monotone mapping method. An inverse controllability problem is introduced, and an abstract maximum principle is formulated in (B)-spaces. For PDE in Hilbert (H)-spaces and for ODE in \({{\mathbb{R}}^{n}}\), an integral maximum principle is proved and an optimality system is presented.