Controllability and Optimal Controllability for Operator Equations of the First Kind in (B)-Spaces: Examples for ODE in \({{\mathbb{R}}^{n}}\)

Abstract

For control and observation problems considered for operator equations of the first kind in Banach spaces, an controllability criterion is stated. In the case of reflexive strictly convex (B)-spaces, the BUME method and the method of monotone mappings are used to find optimal controls and an abstract maximum principle is formulated. The indicated problems for ODE systems in \({{\mathbb{R}}^{n}}\) are investigated as an example.