Control and Observation Problems in Banach Spaces. Optimal Control and Maximum Principle. Applications to Ordinary Differential Equations in ℝn

Abstract

In a Banach space, we study an equation of the first kind as an observation problem, with the adjoint equation considered as a control problem. The Banach uniqueness and existence method and the monotone mapping method are applied to the study of these observation and control problems. For the case of reflexive Banach spaces, a controllability criterion and an abstract maximum principle are proved. In particular, it is established that continuous observability implies the existence and uniqueness of the solution of the inverse controllability problem and an estimate for the solution.