Boundary value problem for multivalued differential equations and controllability

Abstract

Control process of the type x = f( t, x, u), u ϵ U( t, x), can be deparametrized by writing them in terms of multivalued differential equations of the form x ϵ F( t, x) = { f( t, x, u): u ϵ U( t, x)}. So, under suitable hypotheses, the controllability problem turns out to be equivalent to a two-point boundary value problem for a multivalued differential equation. In this paper an existence theorem is sought for the latter boundary value problem. The result is achieved by using the fixed point argument as a crucial tool.