Continuous Dependence of Solutions of a Differential Inclusion on the Right Hand Side with Applications to Stability of Optimal Control Problems

Abstract

Continuous dependence of the solution set of a differential inclusion on the right hand side is investigated. A mode of convergence for right hand sides, involving the notion of weak convergence of set-valued functions, is determined which is necessary and sufficient for convergence of the solution sets. In the case that the right hand sides depend affinely on the control, perturbations of the control constraint set with respect to which the solution set is stable are more explicitly characterized. Our results are applied to give necessary and sufficient conditions forstability of a general class of control problems under perturbations of the dynamics.