Lipschitzian Stability in Nonlinear Control and Optimization

Abstract

This paper studies Lipschitz properties, relative to the parameter p, of the set of solutions to problems of the form\[{\text{find }}z \in \Omega _p {\text{ such that }}T_p (z) \in F_p (z).\] As applications, various problems in control and optimization are examined, focusing in particular on the stability of the feasible set of a control problem, and the stability of solutions of infinite-dimensional mathematical programs and optimal control problems. In another application, an estimate is obtained for the error in the Euler approximation to an optimal control problem.