Optimal Control Problem for Switched System with the Nonsmooth Cost Functional

Abstract

We examine the relationships between lower exhausters quasidifferentiability (in the Demyanov and Rubinov sense) and optimal control for switching systems. Firstly we get necessary optimality condition for the optimal control problem for switching system in terms of lower exhausters. Then by using relationships between lower exhausters and quasidifferentiability we obtain necessary optimality condition in the case that the minimization functional satisfies quasidifferentiability condition.