Sensitivity analysis for optimal control problems governed by nonlinear evolution inclusions

Abstract

Abstract We consider a nonlinear optimal control problem governed by a nonlinear evolution inclusion and depending on a parameter λ. First we examine the dynamics of the problem and establish the nonemptiness of the solution set and produce continuous selections of the solution multifunction ξ ↦ S ⁢ ( ξ ) ${\xi\mapsto S(\xi\/)}$ (ξ being the initial condition). These results are proved in a very general framework and are of independent interest as results about evolution inclusions. Then we use them to study the sensitivity properties of the optimal control problem. We show that we have Hadamard well-posedness (continuity of the value function), and we establish the continuity properties of the optimal multifunction. Finally, we present an application on a nonlinear parabolic distributed parameter system.