On the degeneracy of optimality conditions for control problems with set-inclusion constraints

Abstract

In this paper, we provide first order necessary conditions of optimality for nonlinear control problems with endpoint and pathwise state constraints in the form of set inclusions. We are interested in strengthened forms of the optimality conditions that are able to avoid the degeneracy phenomenon. We discuss how previous results involving functional inequality pathwise state constraints and fixed initial state might be extended to cover the problems with constraints in the form of set inclusions. The time symmetry of such formulation enables one to immediately established a strengthened form of the maximum principle that, under suitable constraint qualifications, can avoid both left and rightendpoints degeneracy.