Stability and sensitivity of solutions to optimal control problems for systems with control appearing linearly

Abstract

We consider a family of optimal control problems for systems described by nonlinear ordinary differential equations with control appearing linearly. The cost functionals and the control constraints are convex. All data depend on a vector parameter. Using the concept of the second-order sufficient optimality conditions it is shown that the solutions of the problems, as well as the associated Lagrange multipliers, are locally Lipschitz continuous and directionally differentiable functions of the parameter.