OPTIMAL-CONTROL PROBLEMS UNDER DISTURBANCES

Perturbations in optimal control problems are discussed. Problems including those with state and/or control constraints and discontinuities are considered. The perturbations may appear in the functional, as well as in the dynamics, the boundary conditions or the inequality constraints. It is shown that an optimal solution of the disturbed control problem depending continuously differentiably upon the perturbations exists in a neighborhood of an optimal solution of the undisturbed problem under an assumption which has to be intrinsically fulfilled for virtually all of the important numerical methods for the computation of boundary value problems. These methods may be used when the multipoint boundary value problem resulting from the necessary conditions has to be solved.