Optimality and suboptimality criteria in a quadratic problem of optimal control with a piecewise linear entry

Abstract

In the present paper, we intend to minimise a terminal quadratic functional of optimal control with a piecewise linear entry and that by using a support concept. The latter is connected to the existence of a non-degenerate matrix used to calculate the Lagrange multiplier y and the conjugate function Ψ via a direct way, contrary to the traditional maximum principle. We prove the optimality criterion by means of the implicit functions theorem. Then, we reformulate it as a support maximum principle from which we derive a sufficient condition of suboptimality. The obtained results are illustrated by a numerical example on mechanics.