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

Fouzia Ghellab and Mohand Ouamer Bibi

International Journal of Mathematics in Operational Research, 2021, vol. 19, issue 1, 1-18

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.

Keywords: optimality criterion; sufficient condition of suboptimality; quadratic optimal control problem; piecewise linear entry. (search for similar items in EconPapers)
Date: 2021
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