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

Authors: Fouzia Ghellab; Mohand Ouamer Bibi

Addresses: Research Unit LaMOS (Modeling and Optimization of Systems), Bejaia University, Bejaia, 06000, Algeria ' Research Unit LaMOS (Modeling and Optimization of Systems), Bejaia University, Bejaia, 06000, Algeria

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.

DOI: 10.1504/IJMOR.2021.115433

International Journal of Mathematics in Operational Research, 2021 Vol.19 No.1, pp.1 - 18

Received: 28 Feb 2019
Accepted: 23 Jan 2020
Published online: 02 Jun 2021 *

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