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

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  • Fouzia Ghellab
  • Mohand Ouamer Bibi

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.

Suggested Citation

  • Fouzia Ghellab & Mohand Ouamer Bibi, 2021. "Optimality and suboptimality criteria in a quadratic problem of optimal control with a piecewise linear entry," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 19(1), pages 1-18.
    • Handle: RePEc:ids:ijmore:v:19:y:2021:i:1:p:1-18
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