Optimal Control Approaches for a Fourth-Order Parabolic Operator: Least-Regrets Strategies

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Résumé

This paper deals with the control of a nonlinear ill-posed fourth-order parabolic system. To do this, we approach the
initial system by a regularize one, which requires the introduction of a pollution term, since the initial problem is with
missing data. An approach that naturally calls for the use of the notions of least-regret control. More precisely, we use
the concept of adapted least-regret control, because the nonlinearity of the problem does not ensure the uniqueness of an
optimal control. We then managed for a given no-regret control, after having verifying its existence, to characterize the
adapted least-regret control, before ending by establishing its convergence towards the no-regret control.

Mots-clés

Adapted Least-regrets Control, Nonlinear Analysis, Optimal Control, Singular Optimality System, No-regret Control