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

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.