In this presentation, we address optimal control problems involving loss control regions. In this context, the state space is partitioned into disjoint sets referred to as regions, which are classified into two types: control regions and loss control regions. When the state belongs to a control region, the control is permanent (i.e., the control value can be modified at any time). On the other hand, when the state belongs to a loss control region, the control must remain constant, equal to the last assigned value before the state enters the loss control region, and this value is kept until the state exits this region. The goal of this presentation is twofold. First, we reformulate the above setting into a hybrid optimal control problem (with spatially heterogeneous dynamics) involving a regionally switching parameter, and we prove a corresponding hybrid maximum principle. Second, we propose a two-step numerical scheme to solve optimal control problems with loss control regions. The approach is based on a direct numerical method applied to a regularized problem, which initializes an indirect numerical method based on the previously mentioned optimality conditions and applied to the original problem. Lastly, we apply this numerical approach to several illustrative examples.
Articles associés à cette présentation :
https://hal-univ-avignon.archives-ouvertes.fr/ hal-04137550
https://hal-univ-avignon. archives-ouvertes.fr/hal-03985420
https://hal.archives-ouvertes.fr/hal-03638701
