Overcoming challenges in reducing spatially hybrid optimal control problems to classical ones: obtaining a hybrid maximum principle

par Anas Bouali

vendredi 3 févr. 2023, 10:30 → 11:30 Europe/Paris

XR203 (XLIM)

In this presentation we investigate a framework of hybrid optimal control problems that are comparable to well known frameworks in the literature, yet distinct in its approach and elements. Precisely we investigate a general optimal control problem in which the control system is described by a differential equation involving spatially heterogeneous dynamics. In this context the transition times from one set of dynamics to another are determined only by the state position and cannot be treated as additional parameters. We prove, using an explicit counterexample, that the standard augmentation technique used in the literature cannot be directly applied in our setting. However we show that this technique can be adapted by introducing a new concept of local solution to classical optimal control problems and by formulating a corresponding Pontryagin maximum principle. Finally, as an application, we show that our approach can be applied to solve optimal control problems with loss control regions, that is, regions of the state space where the control is constrained to be frozen. As an example we solve the minimum time problem for the double integrator including a loss control region.