Optimal control of ODEs with dynamics uncertainty

Alessandro Scagliotti (Technical University of Munich)

Jeudi 21 novembre, 11h00, salle Coriolis (Galois).

Abstract. In this talk, we focus on problems related to the simultaneous optimal control of ensembles of dynamical systems (ODEs). These questions arise naturally in several situations in Applied Mathematics, for example when a usual control system (eg related to a physical or biomedical model) depends on parameters affected by uncertainty, or when the Cauchy datum is not available with precision due to measurement errors. Here, we typically aim at finding a strategy that should be the same for every system of the ensemble, and that minimizes a proper cost. In these cases, the proposed policy should incorporate the uncertainty that affects the system, and typically we seek one that results in a good performance in the most likely scenarios (averaged optimization), or one that guarantees resilience in the least favourable conjuncture (worst-case optimization).
We focus on the case of control-affine systems, and we derive the necessary optimality conditions for infinite ensembles in terms of the Pontryagin Maximum Principle.