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 (e.g. 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. In this setting, we typically aim at finding a strategy that should be the same for every system of the ensemble, and that minimizes a proper cost.

Here, we focus on minimax problems, whose solutions guarantee resilience in the least favourable conjuncture (worst-case optimization), and we establish a PMP.

We propose as an application the minimax problems related to C^0 approximations of diffeomorphisms.