Seminario di Equazioni Differenziali e Applicazioni: “Minimum time problem for the controlled sweeping process”

Martedì 24 Maggio 2016, ore 12:00 - Aula 2BC30 - Michele Palladino

ARGOMENTI: Seminari

Martedì 24 Maggio 2016 alle ore 12:00 in Aula 2BC30, Michele Palladino (Penn State University, USA) terrà un seminario dal titolo “Minimum time problem for the controlled sweeping process“.

Abstract
In this talk, we address some recent advances in Dynamic Optimization for the Controlled Sweeping Process (also known in the literature as Moreau’s process)
$$(\star) \quad \dot{x} \in -N_{C(t)}(x) + f (t, x, u), \quad u \in U$$
where $C(.)$ is a Lipschitz continuous set-valued mapping. Such a framework is a general way to model optimal control problems with state constraints depending on time, but it also arises in many other applications like crowd motion, electric circuit and mechanical system modelling. Here we present a minimum time problem related $(\star)$ and we characterize the minimum time function $T(t, x)$ as the continuous solution of a set of Hamilton-Jacobi inequalities. The main difficulty is due to the presence of the normal cone $N_{C(t)}(x)$ in the right hand side of $(\star)$, which is a not Lipschitz continuous mapping with respect to $x$ and contains implicitly the state constraint $x(t) \in C(t)$.

Rif. Int. M. Bardi, C. Marchi, G. Colombo