Un workshop franco-chilien en Contrôle Optimal (lien) aura lieu Vendredi 4 juillet dans la salle René Baire de 8h30 à 12h45.

Organization

Xavier Dupuis (Université Bourgogne Europe)
Cristopher Hermosilla (Universidad Técnica Federico Santa María)

Financial Support

Talks

Nicolas Hernandez (Universidad Técnica Federico Santa María)
Pollution regulation for electricity generators in a transmission network

Abstract: In this paper we study a pollution regulation problem in an electricity market with a network structure. The market is ruled by an independent system operator (ISO) who has the goal of reducing the pollutant emissions of the providers in the network by encouraging the use of cleaner technologies. The problem of the ISO formulates as a contracting problem with each one of the providers, who interact among themselves by playing a stochastic differential game. The actions of the providers are not observable by the ISO which faces the moral hazard. By using the dynamic programming approach, we represent the value function of the ISO as the unique viscosity solution to the corresponding Hamilton-Jacobi-Bellman equation. We prove that this solution is smooth and characterize the optimal controls for the ISO. Numerical solutions to the problem are presented and discussed. We consider also a simpler problem for the ISO, with constant production levels, that can be solved explicitly in a particular setting. This is a joint work with Alejandro Jofré (CMM) and Dylan Possamaï (ETH).

Cristopher Hermosilla (Universidad Técnica Federico Santa María)
Self-dual approximations to fully convex Bolza problems

Abstract: The aim of this talk is to present a one-parameter regularization technique for fully convex Bolza (FCB) problems with state constraints. This approach is based on the Goebel’s self-dual smoothing method. The main feature of this regularization technique is that it allows to simultaneously approximate the FCB problem (primal problem) as well as its dual problem (which is also an FCB problem), by a primal-dual pair of FCB problems with no state constraints, and for which it is always possible to ensure the existence of minimizers (absolutely continuous arcs). We demonstrate, under suitable conditions, that the minimizers of the approximated primal problems converge (up to a subsequence) to a minimizer of the primal.

Abderrahim Jourani (Université Bourgogne Europe)
On optimal control of sweeping processes

Abstract : à venir 

Emilio Vilches (Universidad de O’Higgins)
Hamilton-Jacobi-Bellman approach for optimal control problems of sweeping processes

Abstract: In this talk, we are concerned with a state-constrained optimal control problem governed by Moreau’s sweeping process with a controlled drift. We discuss the Bellman approach for an infinite horizon problem. In particular, we establish the regularity of the value function and the Hamilton-Jacobi-Bellman equation it satisfies. We present a uniqueness result and make a comparison with standard state-constrained optimal control problems to highlight the regularizing effect that the sweeping process induces on the value function.

Laila Alsharief (Université Bourgogne Europe)
Optimal control of implicit polyhedral sweeping processes involving the coderivative of the projection mapping

Abstract: This work aims to provide a maximum principle for a class of optimal control problems governed by an implicit sweeping process with a general endpoint constraint. The swept set is assumed to be polyhedral and control-dependent, while the nonautonomous dynamics governing the optimal control problem depend simultaneously on the state and the control. This dependence appears in the differential inclusion as well as in the perturbation term. Our approach is based on computing the coderivative of the metric projection mapping onto a polyhedral convex set. We apply our results to the projection of a Lotka-Volterra type model for two species.