In this paper we are concerned with multiscale modeling, control, and simulation of self-organizing agents leaving an unknown area under limited visibility, with special emphasis on crowds. We firs...

A procedure for the numerical approximation of high-dimensional Hamilton--Jacobi--Bellman (HJB) equations associated to optimal feedback control problems for semilinear parabolic equations is proposed. Its main ingredients are a pseudospectral collocation approximation of the PDE dynamics and an iterative method for the nonlinear HJB equation associated to the feedback synthesis. The latter is known as the successive Galerkin approximation. It can also be interpreted as Newton iteration for the HJB equation. At every step, the associated linear generalized HJB equation is approximated via a separable polynomial approximation ansatz. Stabilizing feedback controls are obtained from solutions to the HJB equations for systems of dimension up to fourteen.

A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton--Jacobi--Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The...

We address the numerical approximation of mean field games with local couplings. For power-like Hamiltonians, we consider a stationary system and also a system involving density constraints modeling hard congestion effects. For finite difference discretization of the mean field game system developed in [Y. Achdou and I. Capuzzo-Dolcetta, SIAM J. Numer. Anal., 48 (2010), pp. 1136--1162], we follow a variational approach. We prove that the aforementioned schemes can be obtained as the optimality system of suitably defined optimization problems. In order to prove the existence of solutions of the scheme with a variational argument, monotonicity assumptions on the coupling term are not needed, which allows us to recover general existence results proved by Achdou and Capuzzo-Dolcetta. Next, assuming that the coupling term is nondecreasing, the variational problem is cast as a convex optimization problem, for which we study and compare several proximal-type methods. These algorithms have several interesting fea...

This paper presents the design of a predictive speed controller for electrical drives. The control scheme does not have a cascaded structure; instead, it uses a single optimization algorithm to generate the control action to be applied at the next sampling instant. The control is based on the optimization of a cost function, which is designed using the insight given by the solution of the minimum-time control problem for a simplified system, namely, the double integrator, which is a reasonable model of the machine dynamic behavior. The experimental results obtained with a permanent-magnet synchronous motor and an induction machine, fed by a two-level three-phase inverter, confirm that this approach reaches a very good dynamic performance without a high computational effort.