A semi-Lagrangian scheme for Lp-penalized minimum time problems

Maurizio Falcone (1) , Dante Kalise (2) , Axel Kröner (3, 4)

1 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
2 RICAM - Johann Radon Institute for Computational and Applied Mathematics
3 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

In this paper we consider a semi-Lagrangian scheme for minimum time problems with Lp-penalization. The minimum time function of the penalized control problem can be characterized as the solution of a Hamilton-Jacobi Bellman (HJB) equation. Furthermore, the minimum time converges with respect to the penalization parameter to the minimum time of the non-penalized problem. To solve the control problem we formulate the discrete dynamic programming principle and set up a semi-Lagrangian scheme. Various numerical examples are presented studying the effects of different choices of the penalization parameters.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Maurizio Falcone, Dante Kalise, Axel Kröner. A semi-Lagrangian scheme for Lp-penalized minimum time problems. 21st International Symposium on Mathematical Theory of Networks and Systems, Jul 2014, Groningen, Netherlands. ⟨hal-01089877⟩