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

Abstract : 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.
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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⟩

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