Two Semi-Lagrangian Fast Methods for Hamilton-Jacobi-Bellman Equations

Abstract : In this paper we apply the Fast Iterative Method (FIM) for solving general Hamilton–Jacobi–Bellman (HJB) equations and we compare the results with an accelerated version of the Fast Sweeping Method (FSM). We find that FIM can be indeed used to solve HJB equations with no relevant modifications with respect to the original algorithm proposed for the eikonal equation, and that it overcomes FSM in many cases. Observing the evolution of the active list of nodes for FIM, we recover another numerical validation of the arguments recently discussed in [1] about the impossibility of creating local single-pass methods for HJB equations.
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Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.74-84, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_7〉
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Simone Cacace, Emiliano Cristiani, Maurizio Falcone. Two Semi-Lagrangian Fast Methods for Hamilton-Jacobi-Bellman Equations. Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.74-84, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_7〉. 〈hal-01286401〉

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