A High-Order Semi-Lagrangian/Finite Volume Scheme for Hamilton-Jacobi-Isaacs Equations

Abstract : We present a numerical scheme for the approximation of Hamilton-Jacobi-Isaacs equations related to optimal control problems and differential games. In the first case, the Hamiltonian is convex with respect to the gradient of the solution, whereas the second case corresponds to a non convex (minmax) operator. We introduce a scheme based on the combination of semi-Lagrangian time discretization with a high-order finite volume spatial reconstruction. The high-order character of the scheme provides an efficient way towards accurate approximations with coarse grids. We assess the performance of the scheme with a set of problems arising in minimum time optimal control and pursuit-evasion games.
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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.105-117, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_10〉
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Maurizio Falcone, Dante Kalise. A High-Order Semi-Lagrangian/Finite Volume Scheme for Hamilton-Jacobi-Isaacs 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.105-117, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_10〉. 〈hal-01286403〉

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