A Patchy Dynamic Programming Scheme for a Class of Hamilton-Jacobi-Bellman Equations

Abstract : In this paper we present a new parallel algorithm for the solution of Hamilton-Jacobi- Bellman equations related to optimal control problems. The main idea is to divide the domain of computation into subdomains following the dynamics of the control problem. This results in a rather complex geometrical subdivision, but has the advantage that every subdomain is invariant with respect to the optimal controlled vector field, so that we can compute the value function in each subdomain assigning the task to a processor and avoiding the classical transmission condition on the boundaries of the subdomains. For this specific feature the subdomains are patches in the sense introduced by Ancona and Bressan in [1]. Several examples in dimension two and three illustrate the properties of the new method.
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SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 34 (5), pp.A2625-A2649. 〈10.1137/110841576〉
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Simone Cacace, Emiliano Cristiani, Maurizio Falcone, Athena Picarelli. A Patchy Dynamic Programming Scheme for a Class of Hamilton-Jacobi-Bellman Equations. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 34 (5), pp.A2625-A2649. 〈10.1137/110841576〉. 〈inria-00628108〉

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