A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games Export

@article{MitchellBayen_TAC05, abstract = {We describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation. While alternative techniques for computing the reachable set have been proposed, the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters. Because the time-dependent equation's solution is continuous and defined throughout the state space, methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions. A numerical implementation of our formulation is described and has been released on the web. Its correctness is verified through a two vehicle, three dimensional collision avoidance example for which an analytic solution is available.}, author = {Mitchell, I. M. and Bayen, A. M. and Tomlin, C. J.}, booktitle = {Automatic Control, IEEE Transactions on}, citeulike-article-id = {3039984}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/TAC.2005.851439}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1463302}, doi = {10.1109/TAC.2005.851439}, journal = {Automatic Control, IEEE Transactions on}, keywords = {dynamic\_games, hjb\_equation, level\_set\_methods, numerical\_hjb}, number = {7}, pages = {947--957}, posted-at = {2008-07-24 15:43:09}, priority = {0}, title = {A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games}, url = {http://dx.doi.org/10.1109/TAC.2005.851439}, volume = {50}, year = {2005} }

TY - JOUR ID - MitchellBayen_TAC05 L3 - citeulike-article-id:3039984 N2 - We describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation. While alternative techniques for computing the reachable set have been proposed, the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters. Because the time-dependent equation's solution is continuous and defined throughout the state space, methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions. A numerical implementation of our formulation is described and has been released on the web. Its correctness is verified through a two vehicle, three dimensional collision avoidance example for which an analytic solution is available. IS - 7 JF - Automatic Control, IEEE Transactions on EP - 957 TI - A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games VL - 50 T2 - Automatic Control, IEEE Transactions on SP - 947 KW - dynamic_games KW - hjb_equation KW - level_set_methods KW - numerical_hjb AU - Mitchell, IM AU - Bayen, AM AU - Tomlin, CJ PY - 2005/// UR - http://dx.doi.org/10.1109/TAC.2005.851439 ER -