A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games
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- 11 July 2005
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 50 (7) , 947-957
- https://doi.org/10.1109/tac.2005.851439
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.Keywords
This publication has 36 references indexed in Scilit:
- On reachability and minimum cost optimal controlAutomatica, 2004
- Continuous Simulation, Differential Inclusions, Uncertainty, and Traveling in TimeSIMULATION, 2004
- Computational techniques for hybrid system verificationIEEE Transactions on Automatic Control, 2003
- Controllers for reachability specifications for hybrid systemsAutomatica, 1999
- Algorithmic analysis of nonlinear hybrid systemsIEEE Transactions on Automatic Control, 1998
- Computation of piecewise quadratic Lyapunov functions for hybrid systemsIEEE Transactions on Automatic Control, 1998
- Some applications of viscosity solutions to optimal control and differential gamesPublished by Springer Nature ,1997
- Analysis of digital circuits through symbolic reductionIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1991
- Some Properties of Viscosity Solutions of Hamilton-Jacobi EquationsTransactions of the American Mathematical Society, 1984
- Two approximations of solutions of Hamilton-Jacobi equationsMathematics of Computation, 1984