Towards efficient computation of solutions to hybrid systems

We present our algorithm for computing reachable sets for hybrid systems, which is based on solving a pair of coupled Hamilton-Jacobi partial differential equations. The algorithm allows for complex nonlinear continuous dynamics, yet the numerical difficulty in computing solutions increases greatly with the order and complexity of these dynamics. We review a level set technique by Osher and Sethian (1988) for numerically solving Hamilton-Jacobi equations, and discuss its adaptation to performing reachability analysis of hybrid systems.