Ian Mitchell
Assistant Professor
Department of Computer Science
University of British Columbia
Hamilton-Jacobi (HJ) partial differential equations (PDEs) have a long history in optimal control and differential games. Only recently, however, has it become computationally practical to solve these PDEs for some systems of engineering interest. In this talk I will discuss algorithms -- based on level set methods -- for two such applications.
The Eikonal equation for first arrival time (a static HJ PDE) has been used previously for continuous path planning. By solving an auxiliary PDE at the same time we can extend this result to find constrained optimal paths.
Reachable sets can be used for safety verification, sythesis of safe control policies, and creation of discrete abstractions. For nonlinear systems, such as aircraft autopilots, a time dependent HJ PDE formulation allows more accurate approximation of the reachable set than any competing method.