97-04702 Burdick, Joel W. California Institute of Technology Postdoc: Planning for Hybrid Systems (This award supports CES associate Milos Zefran) Systems that are governed by discrete and continuous processes are known as "hybrid" systems. Such systems are described by continuous dynamical equations whose structure and/or inputs change in accordance with the state transitions of a finite automaton. Due to the widespread use of computers to control physical devices, hybrid systems abound. Successful hybrid systems must robustly combine high-level planning (planning of the finite automaton transitions) with low-level control (evolution of the dynamic equations). While the planning and control problems have been addressed separately by computer scientists and control theorists, the interaction of the discrete and continuous worlds is largely left to the ingenuity of engineers. As the complexity of the computer controlled physical systems grows, such methods break down and there is a need for rigorous theory to design, build, and evaluate hybrid systems. The proposed research will investigate how to unify discrete and continuous models to help build a foundation for hybrid system engineering. Prior work on planning for a subclass of hybrid systems will be extended in two directions. First, an optimal control framework will be extended to a game-theoretic framework so as to take uncertainty into account. Second, the hybrid control problem will be explored for systems whose dynamics exhibit some simplifying properties, such as Lie group symmetries.
