The time-optimal problem for controlled mechanical systems

Professor Monique Chyba, Department of Mathematics, University of California at Santa Cruz

This talk addresses the time-optimal control problem for a special class of control systems that includes the class of controlled mechanical systems with possible dissipation terms. Lie algebra associated to mechanical systems enjoy certain very special properties. These properties are explored and are used together with the Pontryagin maximum principle to determine the structure of singular extremals, and in particular, time-optimal trajectories. We illustrate the results on an application with the motion planning problem for underwater vehicles.