Singular Trajectories in Multi-Input Time-Optimal Problems: Application to Controlled Mechanical Systems

M. Chyba, N.E. Leonard and E.D. Sontag

This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain special properties. These properties are explored and are used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated with an application to a time-optimal problem for a class of underwater vehicles.