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

Authors:
M. Chyba;N. E. Leonard;E. D. Sontag
Affiliations:
Dept. of Mathematics, 379 Applied Sciences Building, University of Santa Cruz, CA 95064;Dept. of Mechanical and Aerospace Eng., D-234 Engineering Quad., Princeton University, Princeton, NJ 08544;Dept. of Mathematics, Hill Center, Rutgers University, Piscataway, NJ 08854-8019
Venue:
Journal of Dynamical and Control Systems
Year:
2003

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Abstract

This paper deals with 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 have certain special properties. These properties are explored and 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 by an application to a time-optimal problem for a class of underwater vehicles.