Singular Trajectories in Multi-Input Time-Optimal Problems:
Application to Controlled Mechanical Systems
M. Chyba, N.E. Leonard and E.D. Sontag
Journal of Dynamical and Control Systems, Vol. 9, No. 1, 2003, 73-88.
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.
(26 pages postscript)
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