Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems

Details Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems

2002-05-02

arxiv.org/abs/math/0205017v1

Mathematics

Optimization and Control

See http://www.math.rutgers.edu/~sontag for related work

Scientific paper

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

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