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Journal of Dynamical and Control Systems

, Volume 9, Issue 1, pp 103–129 | Cite as

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

  • M. Chyba
  • N.E. Leonard
  • E.D. Sontag
Article

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.

Controlled mechanical systems time-optimal problem maximum principle singular extremals 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • M. Chyba
    • 1
  • N.E. Leonard
    • 2
  • E.D. Sontag
    • 3
  1. 1.Dept. of Mathematics, 379 Applied Sciences BuildingUniversity of Santa Cruz
  2. 2.Dept. of Mechanical and Aerospace Eng.Princeton UniversityPrinceton
  3. 3.Dept. of Mathematics, Hill CenterRutgers UniversityPiscataway

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