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

2002/05/02 by M. Chyba, Monique Chyba, Naomi Ehrich Leonard +6
Computer Science · Engineering · Mathematics · #37N05 #57R27 #93B05 #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Robotic Mechanisms and Dynamics #Robotic Path Planning Algorithms #math.OC #msc:37N05 #msc:57R27 #msc:93B05

paper · pdf · doi:10.48550/arxiv.math/0205017

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

arxiv created 2002/05/02 · openalex publication_date 2002/05/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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