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

M. Chyba; N. E. Leonard; E. D. Sontag

doi:10.1023/A:1022159318457

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

M. Chyba
, N. E. Leonard
, E. D. Sontag

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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.

Original language	English (US)
Pages (from-to)	103-129
Number of pages	27
Journal	Journal of Dynamical and Control Systems
Volume	9
Issue number	1
DOIs	https://doi.org/10.1023/A:1022159318457
State	Published - Jan 2003

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Algebra and Number Theory
Numerical Analysis
Control and Optimization

Keywords

Controlled mechanical systems
Maximum principle
Singular extremals
Time-optimal problem

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10.1023/A:1022159318457

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title = "Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems",

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.",

keywords = "Controlled mechanical systems, Maximum principle, Singular extremals, Time-optimal problem",

author = "M. Chyba and Leonard, \{N. E.\} and Sontag, \{E. D.\}",

note = "Funding Information: Research is partially supported by the Office of Naval Research under grant N00014-98-1-0649 and by the National Science Foundation under grant BES-9502477. Dept. of Mechanical and Aerospace Eng. D-234 Engineering Quad. Princeton University, Princeton, NJ 08544 and E.D. Sontag. Supported in part by US Air Force Grant F49620-01-1-0063.",

year = "2003",

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doi = "10.1023/A:1022159318457",

language = "English (US)",

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AU - Sontag, E. D.

N1 - Funding Information: Research is partially supported by the Office of Naval Research under grant N00014-98-1-0649 and by the National Science Foundation under grant BES-9502477. Dept. of Mechanical and Aerospace Eng. D-234 Engineering Quad. Princeton University, Princeton, NJ 08544 and E.D. Sontag. Supported in part by US Air Force Grant F49620-01-1-0063.

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N2 - 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.

AB - 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.

KW - Controlled mechanical systems

KW - Maximum principle

KW - Singular extremals

KW - Time-optimal problem

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JO - Journal of Dynamical and Control Systems

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IS - 1

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

Abstract

All Science Journal Classification (ASJC) codes

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