Second order switching time optimization for time-varying nonlinear systems

Elliot R. Johnson; Todd D. Murphey

doi:10.1109/CDC.2009.5400282

Second order switching time optimization for time-varying nonlinear systems

Elliot R. Johnson, Todd D. Murphey

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

10 Scopus citations

Abstract

This paper presents second-order switching time optimization techniques for nonlinear time-varying systems that are piecewise second-differentiable. The techniques are based on direct analysis of flows rather than constrained optimization methods, making it possible to take higher order derivatives. The resulting algorithms also use the same number of integrations along the trajectory regardless of the number of switching times. Two examples are included - a linear example seen previously in the literature and a nonlinear example that emphasizes the fast convergence rates of second-order optimizations compared to first order techniques (e.g. convergence in 19 iterations compared to over 25,000).

Original language	English (US)
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5281-5286
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5400282
State	Published - 2009
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: Dec 15 2009 → Dec 18 2009

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	12/15/09 → 12/18/09

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2009.5400282

Cite this

Johnson, E. R., & Murphey, T. D. (2009). Second order switching time optimization for time-varying nonlinear systems. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 5281-5286). Article 5400282 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5400282

Johnson, Elliot R. ; Murphey, Todd D. / Second order switching time optimization for time-varying nonlinear systems. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 5281-5286 (Proceedings of the IEEE Conference on Decision and Control).

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abstract = "This paper presents second-order switching time optimization techniques for nonlinear time-varying systems that are piecewise second-differentiable. The techniques are based on direct analysis of flows rather than constrained optimization methods, making it possible to take higher order derivatives. The resulting algorithms also use the same number of integrations along the trajectory regardless of the number of switching times. Two examples are included - a linear example seen previously in the literature and a nonlinear example that emphasizes the fast convergence rates of second-order optimizations compared to first order techniques (e.g. convergence in 19 iterations compared to over 25,000).",

author = "Johnson, \{Elliot R.\} and Murphey, \{Todd D.\}",

year = "2009",

doi = "10.1109/CDC.2009.5400282",

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series = "Proceedings of the IEEE Conference on Decision and Control",

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booktitle = "Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009",

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note = "48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 ; Conference date: 15-12-2009 Through 18-12-2009",

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Johnson, ER & Murphey, TD 2009, Second order switching time optimization for time-varying nonlinear systems. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5400282, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5281-5286, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 12/15/09. https://doi.org/10.1109/CDC.2009.5400282

Second order switching time optimization for time-varying nonlinear systems. / Johnson, Elliot R.; Murphey, Todd D.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 5281-5286 5400282 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - This paper presents second-order switching time optimization techniques for nonlinear time-varying systems that are piecewise second-differentiable. The techniques are based on direct analysis of flows rather than constrained optimization methods, making it possible to take higher order derivatives. The resulting algorithms also use the same number of integrations along the trajectory regardless of the number of switching times. Two examples are included - a linear example seen previously in the literature and a nonlinear example that emphasizes the fast convergence rates of second-order optimizations compared to first order techniques (e.g. convergence in 19 iterations compared to over 25,000).

AB - This paper presents second-order switching time optimization techniques for nonlinear time-varying systems that are piecewise second-differentiable. The techniques are based on direct analysis of flows rather than constrained optimization methods, making it possible to take higher order derivatives. The resulting algorithms also use the same number of integrations along the trajectory regardless of the number of switching times. Two examples are included - a linear example seen previously in the literature and a nonlinear example that emphasizes the fast convergence rates of second-order optimizations compared to first order techniques (e.g. convergence in 19 iterations compared to over 25,000).

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Johnson ER, Murphey TD. Second order switching time optimization for time-varying nonlinear systems. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 5281-5286. 5400282. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5400282

Second order switching time optimization for time-varying nonlinear systems

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