Nonlinear stabilization via control-Lyapunov measure

Umesh Vaidya, Prashant G. Mehta, Vinayak V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

This paper is concerned with computational methods for Lyapunov-based control design of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. This paper poses and solves the co-design problem of jointly obtaining the control Lyapunov measure and a controller. The computational framework is based upon a set-oriented numerical approach. Using this approach, the codesign problem leads to a finite number of linear inequalities whose solutions define the feasible set of stabilizing controllers. We provide a proof of existence for a stochastic version of such a controller while the deterministic restriction is posed as the solution of a related integer programming problem. Mathematical programming techniques may be employed to obtain such controllers. Finally, an example is provided to illustrate the ideas.

Original languageEnglish (US)
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages1722-1727
Number of pages6
DOIs
StatePublished - Dec 1 2007
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

Fingerprint

Lyapunov
Stabilization
Controller
Co-design
Controllers
Stochastic Representation
Nonlinear dynamical systems
Mathematical programming
Nonlinear Dynamical Systems
Integer programming
Computational methods
Integer Programming
Mathematical Programming
Control Design
Computational Methods
Attractor
Linear Inequalities
Restriction

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Vaidya, U., Mehta, P. G., & Shanbhag, V. V. (2007). Nonlinear stabilization via control-Lyapunov measure. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 1722-1727). [4434956] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4434956
Vaidya, Umesh ; Mehta, Prashant G. ; Shanbhag, Vinayak V. / Nonlinear stabilization via control-Lyapunov measure. Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. 2007. pp. 1722-1727 (Proceedings of the IEEE Conference on Decision and Control).
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Vaidya, U, Mehta, PG & Shanbhag, VV 2007, Nonlinear stabilization via control-Lyapunov measure. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434956, Proceedings of the IEEE Conference on Decision and Control, pp. 1722-1727, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434956

Nonlinear stabilization via control-Lyapunov measure. / Vaidya, Umesh; Mehta, Prashant G.; Shanbhag, Vinayak V.

Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. 2007. p. 1722-1727 4434956 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - This paper is concerned with computational methods for Lyapunov-based control design of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. This paper poses and solves the co-design problem of jointly obtaining the control Lyapunov measure and a controller. The computational framework is based upon a set-oriented numerical approach. Using this approach, the codesign problem leads to a finite number of linear inequalities whose solutions define the feasible set of stabilizing controllers. We provide a proof of existence for a stochastic version of such a controller while the deterministic restriction is posed as the solution of a related integer programming problem. Mathematical programming techniques may be employed to obtain such controllers. Finally, an example is provided to illustrate the ideas.

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Vaidya U, Mehta PG, Shanbhag VV. Nonlinear stabilization via control-Lyapunov measure. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. 2007. p. 1722-1727. 4434956. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4434956