Dissipation analysis and H∞ control of stochastic nonlinear systems based on Hamiltonian realization

Yanhong Liu, Guizhou Cao, Shuxia Tang, Xiushan Cai

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

3 Scopus citations

Abstract

This paper proposes a novel dissipation analysis and a constructive H∞ control method for stochastic nonlinear systems. First, we put forward a sufficient condition for the dissipation of stochastic nonlinear systems by completing their Hamiltonian realization. The internal structure and energy property of the system is explored as well. Then, we show that the dissipation property is preserved for parallel and feedback interconnected dissipative stochastic Hamiltonian systems. Moreover, based on the dissipation property of the subsystems, a feedback dissipation controller is proposed for series interacted dissipative stochastic Hamiltonian systems. Finally, we propose an H∞ controller based on the stochastic dissipative Hamiltonian realization of uncertain stochastic nonlinear systems and show that the Hamiltonian function can be chosen to construct a solution of Hamiltonian- Jacobi inequality. Numerical simulation results illustrate the effectiveness of the proposed method.

Original languageEnglish
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3892-3897
Number of pages6
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Publication series

NameProceedings of the American Control Conference
Volume2016-July
ISSN (Print)0743-1619

Conference

Conference2016 American Control Conference, ACC 2016
CountryUnited States
CityBoston
Period07/6/1607/8/16

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    Liu, Y., Cao, G., Tang, S., & Cai, X. (2016). Dissipation analysis and H∞ control of stochastic nonlinear systems based on Hamiltonian realization. In 2016 American Control Conference, ACC 2016 (pp. 3892-3897). [7525520] (Proceedings of the American Control Conference; Vol. 2016-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525520