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New results in global stabilization for stochastic nonlinear systems

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Abstract

This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.

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Authors and Affiliations

  1. Control and Networks Lab, Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, 5 Metrotech Center, Brooklyn, NY, 11201, USA

    Tao Bian & Zhong-Ping Jiang

Authors
  1. Tao Bian
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  2. Zhong-Ping Jiang
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Corresponding author

Correspondence to Tao Bian.

Additional information

This work was partially supported by the National Science Foundation (Nos. ECCS-1230040, ECCS-1501044).

Tao BIAN received the B.Eng. degree in Automation from Huazhong University of Science and Technology, Wuhan, China, in 2012, and the M.Sc. degree in Electrical Engineering from New York University, NY, in 2014, where he is currently working toward the Ph.D. degree. His research interests include approximate/adaptive dynamic programming, nonlinear control, and stochastic control systems.

Zhong-Ping JIANG received the B.Sc. degree in Mathematics from the University of Wuhan, Wuhan, China, in 1988, the M.Sc. degree in Statistics from the Universite de Paris-sud, France, in 1989, and the Ph.D. degree in Automatic Control and Mathematics from the Ecole des Mines de Paris, France, in 1993. Currently he is a Professor of Electrical and Computer Engineering at New York University Tandon School of Engineering (formerly called Polytechnic University). His main research interests include stability theory, the theory of robust and adaptive nonlinear control, and their applications to underactuated mechanical systems, congestion control, wireless networks, multi-agent systems and systems physiology. Dr. Jiang has served as a Subject Editor for the International Journal of Robust and Nonlinear Control, and as an Associate Editor for Systems & Control Letters, IEEE Transactions on Automatic Control and European Journal of Control. Dr. Jiang is a recipient of the prestigious Queen Elizabeth II Fellowship Award from the Australian Research Council, the CAREER Award from the U.S. National Science Foundation, and the Young Investigator Award from the National Natural Science Foundation of China. He (together with coauthor Yuan Wang) received the Best Theoretic Paper Award at the 2008 World Congress on Intelligent Control and Automation, June 2008, for the paper “A Generalization of the Nonlinear Small-Gain Theorem for Large-Scale Complex Systems”. Dr. Jiang is a Fellow of the IEEE and a Fellow of IFAC.

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Bian, T., Jiang, ZP. New results in global stabilization for stochastic nonlinear systems. Control Theory Technol. 14, 57–67 (2016). https://doi.org/10.1007/s11768-016-5117-7

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  • DOI: https://doi.org/10.1007/s11768-016-5117-7

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