Abstract
This paper addresses the global adaptive control problem for a class of uncertain stochastic nonlinear systems in the output-feedback form. Due to the unknown output gain, we construct a full-order homogeneous observer instead of using the system output. Then, by adding a power integrator technique, an output-feedback controller is designed, as well as an adaptive law to deal with the unknown nonlinear growth rates. Based on the generalized stochastic Lyapunov stability theorem, it can be proved that all the signals of the closed-loop system are bounded in probability, and the system states converge to the origin almost surely.
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Recommended by Associate Editor Juhoon Back under the direction of Editor Ju Hyun Park. This work was supported in part by National Natural Science Foundation of China (61473082,61273119), the Fundamental Research Funds for the Central Universities, Six Talents Peaks Program of Jiangsu Province (2014-DZXX-003) and PAPD.
Wenting Zha received her Bachelor’s degree from the Department of Mathematics, Southeast University in 2011. Now, she is a Ph.D. candidate at the School of Automation, Southeast University. From September 2014 to September 2015, she was a joint Ph.D. student at the University of Texas at San Antonio. Her research interests include nonlinear system control, adaptive control and stochastic systems.
Junyong Zhai received his Ph.D. degree in Automatic Control from Southeast University in 2006. From September 2009 to September 2010, he was a postdoctoral research fellow at the University of Texas at San Antonio. He is currently a professor at the School of Automation, Southeast University. His current research interests include nonlinear systems control, robot control, stochastic time-delay systems, and multiple models switching control.
Shumin Fei received his Ph.D. degree from Beijing University of Aeronautics and Astronautics in 1995. From 1995 to 1997, he was a postdoctoral research fellow at Southeast University. Presently, he is a professor and doctoral advisor at the School of Automation, Southeast University. He has published more than 100 journal papers. His research interests include nonlinear systems, stability theory of delayed system, complex systems and so on.
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Zha, W., Zhai, J. & Fei, S. Global adaptive control for a class of uncertain stochastic nonlinear systems with unknown output gain. Int. J. Control Autom. Syst. 15, 1125–1133 (2017). https://doi.org/10.1007/s12555-016-0023-9
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DOI: https://doi.org/10.1007/s12555-016-0023-9