Abstract
For a class of nonlinear systems with dynamic uncertainties, robust adaptive stabilization problem is considered in this paper. Firstly, by introducing an observer, an augmented system is obtained. Based on the system, we construct an exp-ISpS Lyapunov function for the unmodeled dynamics, prove that the unmodeled dynamics is exp-ISpS, and then obtain a dynamic normalizing signal to counteract the dynamic disturbances. By the backstepping technique, an adaptive controller is given, it is proved that all the signals in the adaptive control system are globally uniformly ultimately bounded, and the output can be regulated to the origin with any prescribed accuracy. A simulation example further demonstrates the efficiency of the control scheme.
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This work was supported by the National Natural Science Foundation of China (No. 60304003) and Program for New Century Excellent Talents in University (No. NCET-05-0607).
Haixia SU received her B.S. degree from Department of Mathematics at Qufu Normal University in 2003. Currently, she is pursuing her M.S. degree in Institute of Automation of the same university. Her research interest is non-linear adaptive control.
Xuejun XIE received his Ph.D. degree from the Institute of Systems Science, Chinese Academy of Sciences in 1999. He is currently a professor in Institute of Automation at Qufu Normal University. His research interests include adaptive control for complex systems.
Haikuan LIU received his B.S. degree from Harbin Institute of Technology at 1991. He is a professor at Xuzhou Normal university. His research interests include robust control, power source technology, and computer integrated system with application.
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Su, H., Xie, X. & Liu, H. Robust adaptive output stabilization using dynamic normalizing signal. J. Control Theory Appl. 5, 89–93 (2007). https://doi.org/10.1007/s11768-005-5312-4
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DOI: https://doi.org/10.1007/s11768-005-5312-4