Abstract
This paper studies the problem of controller design for pure-feedback nonlinear systems with asymmetric time-varying full state constraints. The mean value theorem is employed to transform a pure-feedback system into a strict-feedback structure with non-affine terms. For the transformed system, a time-varying asymmetric Barrier Lyapunov Function (ABLF) with the error variables is employed to ensure the time-varying constraints satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed efficiently. The presented control scheme can guarantee that all signals in the closed-loop system are ultimately bounded. It is also proved that the tracking error converges to an adjustable neighborhood of the origin even in the presence of disturbance. The performance of the ABLF-based control are illustrated through two examples.
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Recommended by Associate Editor Hyo-Sung Ahn under the direction of Editor Jessie(Ju H.) Park. This work is supported by National Natural Science Foundation (NNSF) of China under Grant 61673243, 61273091, 61303198 and 61304008, the Project of Taishan Scholar of Shandong Province of China, the PhD Programs Foundation of Ministry of Education of China under Grant 20123705110002.
Chun-Xiao Wang is currently a Ph.D. candidate in Control Theory of Qufu Normal University. She is also an Associate Professor in School of Science, Shandong Jianzhu University. Her research interests include adaptive nonlinear control and constraint control.
Yu-Qiang Wu received the Ph.D. degree in Automatic Control from Southeast University in 1994. He is currently a professor in the Research Institute of Automation, Qufu Normal University, Qufu, China. His research interests include variable structure control and nonlinear system control.
Jiang-Bo Yu received the Ph.D. degree in Control Science and Engineering from Southeast University in 2012. He is currently an Associate Professor in School of Science, Shandong Jianzhu University. His research interests include robust and adaptive nonlinear control, as well as their applications into nonholonomic mobile robots, etc.
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Wang, C., Wu, Y. & Yu, J. Barrier Lyapunov functions-based adaptive control for nonlinear pure-feedback systems with time-varying full state constraints. Int. J. Control Autom. Syst. 15, 2714–2722 (2017). https://doi.org/10.1007/s12555-016-0321-2
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DOI: https://doi.org/10.1007/s12555-016-0321-2