Abstract
In this paper, we consider a class of high-order nonlinear systems with unmodelled dynamics from the viewpoint of maintaining the desired control performance (e. g., asymptotical stability) and reducing the control effort. By introducing a new rescaling transformation, adopting an effective reduced-order observer, and choosing an ingenious Lyapunov function and appropriate design parameters, this paper designs an improved output-feedback controller. The output-feedback controller guarantees the globally asymptotical stability of the closed-loop system. Subsequently, taking a concrete system for an example, the smaller critical values for gain parameter and rescaling transformation parameter are obtained to effectively reduce the control effort.
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W. Lin. [Online], Available: http://nonlinear.case.edu/~linwei.
W. Lin, C. J. Qian. Adding One Power Integrator: A Tool for Global Stabilization of High-order Lower-triangular Systems. Systems & Control Letters, vol. 39, no. 5, pp. 339–351, 2000.
W. Lin, C. J. Qian. Adaptive Regulation of High-order Lower-triangular Systems: An Adding a Power Integrator Technique. Systems & Control Letters, vol. 39, no. 5, pp. 353–364, 2000.
W. Lin, C. J. Qian. Robust Regulation of a Chain of Power Integrators Perturbed by a Lower Triangular Vector Field. International Journal of Robust and Nonlinear Control, vol. 10, no. 5, pp. 397–421, 2000.
C. J. Qian, W. Lin. Smooth Output Feedback Stabilization of Planar Systems without Controllable/Observable Linearization. IEEE Transactions on Automatic Control, vol. 47, no. 12, pp. 2068–2073, 2002.
C. J. Qian, W. Lin. Nonsmooth Output Feedback Stabilization of a Class of Genuinely Nonlinear Systems in the Plane. IEEE Transactions on Automatic Control, vol. 48, no. 10, pp. 1824–1829, 2003.
B. Yang, W. Lin. Homogeneous Observers, Iterative Design, and Global Stabilization of High-order Nonlinear Systems by Smooth Output Feedback. IEEE Transactions on Automatic Control, vol. 49, no. 7, pp. 1069–1080, 2004.
B. Yang, W. Lin. Robust Output Feedback Stabilization of Uncertain Nonlinear Systems with Uncontrollable and Unobservable Linearization. IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 619–630, 2005.
J. Li, C. J. Qian. Global Finite-time Stabilization by Dynamic Output Feedback for a Class of Continuous Nonlinear Systems. IEEE Transactions on Automatic Control, vol. 51, no. 5, pp. 879–884, 2006.
C. J. Qian, W. Lin. Recursive Observer Design, Homogeneous Approximation, and Nonsmooth Output Feedback Stabilization of Nonlinear Systems. IEEE Transactions on Automatic Control, vol. 51, no. 9, pp. 1457–1471, 2006.
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This work was supported by National Natural Science Foundation of China (No. 60774010), Natural Science Foundation of Jiangsu Province, Jiangsu “Six Top Talents” (No. 07-A-020), Program for Fundamental Research of Natural Sciences in Universities of Jiangsu Province (No. 07KJB510114), and Natural Science Foundation of Xuzhou Normal University (No. 08XLB20).
Na Duan is currently a Ph. D. candidate at Qufu Normal University, PRC and an assistant at Xuzhou Normal University, PRC.
Her research interests include nonlinear adaptive control and stochastic nonlinear control.
Fu-Nian Hu is a professor at Xuzhou Normal University, PRC.
His research interests include control of power systems and theory of electricity market.
Xin Yu is a master student at Qufu Normal University, PRC.
His research interests include nonlinear adaptive control and stochastic nonlinear control.
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Duan, N., Hu, FN. & Yu, X. An improved control algorithm for high-order nonlinear systems with unmodelled dynamics. Int. J. Autom. Comput. 6, 234–239 (2009). https://doi.org/10.1007/s11633-009-0234-0
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DOI: https://doi.org/10.1007/s11633-009-0234-0