An Improved Control Algorithm for High-order Nonlinear Systems with Unmodelled Dynamics

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. 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.