Supervisory grey-based tracking control for non-linear dynamical systems

Abstract

Because the dynamic characteristics of many physical systems are non-linear and time varying, it is difficult to evaluate appropriate control effort to track the desired trajectory. To deal with this problem, a novel supervisory state feedback controller for unknown non-linear dynamical systems is proposed in this paper to achieve high-precision tracking performance. The proposed scheme comprises a grey uncertainty predictor and a state feedback linearization controller, which evaluates the control effort according to the forecasted data on line. Moreover, to stabilize the system states around a predefined bound region, a supervisory controller is added to adjust the control effort. The design process, theoretical and stability analysis are discussed in detail. Finally, three applications are provided to demonstrate the effectiveness of the proposed strategy. Compared with other methods, the proposed scheme possesses the salient advantages of a simple framework, free from chattering, stable tracking control performance, and robust to uncertainty.