Nonlinear Dynamic Surface Control for a Class of Uncertain Systems With Novel Nonlinear Filters

Novel nonlinear functions are introduced to construct first-order nonlinear filters to address the following critical issues encountered in widely used dynamic surface control (DSC) methods. Firstly, there is no guideline for selecting the parameters of the first-order filters which depend on the upper bounds of complicated composite functions. Secondly, the parameters of the filters cannot be obtained for adaptive dynamic surface control (ADSC) in the presence of totally unknown parameters since the composite functions involve the parameter estimate errors and their upper bounds which are not available. Therefore, it is not possible to determine the parameters of the filters. Thirdly, the initial states of the filters depend on the initial conditions of the system directly, thus a DSC-based scheme renders the control system only locally or semi-globally stable. Our designed nonlinear filters not only avoid repeated differentiations of virtual controls, but also guarantee the global boundedness of all the signals in the closed-loop system. Furthermore, instead of calculating the upper bounds of composite functions to obtain the parameters for the traditional DSC, the control parameters of the proposed NDSC and ADSC methods can be chosen arbitrarily. Simulation results verify the effectiveness of the proposed methods.