Adaptive Improved Dynamic Surface Control for a Class of Uncertain Nonlinear Systems in the presence of Input Hysteresis and Unknown Control Direction

This paper designs an adaptive improved dynamic surface controller for a class of uncertain nonlinear systems in the presence of input hysteresis and uncertain control direction. It is assumed that nonlinear functions in the system dynamics and parameters of the input nonlinearity are uncertain. At first, uncertain dynamics of the system is identified by the fuzzy system as a linear approximator. Then, the proposed improved dynamic surface controller is designed. In the proposed controller, a Nussbaum-type function is used to deal with the uncertain control direction problem. Also, for eliminating the “explosion of complexity” problem in the backstepping approach and sensitivity to the time constant of the filters in the dynamic surface control approach, a nonlinear tracking differentiator is used to obtain the virtual inputs derivative. Furthermore, by considering the norm of the adjustable parameters as an adaptive parameter, number of adaptive parameters and consequently computational burden are decreased considerably. Stability analysis of the proposed controller guarantees that all of the closed-loop signals are uniformly ultimately bounded. Also, adaptive laws for online tuning of adjustable parameters are proposed based on the Lyapunov method. Simulation results on two numerical and application examples verify the effectiveness and proper performance of the proposed controller.