Robust Backstepping Control for A Class of Nonlinear Uncertain Systems with Input Quantization

In this paper, a robust backstepping controller is proposed for a class of nonlinear dynamic systems involving uncertain parameters and input quantization. The consideration of quantization is of practical importance, especially for networked control systems with limited communication bandwidth. Specifically, the logarithmic quantizer is employed to quantize the control signal prior to being transmitted over the communication channel to the remotely located nonlinear system. A robust control law is designed based on the backstepping method, which is able to compensate for the model parameter uncertainty, dynamic nonlinearities, and quantization errors effectively. The closed-loop stability and trajectory tracking performance are analyzed using the Lyapunov method. Simulation results are provided to show that (i) the states of the closed-loop system are globally bounded, and (ii) under any initial conditions, the tracking errors can converge to an arbitrarily small neighborhood of origin by increasing the control gains.