Quantized feedback adaptive command filtered backstepping control for a class of uncertain nonlinear strict-feedback systems

Abstract

An adaptive command filtered backstepping control design strategy in the presence of quantized states is presented for uncertain nonlinear systems in the strict-feedback form. A uniform quantizer quantizes all state variables, and the quantized state variables are only available for feedback. The existing quantized feedback recursive control design is only applicable to systems with nonlinearities matched to the control input because of its restriction that the partial derivatives of the virtual control laws with respect to state variables should be constants. Compared with the existing result, the primary contribution of this paper is to develop a quantized feedback recursive design using the command filtered backstepping technique for dealing with unmatched nonlinearities without this restriction. An adaptive tracking scheme using quantized states is constructed to compensate for quantization effects, and a new stability analysis strategy is established by analyzing the boundedness of the quantization errors of signals in the command filtered backstepping design framework. The stability of the closed-loop system is analyzed in the sense of uniform ultimate boundedness.