Approximation-based Adaptive Tracking of Uncertain Input-quantized Nonlinear Systems in the Presence of Unknown Quantization Parameter and Control Directions

Abstract

This paper investigates an adaptive tracking problem of input-quantized strict-feedback nonlinear systems with unknown quantization parameters, unmatched nonlinearities, and control directions. The hysteresis quantizer is considered to quantize the control input. Compared with the existing literature related to the input quantization, the main contribution of this paper is to design an adaptive neural network control scheme without requiring the exact knowledge of both the quantization parameters of the hysteresis quantizer and the control directions. A low-pass filter is employed to to overcome an algebraic-loop problem of the control input caused by the quantization error depending on the unknown quantization parameters and the control input. Furthermore, in order to deal with the unknown control direction problem in the presence of unknown quantization parameters, a bounding lemma for the parameter of Nussbaum gain function is presented in the dynamic surface design framework. The stability problem of the proposed adaptive control scheme is thoroughly investigated in the Lyapunov sense.