Adaptive State-Quantized Control for Mismatched Nonlinear Systems via a Dynamic Gain Approach
针对输入和状态量化导致反步设计失效的失配不确定非线性系统，提出一种基于动态增益的新补偿机制，将控制问题转化为动态变量设计，并证明闭环系统信号全局一致有界。
In this article, the adaptive backstepping control problem is investigated for a class of mismatched uncertain nonlinear systems with input and state quantization. All available states are generated by the static bounded quantizers, which can cause the failure of the recursive backstepping design. Previous results are based on linear-like virtual controllers to ensure that the partial derivatives of virtual controllers are constants, therefore, the systems are required to be an integral form or to meet matched conditions. Based on a dynamic gain approach, this article presents a new compensation mechanism to solve the difficulty of recursive backstepping design caused by discontinuous states, the control problem is transformed into a design problem of the dynamic variable. First, the dynamic variable is introduced based on a coordinate transformation, its derivative is used to compensate for discontinuous mismatched nonlinear terms. Then, with the help of the Lyapunov stability theorem, it is strictly proved that all signals of the closed-loop system are globally uniformly bounded. Finally, numerical simulations are provided to validate the effectiveness of the developed algorithm.