Adaptive Control via Neural Output Feedback for a Class of Nonlinear Discrete-Time Systems in a Nested Interconnected Form
针对一类多输入多输出非仿射非线性离散时间系统，提出一种自适应输出反馈控制方法，通过坐标变换和隐函数定理设计控制器，并利用李雅普诺夫方法保证信号有界和跟踪误差收敛。
In this paper, an adaptive output feedback control is framed for uncertain nonlinear discrete-time systems. The considered systems are a class of multi-input multioutput nonaffine nonlinear systems, and they are in the nested lower triangular form. Furthermore, the unknown dead-zone inputs are nonlinearly embedded into the systems. These properties of the systems will make it very difficult and challenging to construct a stable controller. By introducing a new diffeomorphism coordinate transformation, the controlled system is first transformed into a state-output model. By introducing a group of new variables, an input-output model is finally obtained. Based on the transformed model, the implicit function theorem is used to determine the existence of the ideal controllers and the approximators are employed to approximate the ideal controllers. By using the mean value theorem, the nonaffine functions of systems can become an affine structure but nonaffine terms still exist. The adaptation auxiliary terms are skillfully designed to cancel the effect of the dead-zone input. Based on the Lyapunov difference theorem, the boundedness of all the signals in the closed-loop system can be ensured and the tracking errors are kept in a bounded compact set. The effectiveness of the proposed technique is checked by a simulation study.