This paper presents a new study on adaptive state feedback output tracking control problem for uncertain discrete-time nonlinear systems in a general non-canonical form. Time-advance operations on the output of such systems result in the output dynamics being nonlinearly dependent on the control input and unknown parameters, which leads to three technical issues: implicit relative degree; nonlinearly parameterized uncertainties; and non-affine control input. To address these issues, this paper first employs feedback linearization and implicit function theory to construct a relative degree dependent normal form; then proposes an adaptive parametric reconstruction based method to simultaneously deal with linearly and nonlinearly parameterized uncertainties in the output dynamics; and finally constructs a key implicit function equation to derive a unique adaptive control law which ensures closed-loop stability and asymptotic output tracking. An explicitly iterative solution based adaptive control law is also proposed to ensure closed-loop stability and bounded output tracking within any degree of accuracy. The simulation verifies the effectiveness of the proposed adaptive control method.

本文提出了一种不确定的离散时间非线性系统的一般非规范形式的自适应状态反馈输出跟踪控制问题的新研究。在此类系统的输出上进行时间前移操作会导致输出动力学非线性地取决于控制输入和未知参数，从而导致三个技术问题：隐式相对度；非线性参数化不确定性；和非仿射控制输入。为了解决这些问题，本文首先采用反馈线性化和隐函数理论构造相对度相关的范式。然后提出了一种基于自适应参数重构的方法，可以同时处理输出动力学中线性和非线性参数化的不确定性。最后构造一个关键的隐函数方程，以导出独特的自适应控制律，从而确保闭环稳定性和渐近输出跟踪。还提出了基于显式迭代解决方案的自适应控制律，以确保闭环稳定性和在任何精度范围内的有界输出跟踪。仿真验证了所提出的自适应控制方法的有效性。