This paper presents a nonlinear output tracking controller for non-minimum phase affine nonlinear systems. A new analytical method is given to find a proper synthetic output which makes the system minimum phase under a condition of static equivalence. This method is fully derived based on the closed form solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with the cheap control problem. The new methodology employs an algebraic equation for any system with scalar internal dynamics and a differential equation for those with an internal dynamics of higher order. Furthermore, a numerical simulation is carried out to show how the results of the experiment are consistent with those of the theoretical analysis.

本文提出了一种用于非最小相位仿射非线性系统的非线性输出跟踪控制器。给出了一种新的分析方法以找到合适的合成输出，该输出在静态等价条件下使系统处于最小相位。该方法是基于与廉价控制问题相关的Hamilton-Jacobi-Bellman（HJB）方程的闭合形式解而完全推导的。对于任何具有标量内部动力学的系统，新方法均采用代数方程，对于内部动力学较高的系统，则采用微分方程。此外，进行了数值模拟，以显示实验结果与理论分析的结果如何一致。