High-Order Fully Actuated System Approaches for a Class of Pseudo Pure-Feedback Nonlinear Systems
本文针对一类广义伪纯反馈非线性系统，提出一种递归设计方法将其转化为高阶全驱动系统，从而避免传统反步法的复杂性爆炸问题，并实现期望的控制性能。
The high-order fully actuated (HOFA) system approaches are utilized in this article to solve the synthesis problem of a class of generalized pseudo pure-feedback nonlinear control systems (PPFNCSs). Contrary to the traditional state space method, a recursive design approach is proposed to transform the generalized PPFNCSs into HOFA systems by adopting the idea of “ascending order and descending dimension.” In this framework, a class of generalized first-order, second-order, and mixed-order PPFNCSs are transformed into HOFA models based on the newly proposed generalized inverse function lemma, which overcomes the problem that traditional backstepping design methods are not applicable to such systems without any restrictions. Based on this, the linear time-invariant systems with the desired characteristic structure are derived by designing control strategies for the transformed HOFA systems, which not only achieves the desired control performance but also successfully avoids the problem of “explosion of complexity.” To demonstrate the effect of the approach, two examples are performed at final.