非线性系统的LPV控制中保证渐近稳定的陷阱
Pitfalls of Guaranteeing Asymptotic Stability in LPV Control of Nonlinear Systems
摘要：
近年来，针对非线性系统的线性变参数（LPV）控制综合，提出了一种新的控制方法，该方法用于实现系统的渐近输出跟踪和扰动抑制，但当系统的调度变量保持在设计过程中考虑的有界区域内时，该方法却不能实现期望的渐近跟踪和扰动抑制。已经观察到，即使存在积分作用，在有界常数输入扰动存在下，被控系统也可能表现出围绕平衡点的振荡运动。这项工作的目的是调查如何和为什么基线李雅普诺夫稳定性的概念，目前广泛使用的LPV框架，无法保证所需的系统行为。具体而言，它示出了为什么二次李雅普诺夫概念是不足以始终保证渐近稳定的参考跟踪和扰动抑制的情况下，为什么平衡独立的稳定性概念是需要LPV稳定性分析和控制器的合成。所介绍的概念和明显的陷阱，通过一个仿真例子证明。
英文摘要：
Recently, a number of counter examples have surfaced where Linear Parameter-Varying (LPV) control synthesis applied to achieve asymptotic output tracking and disturbance rejection for a nonlinear system, fails to achieve the desired asymptotic tracking and rejection behavior even when the scheduling variations remain in the bounded region considered during design. It has been observed that the controlled system may exhibit an oscillatory motion around the equilibrium point in the presence of a bounded constant input disturbance even if integral action is present. This work aims at investigating how and why the baseline Lyapunov stability notion, currently widely used in the LPV framework, fails to guarantee the desired system behavior. Specifically, it is shown why the quadratic Lyapunov concept is insufficient to always guarantee asymptotic stability under reference tracking and disturbance rejection scenarios, and why an equilibrium independent stability notion is required for LPV stability analysis and synthesis of controllers. The introduced concepts and the apparent pitfalls are demonstrated via a simulation example.
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