A general invariance principle for nonlinear time-varying systems and its applications
A general invariance principle for nonlinear time-varying systems and its applications
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DOI：
10.1109/cca.2000.897465
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发表时间：
2000-09
期刊：
影响因子：
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通讯作者：
Ti-Chung Lee;Der-Cherng Liaw;Bor‐Sen Chen
中科院分区：
文献类型：
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作者：
Ti-Chung Lee;Der-Cherng Liaw;Bor‐Sen Chen
针对一类非线性时变系统，从输出到状态的观点提出了一种广义不变性原理。这是通过使用涉及输出函数的积分不等式和修改的可检测性条件来构造简单而直观的准则来实现的。当给出一个Lyapunov函数给应用系统时，证明了著名的“LaSalle不变性原理”是由所提出的方法导出的。对于非线性时不变系统，Byrnes和Martin(1995)也提出了一个类似的判据，即所谓的“积分不变原理”。然而，一般来说，这两种方法不能直接应用于时变系统。该方法可以看作是时不变系统积分不变性原理在时变系统中的推广。这种推广是非平凡的，可用于各种研究领域，如自适应控制、跟踪控制和无漂移系统的控制。通过在四轮移动机器人全局跟踪控制中的应用，验证了该方法的可行性和有效性。
A general invariance principle is proposed from the output-to-state viewpoint for a class of nonlinear time-varying systems. This is achieved by the construction of a simple and intuitive criterion using integral inequality involving the output function and modified detectability conditions. The well-known "LaSalle invariance principle" is shown to be deduced from the proposed approach when a Lyapunov function is given to the applied systems. A similar criterion, the so-called "integral invariance principle", was proposed by Byrnes and Martin (1995) for nonlinear time-invariant systems. However, in general, these two approaches cannot be applied to time-varying systems directly. The proposed scheme can be viewed as an extension of the integral invariance principle for time-invariant systems to time-varying systems. Such extension is non-trivial and can be used in various research areas, such as adaptive control, tracking control and the control of driftless systems. Applications to the global tracking control of four-wheeled mobile robots are given to demonstrate the feasibility and validity of the proposed approach.