Event triggering based adaptive tracking of uncertain nonlinear systems with unknown control coefficients

Xinxu Ju, X. Jia, Tian Ji, Wenhui Liu
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Abstract

In the framework of event-triggered control, the question of practical tracking of a sort of nonlinear systems with serious uncertainty is addressed in this work by virtue of adaptive output feedback control scheme. Especially, system nonlinearities not only depend on the unmeasurable states, but also allows the existence of output polynomial function. By combining extended Lyapunov matrix inequalities, non-identification adaptive technology and dynamic scaling transformation technology, this article proposes an adaptive output feedback control scheme within the event triggering control framework to realize global practical tracking control of closed-loop system. Simultaneously, it must be mentioned that the proposed control method includes dual gain: static gain and dynamic gain, where the latter can effectively compensate for severe uncertainty, output polynomial functions, time-varying control coefficients, and errors caused by event triggering mechanism; in addition, so as to reduce the transmission frequency of control signals, the event triggering mechanism on account of fixed threshold strategy is adopted. By means of Barbălat’s lemma and Lyapunov’s stability theorem, one can prove that the designed control strategy insures that the closed-loop system states are bounded under any initial conditions, while the tracking error is driven to a prescribed interval after a limited time. Also, the Zeno behavior is successfully ruled out. Eventually, one illustrative example is put forward to verify the correctness of the presented approach.
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未知控制系数不确定非线性系统的事件触发自适应跟踪
在事件触发控制的框架下,利用自适应输出反馈控制方案解决了一类具有严重不确定性的非线性系统的实际跟踪问题。特别是,系统的非线性不仅依赖于不可测状态,而且允许输出多项式函数的存在。结合扩展Lyapunov矩阵不等式、非辨识自适应技术和动态尺度变换技术,提出了一种事件触发控制框架内的自适应输出反馈控制方案,实现闭环系统的全局实际跟踪控制。同时,必须提到的是,所提出的控制方法包括双增益:静态增益和动态增益,其中动态增益可以有效补偿严重的不确定性、输出多项式函数、时变控制系数以及事件触发机制引起的误差;此外,为了降低控制信号的传输频率,采用了基于固定阈值策略的事件触发机制。利用barbarurlat引理和Lyapunov稳定性定理,可以证明所设计的控制策略保证闭环系统在任何初始条件下状态是有界的,同时在有限时间后将跟踪误差驱动到规定的区间内。此外,还成功地排除了芝诺行为。最后,通过一个实例验证了所提方法的正确性。
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