If a control input signal constructed by backstepping is used to generate an event-triggered control signal, then not only the real control input is discontinuous, but all the virtual control signals that make up the control signal are also discontinuous and have the same triggering instants with the control input. This fact makes the control design and stability analysis more difficult and complex via backstepping. This article focuses on this problem and works at coming up a new backstepping design procedure of event-triggered fuzzy adaptive control for nonlinear strict feedback systems. A concurrent event-triggered mechanism is proposed to ensure that the real control input and the virtual control signals have the same triggering instants. Then, a systemic backstepping design procedure is developed to construct event-triggered fuzzy adaptive controller. The Lyapunov technique for nonlinear impulsive system is employed to provide the closed-loop stability analysis. It is shown that the derived event-triggered fuzzy adaptive controller ensures that the closed-loop system output well follows the desired tracking trajectory and the other closed-loop signals remain bounded. Eventually, two examples are provided to further verify the applicability and reliability of the presented control scheme.

中文翻译：

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非线性严格反馈系统模糊自适应控制的并行事件触发方法


如果使用反步构造的控制输入信号来生成事件触发的控制信号，那么不仅真实的控制输入是不连续的，而且组成该控制信号的所有虚拟控制信号也是不连续的并且具有相同的触发时刻与控制输入。这一事实使得通过反步进行控制设计和稳定性分析变得更加困难和复杂。本文针对这一问题，致力于提出一种新的非线性严格反馈系统事件触发模糊自适应控制的反步设计方法。提出了一种并发事件触发机制，以确保真实控制输入和虚拟控制信号具有相同的触发时刻。然后，开发了系统的反步设计程序来构建事件触发的模糊自适应控制器。采用非线性脉冲系统的李亚普诺夫技术来提供闭环稳定性分析。结果表明，推导的事件触发模糊自适应控制器确保闭环系统输出很好地遵循期望的跟踪轨迹，并且其他闭环信号保持有界。最后提供了两个算例进一步验证了所提出的控制方案的适用性和可靠性。