The problem of asymptotic tracking control for a class of uncertain switched nonlinear systems under fuzzy approximation framework is solved in this paper. Superior to most existing results based on fuzzy adaptive control strategy that can only achieve bounded error tracking performance, our proposed control scheme can guarantee the local asymptotic tracking performance for the uncertain switched nonlinear systems under consideration. This is accomplished by constructing a nonsmooth Lyapunov function and introducing a novel discontinuous controller with dynamic feedback compensator in the design procedure. Meanwhile, some concepts, such as differential inclusion and set-valued map, are introduced to theoretically verify the local asymptotic tracking performance of the systems with our proposed controller. With the help of set-valued Lie derivative, the common virtual control functions, the desired controller, and the adaptive laws can be precisely constructed. Finally, simulation results are given to show the effectiveness of the proposed method.

中文翻译：

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一类不确定切换非线性系统的模糊逼近渐近跟踪控制


本文解决了模糊逼近框架下一类不确定切换非线性系统的渐近跟踪控制问题。优于大多数基于模糊自适应控制策略的现有结果（只能实现有界误差跟踪性能），我们提出的控制方案可以保证所考虑的不确定切换非线性系统的局部渐近跟踪性能。这是通过构造非平滑李亚普诺夫函数并在设计过程中引入带有动态反馈补偿器的新型不连续控制器来实现的。同时，引入微分包含和集值映射等概念，从理论上验证了我们提出的控制器的系统的局部渐近跟踪性能。借助集值李导数，可以精确构造常见的虚拟控制函数、期望的控制器和自适应律。最后给出仿真结果，证明了所提方法的有效性。