This paper investigates the adaptive control problem for nonlinear time-varying systems with unknown parameters and model uncertainties. A novel class of switching functions is designed, and its construction method is detailed, along with a proof of the continuity of its n−1 order derivatives. Two simple examples are provided to illustrate how the proposed congelation of variables method handles unknown high-frequency time-varying parameters in both the feedback and input paths. A new neural network control scheme is then developed, integrating an adaptive neural network controller with a robust controller. The smooth transition between these two controllers is ensured by the novel switching function, which guarantees global system stability. Furthermore, by combining the congelation of variables method with adaptive backstepping, a new adaptive tracking control scheme is proposed. This scheme effectively handles unknown high-frequency time-varying parameters while achieving asymptotic tracking of arbitrary reference signals. Simulation results show that the proposed novel adaptive control method delivers superior control accuracy while reducing energy consumption: it achieves an order of magnitude improvement over the traditional adaptive robust control method and two orders of magnitude improvement over the conventional sliding mode control method.

中文翻译：

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未知参数和模型不确定性的非线性时变系统的自适应控制


本文研究了参数未知且模型不确定性未知的非线性时变系统的自适应控制问题。设计了一类新颖的开关函数，详细介绍了其构造方法，并证明了其 n-1 阶导数的连续性。提供了两个简单的示例来说明所提出的变量凝结方法如何处理反馈和输入路径中的未知高频时变参数。然后开发了一种新的神经网络控制方案，将自适应神经网络控制器与稳健控制器集成在一起。新颖的开关功能确保了这两个控制器之间的平滑过渡，保证了全局系统的稳定性。此外，通过将变量归聚法与自适应反步相结合，提出了一种新的自适应跟踪控制方案。该方案有效地处理了未知的高频时变参数，同时实现了任意参考信号的渐近跟踪。仿真结果表明，所提出的新型自适应控制方法在降低能耗的同时提供了卓越的控制精度：它比传统的自适应鲁棒控制方法提高了一个数量级，比传统的滑模控制方法提高了两个数量级。