This article investigates the adaptive control problem for systems with time-varying parameters using the so-called congelation of variables method. First, two scalar examples to illustrate how to deal with time-varying parameters in the feedback path and in the input path, respectively, are discussed. The control problem for an $n$ -dimensional lower triangular system via state feedback is then discussed to show how to combine the congelation of variables method with adaptive backstepping techniques. To achieve output regulation problem via output feedback, problem which cannot be solved directly due to the coupling between the input and the time-varying perturbation, the ISS of the inverse dynamics, referred to as strong minimum-phaseness, is exploited. This allows converting such coupling into the coupling between the output and the time-varying perturbation. A set of filters, resulting in ISS state estimation error dynamics, are designed to cope with the unmeasured state variables. Finally, a controller is designed based on a small-gain-like analysis that takes all subsystems into account. Simulation results show that the proposed controller achieves asymptotic output regulation and outperforms the classical adaptive controller, in the presence of time-varying parameters that are neither known nor asymptotically constant.

中文翻译：

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时变参数系统的自适应控制

本文研究了具有时变参数的系统的自适应控制问题，即所谓的 变量汇总方法。首先，讨论了两个标量示例，分别说明了如何处理反馈路径和输入路径中的时变参数。一个控制问题$ n $ 然后讨论了通过状态反馈的三维下三角系统，以说明如何组合 变量汇总 方法 自适应反推技术。为了通过输出反馈实现输出调节问题，由于输入和时变摄动之间的耦合而无法直接解决的问题，利用了逆动力学的ISS（称为强最小相位）。这允许将这种耦合转换为输出和时变扰动之间的耦合。一组导致ISS状态估计误差动态的过滤器旨在应对未测得的状态变量。最终，基于类似小增益的分析设计了控制器，该分析考虑了所有子系统。仿真结果表明，在时变参数既未知也不渐近恒定的情况下，所提出的控制器实现渐近输出调节并优于经典自适应控制器。