AI 中文总结
针对带切换未知参数的自主切换非线性系统，本文提出模式自适应观测器，解决切换扰动与无输入下持续激励问题，通过专用观测器及相关条件实现误差特性，经学术与实际示例验证性能。
AI 中文摘要
在数字孪生范式中，在线参数更新至关重要。与静态模型不同，数字孪生必须持续适应其所代表系统的演化动力学。因此，自适应观测器（可从在线数据联合估计状态与参数）正成为日益重要的工具。本研究针对一类具有切换未知参数的自主切换非线性系统，构建了模式自适应观测器。主要挑战有二：消除切换注入参数误差动力学的扰动，以及在不依赖输入信号的情况下保证有限时间窗内的持续激励。为解决这些问题，我们为每个模式分配专用自适应观测器，仅在其对应区间激活，直接消除切换引发的零输入扰动。随后引入有限窗持续激励条件与最小驻留时间条件，在此条件下参数估计误差具有收缩性，状态估计误差在每个模式的激活区间内有界。本文通过一个学术示例与进化疗法的实际示例，说明了所提方法的性能。
英文摘要
In the digital twin paradigm, online parameter updating is essential. Unlike a static model, a digital twin must continuously adapt to the evolving dynamics of the system it represents. Adaptive observers, which jointly estimate states and parameters from online data, are therefore an increasingly important tool. In this work, we formulate a mode-wise adaptive observer for a class of autonomous switched nonlinear systems with switched unknown parameters. The main challenges are twofold: removing the disturbance that switching injects into the parameter-error dynamics and guaranteeing persistence of excitation over a finite-time window without relying on an input signal. To address them, we assign a dedicated adaptive observer to each mode, active only on its corresponding interval, which directly removes the zero-input disturbance caused by switching. We then introduce a finite-window persistence-of-excitation condition together with a minimum dwell-time condition, under which the parameter estimation error is contractive and the state estimation error is bounded within the active interval of each mode. The performance of the proposed approach is illustrated with an academic example and with a practical example of evolutionary therapies.
