基于观测器的线性系统事件触发采样与动态量化反馈稳定化
Observer-Based Feedback Stabilization of Linear Systems with Event-triggered Sampling and Dynamic Quantization
AI总结：
本文提出一种新的事件触发采样算法，用于线性系统输出反馈稳定化，通过动态量化器实现渐进稳定，同时证明了闭环系统的渐进稳定性。
摘要：
我们考虑了在测量输出和控制输入受事件触发采样和动态量化影响时，线性系统的输出反馈稳定化问题。提出了一种新的采样算法，该算法不会导致采样时间的累积，并实现系统的渐进稳定。输出采样的方法基于定义一个事件函数，该函数不仅比较当前输出与最近传输的输出样本之间的差异，还考虑了先前传输的输出样本。这使得能够使用具有采样保持测量的观测器来重构状态。估计的状态用于生成控制输入，该输入受到不同的事件触发采样程序的处理；因此，输入和输出的采样时间是异步的。通过基于Lyapunov的方法，我们证明了闭环系统的渐进稳定性，并展示了控制输入和输出存在最小的采样间隔。为了证明这些采样程序对传输错误具有鲁棒性，仅传输输出和输入的量化（在空间上）值到控制器和被控对象。为此采用了动态量化器，并提出了一种更新量化器范围和中心的算法，以实现渐进稳定的闭环系统。
英文摘要：
We consider the problem of output feedback stabilization in linear systems when the measured outputs and control inputs are subject to event-triggered sampling and dynamic quantization. A new sampling algorithm is proposed for outputs which does not lead to accumulation of sampling times and results in asymptotic stabilization of the system. The approach for output sampling is based on defining an event function that compares the difference between the current output and the most recently transmitted output sample not only with the current value of the output, but also takes into account a certain number of previously transmitted output samples. This allows us to reconstruct the state using an observer with sample-and-hold measurements. The estimated states are used to generate a control input, which is subjected to a different event-triggered sampling routine; hence the sampling times of inputs and outputs are asynchronous. Using Lyapunov-based approach, we prove the asymptotic stabilization of the closed-loop system and show that there exists a minimum inter-sampling time for control inputs and for outputs. To show that these sampling routines are robust with respect to transmission errors, only the quantized (in space) values of outputs and inputs are transmitted to the controller and the plant, respectively. A dynamic quantizer is adopted for this purpose, and an algorithm is proposed to update the range and the centre of the quantizer that results in an asymptotically stable closed-loop system.
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