不确定离散时间系统的状态逼近事件触发控制  

Event-triggered control for uncertain discrete-time systems via state approximation approach

作　　者：丁三波 刘亚拴 DING Sanbo;LIU Yashuan(School of Artificial Intelligence,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学人工智能与数据科学学院,天津300401

出　　处：《哈尔滨工业大学学报》2022年第12期80-86,共7页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金(61903121);河北省自然科学基金(F2020202063);河北省创新能力提升计划项目(18961604H)。

摘　　要：为减少不确定离散时间线性/非线性系统的事件触发次数,节省通讯资源,提出了基于状态逼近的事件触发控制方法。首先,针对不确定离散线性系统,利用采样信号、系统矩阵和确定离散线性系统解析解的定义,逐段构造不确定离散系统的状态逼近解。将测量误差定义为系统当前状态与逼近解之间的差,构造事件触发条件和控制器,通过设计Lyapunov泛函得到离散线性系统的稳定性条件。其次,对于一类Lipschitz离散非线性系统,将该系统进行线性化处理。根据无扰动离散线性系统解析解的定义,类似于线性系统的处理方法,逐段构造状态逼近解,重新定义测量误差,设计事件触发条件和控制器,并建立离散非线性系统的稳定性条件。将状态逼近技术与动态事件触发策略相结合,在减小测量误差的同时,降低触发阈值,进一步减少事件发生的次数,实现更好的控制效果。通过倒立摆系统和蔡氏电路两个数值例子表明,相比于传统事件触发方案,状态逼近法可以显著降低事件触发的次数,避免了通讯资源的浪费。To reduce the event-triggered times of uncertain discrete-time linear/nonlinear systems and save communication resources,we proposed an event-triggered control(ETC)strategy based on state approximation.First,the approximate solution of the uncertain discrete-time linear system was constructed piece-wisely by using the analytical solution of the certain linear system,sampled signals,and system matrices.The measurement error was defined as the difference between the current system state and the approximate solution.The event-triggered condition and controller were constructed,and the stability conditions were established by designing Lyapunov functions.Then,for a class of Lipschitz discrete-time nonlinear system,linearization was performed.According to the analytical solution of undisturbed linear system,similar to the technique for linear system,the piece-wise approximate solution was constructed,and the measurement error was redefined.The event-triggered condition and controller were designed respectively,and the stability conditions of the system were developed.By combining the state approximation technique with dynamic triggered method,the measuring error and the trigger threshold were reduced,and the event-triggered times were further decreased,indicating better control effects.Simulation results of inverted pendulum system and Chua s circuit showed that compared with the traditional event-triggered scheme,the state approximation approach significantly reduced the event-triggered times and avoided wasting communication resources.

关 键 词：事件触发控制 不确定参数 LIPSCHITZ非线性 状态逼近技术 动态触发 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]