学术论文

      基于一般二次函数的非周期事件触发的H∞控制

      Aperiodic event-triggered H∞ control base on general quadratic functions

      摘要:
      在事件触发控制框架下,采样数据发送到控制器的传输时间是由预先给定的事件条件确定.相对于时间触发控制,事件触发控制能有效地降低对通讯资源的占用.到目前为止,周期事件触发策略是实现事件触发控制最常用的方法,其局限性是忽视了相邻采样时刻间的系统信息,从而可能导致控制性能下降.为此,文中提出了基于一般二次函数的非周期事件触发策略,既可减少控制任务的执行数量,同时,通过对系统输出的连续监测能有效避免最坏情况对系统性能的影响.为降低结果的保守性,根据闭环系统的混杂结构特征,构造了分段时间依赖的非正定Lyapunov泛函.运用凸组合和矩阵不等式方法,建立了系统具有指数稳定性和给定L2-增益的充分条件.将事件触发参数矩阵的设计问题转化为一组线性矩阵不等式(LMI)的求解问题.最后,通过模型的数值仿真证实了文中方法在保证系统具有一定的L2-增益性能的前提下能有效减少量测数据的传输次数.
      Abstract:
      In the framework of event-triggered control, the times at which the newly sampled-data sent to the controller are determined by a predetermined event condition.Compared with the time-triggered control mechanism, the event-triggered control can effectively reduce the utilization of communication resources.The periodic event-triggered control strategy is so far the most common approach to realize the event-triggered control.However, the limitation of this control strategy lies in that the system information inside the transmission times is neglected, which may degrade the control performance.To remedy the imitation,anaperiodic event-triggered strategy based on general quadratic functions is proposed in this paper.The new strategy is capable of reducing the number of control task executions and avoiding effectively the effects of the worst cases on system performance by monitoring continuously the system output.In order to obtain less conservative results, a piecewise time-dependent non-positive definite Lyapunov functional is constructed by considering the hybrid structure features of the closed-loop system.Through employing the techniques of convex combination and matrix inequalities (LMI), a sufficient condition is derived, which ensures the internal exponential stability and guarantees a prescribed level on L2-gain.Furthermore, the event-triggering parameter matrix can be designed by solving a set of linear matrix inequalities.Finally, numerical simulations show that the proposed control scheme can effectively reduce the amount of measurements to be sent when maintaining a prescribed L2-gain performance.
      Author: RUAN Zhen CHEN Wu-hua LU Xiao-mei
      作者单位: 广西大学数学与信息科学学院,广西南宁,530004
      年,卷(期): 2017, 42(2)
      分类号: O231.1
      在线出版日期: 2017年5月16日
      基金项目: 国家自然科学基金资助项目,国家自然科学基金重点项目,广西自然科学基金资助项目