时延转移概率部分未知的网络控制系统鲁棒H∞故障检测

Robust H-infinity fault detection for networked control systems with partly unknown time-delay transition probabilities

针对具有时延的离散网络控制系统,研究了时延转移概率部分未知条件下的鲁棒H∞故障检测问题.首先,利用两个独立的有限维数的Markov链分别描述传感器至控制器时延及控制器至执行器时延,把网络控制系统建模为具有两个Markov链的控制系统.在此基础上构造了故障检测滤波器,利用状态增广的方法建立了闭环系统模型.然后,以矩阵不等式的形式得到了闭环系统随机稳定并满足给定H_∞性能的条件,给出了相应控制器、滤波器增益矩阵及最小H_∞衰减水平的求解方法,并得到了转移概率和最小H_∞衰减水平之间的关系.最后实例仿真表明,所得到的故障检测滤波器不仅对故障敏感而且对外部扰动具有鲁棒性.

This paper investigates the robust H-infinity fault detection problem for the discrete networked control system with time-delays on condition that the transition probabilities of time-delays are partly unknown. First, the time-delay from sensor to controller and the time-delay from sensor to actuator are both considered which are described by two independent Markov chains of finite dimensions. The networked control system is molded as a control system which contains two Markov chains. Furthermore, the fault detection filter is constructed and the closed-loop system is established by the state augmented method. Next, the conditions which make the closed-loop system stochastically stable and achieve prescribed H-infinity performance are obtained in terms of linear matrix inequalities, and the method of calculating the corresponding controller, fault detection filter gain matrices and the minimum H-infinity attenuation level is given. The relationship between transition probabilities and minimum H-infinity attenuation level is also obtained. Finally, the simulation example shows that the proposed fault detection filter is not only sensitive to fault and but also robust to exogenous disturbance.