一类随机不确定网络控制系统的H∞滤波器设计

H_∞ Filter Design for a Class of Stochastic Networked Control Systems with Uncertainties

当网络控制系统信道中存在乘性噪声和丢包、时滞时,数据在传输中会受到干扰甚至丢失。本文针对带有乘性噪声、丢包和一步随机时滞的一类网络控制系统,通过状态增广,将信道特性转化为随机系统参数,并利用线性矩阵不等式方法推导了其H∞滤波器,使得滤波误差满足给定的H∞性能指标。本文算法将H∞滤波器设计转化为便于计算机求解的约束凸优化问题,并通过仿真和对比验证了算法的有效性。

In networked control systems,the input and output data is transimtted through communication channels.Data is always contaminated seriously or even lost because of the multiplicative noise,additive noise,dropouts and delays existing in channels.In this paper,an H∞filter for a class of networked control system(NCS)with the above uncertainties is designed.First,a stochastic system contains multilicative noise,dropouts and random one-step delays in both sensor-to-estimator and controller-to-actutor channels are presented.It is noticed that package is not time-stampled,which means the probability of dropouts and one-step delays are known while the status of a package on a certain instant is unkonwn.Second,the charaters of channels are transformed into stochastic parameters of a new system by dimension expansion,an error system is introduced based on the augmented system.Then a sufficient condition of the H∞performance of the error system is concluded as a matrix inequality.In order to design a filter with optimal H∞performance,the matrix inequality is transformed into a linear matrix inequality utilizing congruent transformation,which can be easily solved by existing tools.Thereby,the design of H∞filter is formulated into a convex programming problem restrited by a set of linear matrix inequality(LMI).Finally,some numerical examples are given to validate the effectiveness of the proposed algorithms,and the advantage of the present filter over some existing literature is proved.