文章快速检索 高级检索

1. 哈尔滨理工大学自动化学院, 黑龙江 哈尔滨 150080;
2. 哈尔滨理工大学电气与电子工程学院, 黑龙江 哈尔滨 150080

H Filter Design for a Class of Stochastic Non-linear Time-delay Control Systems
HUANG Ling1 , XIE Xuhuan1, XIE Wenbo1, LIU Ji2
1. School of Automation, Harbin University of Science and Technology, Harbin 150080, China;2. School of Electrical and Electronic Engineering, Harbin University of Science and Technology, Harbin 150080, China
Abstract:In this paper, we investigate the H filter design problem for a class of non-linear time-delay control systems with random sensor failure and process. The main aspects of our work are as follows. (a) We use a Takagi-Sugeno (T-S) fuzzy model to describe non-linear time-delay dynamic systems with process. (b) We model a system with a random sensor failure. (c) Using the delay partitioning technique, we deduce the sufficiency condition that the filtering error system is asymptotically stable in the global probability space and that it reaches H performance. (d) We provide further filter parameters, and determine the filter coefficient matrices by solving a set of linear matrix inequalities (LMIs). Finally, we give a numerical example to show the effectiveness and reliability of the proposed method.
sensor random failure     H filter     T-S fuzzy model     itô process     delay decomposition approach     linear matrix inequalities (LMIs)

1 引言

2 问题描述

${\hat{y}}$i(t)为滤波器接收到的来自第i个传感器发来的信号； Λi∈[0，σ]，σ≥1. Λi为描述第i个传感器工作状态的随机变量，Λi=0代表传感器完全失效； Λi=1代表传感器正常工作； 0<Λi<1和1<Λi≤σ分别代表传感器测量数据比实际值偏小和偏大，此时传感器测量到的数据有些失真. Λi的期望和方差分别为${\bar{\Lambda }}$iβi2

(1) 假定存在一个正定的、 发散的及二次连续的可微的函数V(χ，t)，使得

(2) 对于所有的非零干扰v(t)∈￡2[0，∞)，给定一个标量γ，满足：

3 增广系统的H控制

A+AT记为〈As，以下同.

4 H滤波器设计

JJT分别左乘和右乘式(14)的两端，并引进如下新变量：

5 仿真算例

(1) 第1个局部线性子系统参数：

(2) 第2个局部线性子系统参数：

 图 1 状态响应 Fig. 1 State response 图选项

 图 2 滤波误差 Fig. 2 Error of filtering 图选项

6 结论

 [1] Kalman R E. A new approach to linear filtering and prediction problem[J]. Journal of Basic Engineering, 1960, 82(1): 35-45. [2] Elsayed A, Grimble M J. A new approach to the H∞design of optimal digital linear filters[J]. IMA Journal of Mathematical Control and Information, 1989, 6(2): 233-251. [3] Gao H J, Lam J, Shi P, et al. Parameter-dependent filter design with guaranteed H∞ performance[J]. IEE Proceedings-Control Theory and Applications, 2005, 152(5): 531-537. [4] 扶凌云, 何勇, 吴敏. 基于时滞的H∞滤波器设计及其在网络中的应用[J]. 控制理论与应用, 2010, 27(4): 517-522. Fu L Y, He Y, Wu M. H∞ filter design based on time-delay and its application to network[J]. Control Theory and Applications, 2010, 27(4): 517-522. [5] Coutinho D F, Souza C E D, Barbosa K A, et al. Robust linear H∞ filter design for a class of uncertain nonlinear systems: An LMI approach[J]. Siam Journalon Control and Optimization, 2009, 48(3): 1452-1472. [6] Yang R Y, Shi P, Liu G P. Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts[J]. IEEE Transactions on Automatic Control, 2011, 56(11): 2655-2660. [7] Shao H Y. Robust H∞ filtering for class of non-linear discrete time-delay systems with parameter uncertainties[J]. Control Theory and Applications, 2007, 24(1): 148-154. [8] Huang S J, He X Q, Zhang N N. New results on H∞ filter design for non-linear systems with time-delay via T-S fuzzy models[J]. IEEE Transactions on Fuzzy Systems, 2011, 19(1): 193-199. [9] Mad Z, Zhang H G, Wang Z S, et al. The robust H∞ filter design for a class of non-linear time-delay systems[J]. Acta Electronica Sinica, 2010, 38(9): 2172-2178. [10] Deng Z, Shi P, Yang H, et al. Robust H∞ filtering for non-linear systems with interval time-varying delays[J]. International Journal of Innovative Computing Information and Control, 2010, 6(12): 5527-5538. [11] Gao H J, Lam J, Wang C H. Robust energy-to-peak filter design for stochastic time-delay systems[J]. Systems and Control Letters, 2006, 55(2): 101-111. [12] Yan H C, Zhang H, Shi H B, et al. Robust H∞ filtering for uncertain non-linear stochastic systems with mode-dependent time-delays and Markovian jump parameters[J]. Circuits Systems and Signal Processing, 2011, 30(2): 303-321. [13] Zhao F, Zhang Q L, Liu C, et al. H∞ filtering for a class of stochastic time-delay non-linear systems[C]//Control and Decision Conference. Piscataway, NJ, USA: IEEE, 2014: 3119-3124. [14] Tseng C S. Robust fuzzy filter design for a class of non-linear stochastic systems[J]. IEEE Transactions on Fuzzy Systems, 2007, 15(2): 261-274. [15] Tian E G, Yue D. Reliable H∞ filter design for T-S fuzzy model based networked control systems with random sensor failure[J]. International Journal of Robust and Non-linear Control, 2013, 23(1): 15-32. [16] Chen B, Yu L, Zhang W A, et al. Robust information fusion estimator for multiple delay-tolerant sensors with different failure rates[J]. IEEE Transaction on Circuits and Systems, 2013, 60(2): 401-414. [17] Wang X, Yaz E E, Jeong C S, et al. A resilient extended Kalman filter for discrete-time nonlinear stochastic systems with sensor failures[C]//American Control Conference (ACC). Piscataway, NJ, USA: IEEE, 2012: 4783-4788. [18] 吴立刚, 王常虹, 高会军, 等. 时滞不确定随机系统基于参数依赖Lyapunov函数的稳定性条件[J]. 控制理论与应用, 2006, 10(1): 607-612. Wu L G, Wang C H, Gao H J, et al. Stability of uncertain stochastic systems with time-varying delays based on parameter-dependent Lyapunov functional[J]. Control Theory and Applications, 2006, 10(1): 607-612. [19] Boyd S P, Ghaoui L E, Feron E, et al. Linear matrix inequalities in systems and control theory[J]. Proceedings of Symposia in Pure Mathematics, 1994, 85(5): 798-799. [20] Yang R N, Gao H J, Shi P. Delay-dependent robust H∞ control for uncertain stochastic time-delay systems[J]. International Journal of Robust and Nonlinear Control, 2010, 20(16): 1852-1865. [21] Lin C, Wang Q G, Lee T H, et al. H∞ filter design for non-linear systems with time-delay through T-S fuzzy model approach[J]. IEEE Transactions on Fuzzy Systems, 2008, 16(3): 739-746.
"http://dx.doi.org/10.13976/j.cnki.xk.2016.0020"

0

#### 文章信息

HUANG Ling, XIE Xuhuan, XIE Wenbo, LIU Ji

H Filter Design for a Class of Stochastic Non-linear Time-delay Control Systems

INFORMATION AND CONTROL, 2016, 45(1): 20-26.
http://dx.doi.org/10.13976/j.cnki.xk.2016.0020