Fuzzy $H_{\infty}$ Filtering for Nonlinear Networked Systems Subject to Sensor Saturations
-
摘要: 研究了基于T-S模糊模型描述的非线性网络化系统$H_{\infty}$滤波器设计问题.由于网络诱导时滞的存在, 使得一个采样周期内, 到达接收端的数据可能是一个或多个, 也可能没有任何数据.提出传感器冗余策略解决由于饱和而引起的传感器件失效的问题.为降低结果的保守性, 选择模糊规则依赖的Lyapunov函数对滤波误差系统进行稳定性分析, 给出使滤波误差系统均方渐近稳定且具有指定$H_{\infty}$性能的充分条件, 滤波器参数通过求解一组线性矩阵不等式(Linear matrix inequalities, LMIs)得到.仿真研究结果表明算法的有效性.Abstract: The $H_{\infty}$ filter design problem is investigated for T-S fuzzy-model-based nonlinear networked systems. The existing of transmission delay makes that there may be one or multiple data, even no data arriving at the receiver side within one sampling period. A redundant strategy is proposed to solve the problem of sensor failure caused by sensor saturation. In order to reduce the conservatism, the fuzzy-dependent-basis Lyapunov function is chosen to analyze the stability of filtering error systems and a sufficient condition is given to make the filtering error system mean-square asymptotically stable with a specified $H_{\infty}$ performance. The parameters of the filter are obtained by solving a set of linear matrix inequalities (LMIs). The simulation results illustrate the effectiveness of the algorithm.
-
Key words:
- Networked system /
- T-S fuzzy model /
- sensor saturation /
- H∞ filter /
- packet dropout /
- time delay
1) 本文责任编委 王占山 -
表 1 接收端接收数据情况举例
Table 1 An example case of the received data at the receiver side
$k $ $\xi_k^{(0)}$ $\xi_k^{(1)}$ $\tilde {y}_k$ 1 1 0 $y_1$ 2 1 1 $y_2$ 3 0 0 0 4 0 1 $y_3$ 5 1 1 $y_5+y_4 $ 
下载: 导出CSV
表 2 模糊规则依赖与模糊规则独立的$\gamma^*$比较
Table 2 Comparison of $\gamma^*$ between fuzzy- basis-dependent and fuzzy-basis-independent methods
$ \xi_k^{(0)}$ 模糊规则依赖情况 模糊规则独立情况 0.1 5.8237 7.7774 0.3 5.7774 7.2734 0.5 5.1049 6.0407 0.7 4.1155 4.6130 0.9 3.2347 3.4826
下载: 导出CSV
表 3 最优$H_{\infty}$性能指标与传感器饱和发生概率$\bar\delta$的关系
Table 3 Relation between optimal $H_{\infty}$ performance and the sensor saturation occurrence rate
$\bar\delta$ $\gamma^{*}$ 0.2 5.6159 0.4 5.7171 0.6 5.7774 0.8 5.8047 1 5.8116
下载: 导出CSV
表 4 最大时滞为一步与两步时的$\gamma^*$比较
Table 4 Comparison of $\gamma^*$ between one-step and two-step maximum delays
${\bar\xi}_0/{\bar\xi}_1/{\bar\xi}_2$ $ P_{1d}$ $P_{2d}$ $ P_{drop}$ $\gamma^*$ 0.2/0.3 0.24 0 0.56 5.8221 0.2/0.1/0.2222 0.08 0.16 0.56 16.6811 0.4/0.3 0.21 0 0.42 5.7386 0.4/0.1/0.2222 0.07 0.14 0.42 13.6758 0.6/0.3 0.12 0 0.28 4.8987 0.6/0.1/0.2222 0.04 0.08 0.28 10.2688 0.8/0.3 0.06 0 0.14 3.7947 0.8/0.1/0.2222 0.02 0.04 0.14 8.2085
下载: 导出CSV
-
[1] Zhang D, Shi P, Wang Q, Yu L. Analysis and synthesis of networked control systems: A survey of recent advances and challenges. ISA Transactions, 2017, 66(1): 376-392 https://www.sciencedirect.com/science/article/pii/S0019057816304475 [2] Song Y, Wei G, Yang G. Distributed filtering for a class of sensor networks with uncertain rates of packet losses. Signal Processing, 2014, 104(11): 143-151 http://www.ingentaconnect.com/content/el/01651684/2014/00000104/00000001/art00014 [3] Qiu J, Feng G, Gao H. Asynchronous output-feedback control of networked nonlinear systems with multiple packet dropouts: T-S fuzzy affine model-based approach. IEEE Transactions on Fuzzy Systems, 2011, 19(6): 1014-1030 doi: 10.1109/TFUZZ.2011.2159011 [4] Wang T, Qiu J, Gao H, Wang C. Network-based fuzzy control for nonlinear industrial processes with predictive compensation strategy. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, 47(8): 2137-2147 doi: 10.1109/TSMC.2016.2616904 [5] Zhu C, Xia Y, Xie L, Yan L. Optimal linear estimation for systems with transmission delays and packet dropouts. IET Signal Processing, 2013, 7(9): 814-823 doi: 10.1049/iet-spr.2012.0348 [6] Li X, Sun S. $H_{\infty}$ filtering for network-based systems with delayed measurements, packet losses, and randomly varying nonlinearities. IEEE Sensor Journal, 2016, 16(12): 4909-4918 doi: 10.1109/JSEN.2016.2553674 [7] Takagi T, Sugeno M. Fuzzy identification of systems and its application to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 1985, 15(1): 116-132 [8] 肖会芹, 何勇, 吴敏, 肖伸平. 基于T-S模糊模型的采样数据网络控制系统$H_{\infty}$输出跟踪控制. 自动化学报, 2015, 41(3): 661-668 https://www.cnki.com.cn/Article/CJFDTOTAL-MOTO201503019.htmXiao Hui-Qin, He Yong, Wu Min, Xiao Shen-Ping. $H_{\infty}$ output tracking control for sampled-data networked control systems in T-S fuzzy model. Acta Automatica Sinica, 2015, 41(3): 661-668 https://www.cnki.com.cn/Article/CJFDTOTAL-MOTO201503019.htm [9] Han F, Feng G, Wang Y, Qiu J, Zhang C. A novel dropout compensation scheme for control of networked T-S fuzzy dynamic systems. Fuzzy Sets and Systems, 2014, 235(1): 44-61 http://dl.acm.org/citation.cfm?id=2562728 [10] Su Y, Zhou Q, Gao F. A new delay-range-dependent $H_{\infty}$ filter design for T-S fuzzy nonlinear systems. Journal of The Franklin Institute, 2014, 351(6): 3305-3321 doi: 10.1016/j.jfranklin.2014.03.003 [11] Wang Z, Shen B, Liu X. $H_{\infty}$ filtering with randomly occurring sensor saturations and missing measurements. Automatica, 2012, 48(3): 556-562 doi: 10.1016/j.automatica.2012.01.008 [12] Wu Y, Su H, Wu Z. $H_{\infty}$ filtering for discrete fuzzy stochastic systems with randomly occurred sensor nonlinearities. Signal Processing, 2015, 108(3): 288-296 [13] Wu Z, Shi P, Su H, Chu J. Asynchronous $l_2$-$l_{\infty}$ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities. Automatica, 2014, 50(1): 180-186 doi: 10.1016/j.automatica.2013.09.041 [14] Ma L, Wang Z, Lam H. Event-triggered mean-square consensus control for time-varying stochastic multi-agent system with sensor saturations. IEEE Transactions on Automatic Control, 2017, 62(7): 3524-3531 doi: 10.1109/TAC.2016.2614486 [15] Liang J, Wang Z, Liu X. $H_{\infty}$ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements. Journal of the Franklin Institute, 2015, 352(3): 1007-1030 doi: 10.1016/j.jfranklin.2014.11.020 [16] Zhang L, Ning Z, Wang Z. Distributed filtering for fuzzy time-delay systems with packet dropouts and redundant channels. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2016, 46(4): 559-572 doi: 10.1109/TSMC.2015.2435700 [17] Zhu Y, Zhang L, Zheng W. Distributed $H_{\infty}$ filtering for a class of discrete-time Markov jump Luré systems with redundant channels. IEEE Transactions on Industrial Electronics, 2016, 63(3): 1876-1885 doi: 10.1109/TIE.2015.2499169 [18] 王丽媛, 郭戈, 庄严. 网络控制系统发送功率分配问题研究. 自动化学报, 2017, 43(8): 1350-1357 doi: 10.16383/j.aas.2017.c150876Wang Li-Yuan, Guo Ge, Zhuang Yan. Transmission power allocation for networked control systems. Acta Automatica Sinica, 2017, 43(8): 1350-1357 doi: 10.16383/j.aas.2017.c150876 [19] Sun S, Wang G. Modeling and estimation for networked systems with multiple random transmission delays and packet losses. Systems and Control Letters, 2014, 73(12): 6-16 [20] Yang F, Wang Z, Hung Y, Gani M. $H_{\infty}$ control for networked systems with random communication delays. IEEE Transactions on Automatic Control, 2006, 51(3): 511-518 doi: 10.1109/TAC.2005.864207 [21] Zhang C, Feng G, Gao H, Qiu J. $H_{\infty}$ filtering for nonlinear discrete-time systems subject to quantization and packet dropouts. IEEE Transactions on Fuzzy Systems, 2011, 19(2): 353-365 doi: 10.1109/TFUZZ.2010.2098880 [22] Li X, Xu Y, Sun S. $H_{\infty}$ filtering for T-S fuzzy systems with random multiple delays and packet dropouts subject to sensor saturations. In: Proceedings of the 16th International Conference on Control, Automation, and Systems. Korea: Gyeongju, 2016. 1061-1066 [23] 唐晓铭, 邓梨, 虞继敏, 屈洪春. 基于区间二型T-S模糊模型的网络控制系统的输出反馈预测控制. 自动化学报, 2019, 45(3): 604-616 doi: 10.16383/j.aas.c170554Tang Xiao-Ming, Deng Li, Yu Ji-Min, Qu Hong-Chun. Output feedback model predictive control for interval type-2 T-S fuzzy networked control systems. Acta Automatica Sinica, 2019, 45(3): 604-616 doi: 10.16383/j.aas.c170554 [24] Sun K K, Mou S S, Qiu J B, Wang T, Gao H J. Adaptive fuzzy control for nontriangular structural stochastic switched nonlinear systems with full state constraints. IEEE Transactions on Fuzzy Systems, 2019, 27(8): 1587-1601 doi: 10.1109/TFUZZ.2018.2883374 [25] Qiu J, Sun K, Wang T, Gao H. Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Transactions on Fuzzy Systems, 2019, 27(11): 2152-2162 doi: 10.1109/TFUZZ.2019.2895560 -
图(1) / 表(5)
计量
- 文章访问数: 1090
- HTML全文浏览量: 200
- PDF下载量: 226
- 被引次数: 0
