Distributed \(H_\infty\)-consensus filtering in sensor networks with multiple missing measurements: the finite-horizon case.

*(English)*Zbl 1204.93122Summary: This paper is concerned with a new distributed \(H_\infty\)-consensus filtering problem over a finite-horizon for sensor networks with multiple missing measurements. The so-called \(H_\infty\)-consensus performance requirement is defined to quantify bounded consensus regarding the filtering errors (agreements) over a finite-horizon. A set of random variables are utilized to model the probabilistic information missing phenomena occurring in the channels from the system to the sensors. A sufficient condition is first established in terms of a set of Difference Linear Matrix Inequalities (DLMIs) under which the expected \(H_\infty\)-consensus performance constraint is guaranteed. Given the measurements and estimates of the system state and its neighbors, the filter parameters are then explicitly parameterized by means of the solutions to a certain set of DLMIs that can be computed recursively. Subsequently, two kinds of robust distributed \(H_\infty\)-consensus filters are designed for the system with norm-bounded uncertainties and polytopic uncertainties. Finally, two numerical simulation examples are used to demonstrate the effectiveness of the proposed distributed filters design scheme.

##### MSC:

93E11 | Filtering in stochastic control theory |

93B51 | Design techniques (robust design, computer-aided design, etc.) |

##### Keywords:

sensor networks; distributed \(H_\infty\)-consensus filtering; discrete time-varying systems; difference linear matrix inequalities; finite-horizon; data missing
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\textit{B. Shen} et al., Automatica 46, No. 10, 1682--1688 (2010; Zbl 1204.93122)

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##### References:

[1] | Bliman, P.A.; Ferrari-Trecate, G., Average consensus problems in networks of agents with delayed communications, Automatica, 44, 8, 1985-1995, (2008) · Zbl 1283.93013 |

[2] | Cattivelli, F. S., Lopes, C. G., & Sayed, A. H. (2008). Diffusion strategies for distributed Kalman filtering: formulation and performance analysis. In Proc. cognitive information processing, Santorini, Greece, June. |

[3] | Gershon, E., Pila, A., & Shaked, U. (2001). Difference LMIs for robust \(H_\infty\) control and filtering. In Proceedings of the European control conference. Porto, Portugal(pp. 3469-3474). |

[4] | Gershon, E.; Shaked, U.; Yaesh, I., \(H_\infty\) control and estimation of state-multiplicative linear systems, (2005), Springer-Verlag London Limited · Zbl 1116.93003 |

[5] | Li, T.; Zhang, J.F., Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions, Automatica, 45, 8, 1929-1936, (2009) · Zbl 1185.93006 |

[6] | Lin, P.; Jia, Y.; Li, L., Distributed robust \(H_\infty\) consensus control in directed networks of agents with time-delay, Systems & control letters, 57, 8, 643-653, (2008) · Zbl 1140.93355 |

[7] | Olfati-Saber, R. (2007). Distributed Kalman filtering for sensor networks. In Proc. 46th IEEE conf. decision and control, New Orleans, LA, December. · Zbl 1112.93369 |

[8] | Olfati-Saber, R.; Murray, R.M., Consensus problems in the networks of agents with switching topology and time delays, IEEE transactions on automatic control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301 |

[9] | Olfati-Saber, R., & Shamma, J. S. (2005). Consensus filters for sensor networks and distributed sensor fusion. In Proc. 44th IEEE conf. decision and control, and the Euro. cont. conf. Seville, Spain, December. · Zbl 1112.68470 |

[10] | Shi, G.; Hong, Y., Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies, Automatica, 45, 5, 1165-1175, (2009) · Zbl 1162.93308 |

[11] | Speranzon, A.; Fischione, C.; Johansson, K.H.; Sangiovanni-Vincentelli, A., A distributed minimum variance estimator for sensor networks, IEEE journal on selected areas in communications, 26, 4, 609-621, (2008) |

[12] | Stankovic, S.S.; Stankovic, M.S.; Stipanovic, D.M., Consensus based overlapping decentralized estimation with missing observations and communication faults, Automatica, 45, 6, 1397-1406, (2009) · Zbl 1166.93374 |

[13] | Sun, Y.G.; Wang, L.; Xie, G., Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Systems & control letters, 57, 2, 175-183, (2008) · Zbl 1133.68412 |

[14] | Wang, Z.; Ho, D.W.C.; Liu, Y.; Liu, X., Robust \(H_\infty\) control for a class of nonlinear discrete time-delay stochastic systems with missing measurements, Automatica, 45, 3, 684-691, (2009) · Zbl 1166.93319 |

[15] | Xiao, L.; Boyd, S., Fast linear iterations for distributed averaging, Systems & control letters, 53, 1, 65-78, (2004) · Zbl 1157.90347 |

[16] | Xiao, F.; Wang, L., Consensus protocols for discrete-time multi-agent systems with time-varying delays, Automatica, 44, 10, 2577-2582, (2008) · Zbl 1155.93312 |

[17] | Yang, F.; Wang, Z.; Feng, G.; Liu, X., Robust filtering with randomly varying sensor delay: the finite-horizon case, IEEE transactions on circuits and systems. I. regular papers, 56, 3, 1310-1314, (2009) |

[18] | Yang, F.; Wang, Z.; Hung, Y.S., Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises, IEEE transactions on automatic control, 47, 7, 1179-1183, (2002) · Zbl 1364.93817 |

[19] | Yu, W.; Chen, G.; Wang, Z.; Yang, W., Distributed consensus filtering in sensor networks, IEEE transactions on systems, man and cybernetics, part B, 39, 6, 1568-1577, (2009) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.