Distributed robust estimation over randomly switching networks using H∞ consensus

Abstract

The paper considers a distributed robust estimation problem over a network with Markovian randomly varying topology. The objective is to deal with network variations locally, by switching observer gains at affected nodes only. We propose sufficient conditions which guarantee a suboptimal H∞ level of relative disagreement of estimates in such observer networks. When the status of the network is known globally, these sufficient conditions enable the network gains to be computed by solving certain LMIs. When the nodes are to rely on a locally available information about the network topology, additional rank constraints are used to condition the gains, given this information. The results are complemented by necessary conditions which relate properties of the interconnection graph Laplacian to the mean-square detectability of the plant through measurement and interconnection channels.

Distributed implementation and design for state estimation

“…In Carli et al (2008), it is proven for a very simple system that when the number of iterations of the consensus steps is finite, the optimal gain differs from the one computed assuming that the consensus is reached. Consensus is also used in the works of Ugrinovskii (see Ugrinovskii (2011), Ugrinovskii (2013), and Wu et al (2015)), in which the author proposes iterative, distributed LMI-based designs of H ∞ filters, and in Acikmese et al (2014), where the consensus and the measurement processes work at different rates. A similar framework is used in Shen et al (2010) for the case of possible data dropouts.…”

Distributed detectability and filter design in homogeneous sensor networks

“…Ugrinovskii([15]) studied distributed robust filter problem for continuous-time target and proposed a sufficient H ∞ filtering condition by solv- ing a convex optimization/feasibility problem subject to LMI constraints. In [16] he extended the results to a network with Markovian randomly varying topology and switching gains, and gave sufficient conditions enable the network gains to be computed by solving certain LMIs.…”

“…One is LMI-based and the other is given by the eigenvalues of the process matrix and Laplacian matrices. In the above listed work on consensusbased observers ( [11]- [16]), the role of the interconnection graph was often hidden behind the design conditions. The proposed conditions in this paper are tightly related to the eigenvalues of the graph Laplacian matrices, and their computations are not increasing with the number of sensors.…”

“…Millán et al([13]) focused on networks with delays and packet losses, and proposed a design approach via solving LMIs. Nelson and Freeman([14]), Ugrinovskii([15], [16]) applied H ∞ consensus filters in sensor networks. Nelson and Freeman([14]) investigated the problem of synthesis of H ∞ consensus filters using the methodology of vector dissipativity.…”

Event-Based Distributed $H_{\infty }$ Filtering Networks of 2-DOF Quarter-Car Suspension Systems

“…In this case, H ∞ filtering provides an alternative way to guarantee certain prescribed H ∞ performance in the design of the distributed filtering. Some initial efforts have been made on H ∞ filtering problem for a variety of systems, such as fuzzy systems [11], stochastic systems [4], switching systems [12], time-varying systems [13], and nonlinear systems [14].…”