Consensus Based Overlapping Decentralized Estimation With Missing Observations and Communication Faults Srdjan S. Stankovi´ c * Miloˇ s S. Stankovi´ c ** Duˇ san M. Stipanovi´ c ** * Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia (email:stankovic@etf.bg.ac.yu) ** Department of Industrial and Enterprise Systems Engineering and Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Illinois, USA.(email:mstanko3@uiuc.edu, dusan@uiuc.edu) Abstract: In this paper a new algorithm for discrete-time overlapping decentralized state estimation of large scale systems is proposed in the form of a multi-agent network based on a combination of local Kalman filters and a dynamic consensus strategy, assuming intermittent observations and communication faults. Conditions are derived for the algorithm to provide, under general conditions concerning the agent resources and the network topology, asymptotic stability in the sense of bounded mean-square estimation error. It is also demonstrated how the consensus gains can be chosen by minimizing the total steady-state mean-square estimation error. Numerical examples illustrate some properties of the proposed algorithm. 1. INTRODUCTION A great deal of attention has been paid to the problem of decentralized state estimation of complex systems. Under this term one can consider different structures that are ei- ther totally decentralized, partially decentralized, or hier- archical. The key requirement is that the large scale system is modelled as an interconnection of subsystems, and that each subsystem has a decision maker (intelligent agent) associated with it. Depending on the available resources, an agent might have access to different information, such as the sensor characteristics, properties and models of the system and its environment and communication channels between the agents. Attempts to provide an insight into the principles and structures for decentralized estimation can be found in e.g. Sanders et al. [1974, 1978], ˇ Siljak [1991], Speranzon et al. [2006], Tacker and Sanders [1980]. It should be noticed, however, that none of the existing methodologies is able to provide a systematic and general way of designing communication strategy between the agents without recurring to a strong fusion center. Also, the important problems of intermittent observations and lossy networks have not been treated in this context. As early as in the 1980s, important results were obtained in the area of distributed asynchronous iterations in parallel computation and distributed optimization (e.g. Bertsekas and Tsitsiklis [1989], Tsitsiklis [1984], Tsitsiklis et al. [1986]). Also, a very intensive research has been carried out recently in the fields of multi-agent systems and sensor networks, including numerous applications (see, e.g. Fax and Murray [2004], Jadbabaie et al. [2003], Lin et al. [2005], Moreau [2005], Olfati-Saber and Murray [2004], Ren and Beard [2005], Ren et al. [2005]). The last refer- ences have a common methodology: they all use some kind of agreement or consensus strategy between the agents. The decentralized state estimation problem itself is deeply embedded in this line of thought either implicitly, through the very definition of the consensus algorithms (e.g., see Ren et al. [2005]), or explicitly, where the dynamic consen- sus strategy between multiple agents is used for obtaining estimates (on the basis of averaging) of the quantities used subsequently for generating optimal parameter or state estimates (e.g., see Olfati-Saber [2005], Xiao and Boyd [2004]). However, none of the mentioned schemes is aimed at establishing any type of real-time collaboration between the local estimators in the overlapping decentralized esti- mation problem. In this paper a novel state estimation algorithm for com- plex linear discrete-time systems is proposed based on: (1) overlapping system decomposition and implementation of local state estimators by intelligent agents according to their sensing and computing resources; (2) application of a consensus strategy providing the global state estimates to all the agents in the network; (3) taking into account influence of intermittent observations and communication faults. The organization of the paper is as follows. The main definition of the problem is given in Section 2. In Section 3 the proposed estimation algorithm is described. The algorithm can be considered as a discrete-time version of the state estimation algorithm proposed in Stankovi´ c et al. [2007a, 2008], or an extension to the state estimation problem of the algorithm proposed in Stankovi´ c et al. [2007b], structurally resembling to the distributed com- putation algorithm proposed in Tsitsiklis [1984], Tsitsiklis et al. [1986]. In Section 4, stability of the proposed scheme is analyzed. Starting from a specially defined matrix norm, sufficient conditions for the convergence of the estimates in the mean and in the sense of preserving boundedness of the Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-11, 2008 978-1-1234-7890-2/08/$20.00 © 2008 IFAC 9338 10.3182/20080706-5-KR-1001.0884