13,279 research outputs found
Interconnected Observers for Robust Decentralized Estimation with Performance Guarantees and Optimized Connectivity Graph
Motivated by the need of observers that are both robust to disturbances and
guarantee fast convergence to zero of the estimation error, we propose an
observer for linear time-invariant systems with noisy output that consists of
the combination of N coupled observers over a connectivity graph. At each node
of the graph, the output of these interconnected observers is defined as the
average of the estimates obtained using local information. The convergence rate
and the robustness to measurement noise of the proposed observer's output are
characterized in terms of bounds. Several optimization problems
are formulated to design the proposed observer so as to satisfy a given rate of
convergence specification while minimizing the gain from noise to
estimates or the size of the connectivity graph. It is shown that that the
interconnected observers relax the well-known tradeoff between rate of
convergence and noise amplification, which is a property attributed to the
proposed innovation term that, over the graph, couples the estimates between
the individual observers. Sufficient conditions involving information of the
plant only, assuring that the estimate obtained at each node of the graph
outperforms the one obtained with a single, standard Luenberger observer are
given. The results are illustrated in several examples throughout the paper.Comment: The technical report accompanying "Interconnected Observers for
Robust Decentralized Estimation with Performance Guarantees and Optimized
Connectivity Graph" to be published in IEEE Transactions on Control of
Network Systems, 201
Towards a minimal order distributed observer for linear systems
In this paper we consider the distributed estimation problem for
continuous-time linear time-invariant (LTI) systems. A single linear plant is
observed by a network of local observers. Each local observer in the network
has access to only part of the output of the observed system, but can also
receive information on the state estimates of its neigbours. Each local
observer should in this way generate an estimate of the plant state. In this
paper we study the problem of existence of a reduced order distributed
observer. We show that if the observed system is observable and the network
graph is a strongly connected directed graph, then a distributed observer
exists with state space dimension equal to , where
is the number of network nodes, is the state space dimension of the
observed plant, and is the rank of the output matrix of the observed
output received by the th local observer. In the case of a single observer,
this result specializes to the well-known minimal order observer in classical
observer design.Comment: 12 pages, 1 figur
Time Complexity of Decentralized Fixed-Mode Verification
Given an interconnected system, this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode (DFM). It is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system. It is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication. This work concludes that the identification of distinct DFMs (by means of a deterministic algorithm, rather than a randomized one) is computationally very easy, although the existing algorithms for solving this problem would wrongly imply that it is cumbersome. This note provides not only a complexity analysis, but also an efficient algorithm for tackling the underlying problem
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