Design of Distributed LTI Observers for State Omniscience

Park, Shinkyu; Martins, Nuno C.

doi:10.1109/tac.2016.2560766

Cited by 164 publications

(166 citation statements)

References 46 publications

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“…As of the writing of this paper, and to the best of the authors' knowledge a single work [22] provides a LTI distributed observer that guarantees ultimate boundedness of the estimation error for any LTI discrete-time system satisfying only collective observability. However, the method of that paper might suffer from shortcomings in terms of performance as will be mentioned briefly in Section III and will be seen in the Illustrative Example section.…”

Section: A Motivationmentioning

confidence: 99%

“…Remark As is shown in the appendix B of [22], assumption A2 is mild since we can design a stable estimator by only estimating the modes of the state associated with the nonzero eigenvalues, since all the other modes will vanish over time.…”

Section: Assumption A2mentioning

confidence: 99%

“…If the network is not strongly connected, it is still possible to use the results of this paper to design a distributed estimator, using some of the methods in [22], given that all source components, strongly connected subsets of the network with no incoming edges from the rest of the network, are collectively observable.…”

Section: Assumption A2mentioning

confidence: 99%

“…In contrast to the previously mentioned works in distributed LTI observers which assume a bound on the 2-norm of the state transition matrix the work in [22] provides a method of designing stable distributed LTI observers with very mild assumptions, which are weaker than strong connectivity of the network. Specifically it is only required that all source components, strongly connected subsets of the network with no incoming edges from the rest of the network, are collectively observable.…”

Section: B Lti Observersmentioning

confidence: 99%

“…In this section we will test the performance of the algorithm proposed in this paper on an academic example and compare to other methods in the literature, namely the scalar gain observer in [16], illustrating the performance of an algorithm that requires a bound on the L 2 norm of the state transition matrix, the distributed Kalman filter with consensus on information (and not on measurements) algorithm in [10], and the method in [22]. In the algorithm proposed in this paper the parameter choice forβ was 0.7.…”

Section: Illustrative Examplementioning

confidence: 99%

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A design method for distributed luenberger observers

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Section: A Motivationmentioning

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Section: Assumption A2mentioning

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Section: Assumption A2mentioning

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Section: B Lti Observersmentioning

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An algebraic, distributed state observer for continuous‐ and discrete‐time linear time‐invariant systems with time‐varying communication graphs

Nuño¹,

Bobtsov

2021

Adaptive Control & Signal

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In this paper we address the problem of distributed state estimation of continuous-and discrete-time stable, LTI systems. The classical observer canonical form representation of the system dynamics is used to identify the observable states for each node (agent). The main novelty of our contribution is to obviate the need of the asymptotically (or finite-time) local Luenberger observers.Instead, following the generalized parameter estimation-based observer design approach, we use the state transition matrix of the system to translate the problem of reconstruction of the observable states into one of parameter estimation---namely, the initial conditions of the associated trajectory. Exploiting the local observability property of the agents we prove that, with a simple sample-and-hold or finite summation operation, it is possible to estimate these parameters algebraically. Consensus strategies are then used to fuse the parameter estimates of all agents to reconstruct the complete state vector. Asymptotic or finite convergence time of the observer are established for several scenarios for the graph, including time-varying, switching and with transmission delays.

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Distributed observers design for a class of nonlinear systems to achieve omniscience asymptotically via differential geometry

Wang

et al. 2021

Intl J Robust & Nonlinear

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Distributed observers are the framework of fusing observed data by constructing a cooperative observer network. This article renders a scheme of distributed observers for a class of nonlinear system. With this scheme, each local nonlinear observer in the cooperative network can estimate the whole states of the underlying system by their own output measurements and information obtained from their neighbor via communication network. The proposed distributed observers are constructed with Partial Observable Canonical Form, which is a technology studied in differential geometry. The common observable subspace pruning and the weight matrix with spatial transformation are innovatively developed to solve the problem that each local observer is not in the same space. The sufficient conditions are proposed to guarantee the achievement of asymptotical omniscience of distributed nonlinear observers. Furthermore, our distributed observers can also be applied to linear systems and systems with some zero outputs. In addition, comparing with some existing methods of distributed nonlinear observers, our method admits some unbounded systems. Four simulations including multi‐Wen‐bridge oscillator systems, multi‐manipulators systems, unbounded nonlinear system and a linear system are employed to show the validity of the main result.

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Design of Distributed LTI Observers for State Omniscience

Cited by 164 publications

References 46 publications

A design method for distributed luenberger observers

A design method for distributed luenberger observers

An algebraic, distributed state observer for continuous‐ and discrete‐time linear time‐invariant systems with time‐varying communication graphs

Distributed observers design for a class of nonlinear systems to achieve omniscience asymptotically via differential geometry

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