32,677 research outputs found

    Towards a minimal order distributed observer for linear systems

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    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 Nn−∑i=1NpiNn - \sum_{i =1}^N p_i, where NN is the number of network nodes, nn is the state space dimension of the observed plant, and pip_i is the rank of the output matrix of the observed output received by the iith 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

    Distributed fault estimation for linear systems with actuator faults

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    This article investigates the problem of designing a distributed fault estimation observer (DFEO) for a given linear time invariant observed system with disturbances. The DFEO consists of a network of local fault estimation observers. The local observers at the network nodes are physically distributed and hence each of them has access to only part of the output of the observed system. Each local fault estimation observer communicates with its neighbors as prescribed by the given network graph. Both full order and reduced order DFEO's are presented in this article. A systematic design procedure for DFEO gains is addressed, enabling the estimation error dynamics to be robust against the effects of the external process disturbance and the derivative of the fault. The numerical design of our DFEO is amounts to solving an optimization problem with constraints of a bank of linear matrix inequalities. Finally, we illustrate the effectiveness of the proposed distributed fault estimation approach by means of a number of simulation results

    State Estimation Using a Network of Distributed Observers With Unknown Inputs

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    State estimation for a class of linear time-invariant systems with distributed output measurements (distributed sensors) and unknown inputs is addressed in this paper. The objective is to design a network of observers such that the state vector of the entire system can be estimated, while each observer has access to only local output measurements that may not be sufficient on their own to reconstruct the entire system’s state. Existing results in the literature on distributed state estimation assume either that the system does not have inputs, or that all the system’s inputs are globally known to all the observers. Accordingly, we address this gap by proposing a distributed observer capable of estimating the overall system’s state in the presence of inputs, while each observer only has limited local information on inputs and outputs. We provide a design method that guarantees convergence of the estimation errors to zero under joint detectability conditions. This design suits undirected communication graphs that may have switching topologies and also applies to strongly connected directed graphs.We also give existence conditions that are consistent with existing results on unknown input observers. Finally, simulation results verify the effectiveness of the proposed estimation scheme for various scenarios

    Distributed H_/L∞ fault detection observer design for linear systems:Proceedings

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    This paper studies the distributed fault detection problem for linear time-invariant (LTI) systems with distributed measurement output. A distributed H_/L∞ fault detection observer (DFDO) design method is proposed to detect actuator faults of the monitored system in the presence of a bounded process disturbances. The DFDO consists of a network of local fault detection observers, which communicate with their neighbors as prescribed by a given network graph. By using finite-frequency H_ performance, the residual in fault detection is sensitive to fault in the interested frequency-domain. The residual is robust against effects of the external process disturbance by L∞ analysis. A systematic algorithm for DFDO design is addressed and the residual thresholds are calculated in our distributed fault detection scheme. Finally, we use a numerical simulation to demonstrate the effectiveness of the proposed distributed fault detection approach

    Observer-based Synchronization of Multi-agent Systems Using Intermittent Output Measurements

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    The problem of synchronizing multiple continuous-time linear time-invariant systems connected over a complex network, with intermittently available measurements of their outputs, is considered. To solve this problem, we propose a distributed observer-based feedback controller that utilizes a local hybrid observer to estimate neighboring states only from output measurements at such potentially nonperiodic isolated event times. Due to the inherent continuous and discrete dynamics emerging from coupling the impulsive measurement updates and the interconnected networked systems, we use hybrid systems to model and analyze the resulting closed-loop system. The problem of synchronization and state estimation is then recast as a set stabilization problem, and, utilizing a Lyapunov-based analysis for hybrid systems, we provide sufficient conditions for global exponential stability of the synchronization and zero estimation error set. A numerical example is provided to illustrate the results

    A Distributed Observer for a Discrete-Time Linear System

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    A simply structured distributed observer is described for estimating the state of a discrete-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to construct the local estimators which comprise the observer so that their state estimation errors all converge exponentially fast to zero at a fixed, but arbitrarily chosen rate provided the network's graph is strongly connected for all time. This is accomplished by exploiting several well-known properties of invariant subspaces plus several kinds of suitably defined matrix norms.This work was supported by NSF grant 1607101.00, AFOSR grant FA9550-16-1-0290, ARO grant W911NF-17-1-0499, and Australian Research Council Grant DP-160104500

    A Hybrid Observer for a Distributed Linear System with a Changing Neighbor Graph

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    A hybrid observer is described for estimating the state of an m>0m>0 channel, nn-dimensional, continuous-time, distributed linear system of the form x˙=Ax,  yi=Cix,  i∈{1,2,…,m}\dot{x} = Ax,\;y_i = C_ix,\;i\in\{1,2,\ldots, m\}. The system's state xx is simultaneously estimated by mm agents assuming each agent ii senses yiy_i and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph N(t)\mathbb{N}(t) whose vertices correspond to agents and whose arcs depict neighbor relations. Agent ii updates its estimate xix_i of xx at "event times" t1,t2,…t_1,t_2,\ldots using a local observer and a local parameter estimator. The local observer is a continuous time linear system whose input is yiy_i and whose output wiw_i is an asymptotically correct estimate of LixL_ix where LiL_i a matrix with kernel equaling the unobservable space of (Ci,A)(C_i,A). The local parameter estimator is a recursive algorithm designed to estimate, prior to each event time tjt_j, a constant parameter pjp_j which satisfies the linear equations wk(tj−τ)=Lkpj+μk(tj−τ),  k∈{1,2,…,m}w_k(t_j-\tau) = L_kp_j+\mu_k(t_j-\tau),\;k\in\{1,2,\ldots,m\}, where τ\tau is a small positive constant and μk\mu_k is the state estimation error of local observer kk. Agent ii accomplishes this by iterating its parameter estimator state ziz_i, qq times within the interval [tj−τ,tj)[t_j-\tau, t_j), and by making use of the state of each of its neighbors' parameter estimators at each iteration. The updated value of xix_i at event time tjt_j is then xi(tj)=eAτzi(q)x_i(t_j) = e^{A\tau}z_i(q). Subject to the assumptions that (i) the neighbor graph N(t)\mathbb{N}(t) is strongly connected for all time, (ii) the system whose state is to be estimated is jointly observable, (iii) qq is sufficiently large, it is shown that each estimate xix_i converges to xx exponentially fast as t→∞t\rightarrow \infty at a rate which can be controlled.Comment: 7 pages, the 56th IEEE Conference on Decision and Contro
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