Necessary and sufficient conditions for the stabilizability of a class of LTI distributed observers

Park, Shinkyu; Martins, Nuno C.

doi:10.1109/cdc.2012.6426092

Cited by 53 publications

(62 citation statements)

References 19 publications

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“…Proof of Theorem 1 is provided in the following. Proof of Theorem 1 In order to show exponential convergence of x i (t) − x(t), i.e., (4), it is equivalent to look at the stability of system (5), i.e., (6) and (7). First, since the spectrum ofĀ i +K iCi , i ∈ m, is assignable withK i , there areK i s so that z 1 (t) ≤ e −λt z 1 (0) whereλ > λ.…”

Section: Discussionmentioning

confidence: 99%

A Distributed Observer for a Continuous-Time Linear System

Wang

Liu

Morse

2019

2019 American Control Conference (ACC)

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A simply structured distributed observer is described for estimating the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to design a gain g in 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. A linear inequality for g is provided when the network's graph is switching according to a switching signal with a dwell time or an average dwell time, respectively. It has also been shown the existence of g when the stochastic matrix of the network's graph is chosen to be doubly stochastic under arbitrarily switching signals. This is accomplished by exploiting several well-known properties of invariant subspaces and properties of perturbed systems.

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Section: Discussionmentioning

confidence: 99%

A Distributed Observer for a Continuous-Time Linear System

Wang

Liu

Morse

2019

2019 American Control Conference (ACC)

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“…x((k + 1)T ) = exp(TĀ)x(kT ) (5) Another approximation to the above model is by using the Tustin's method [12] for discretization of (3) as follows:…”

Section: Mcne Problem Statementmentioning

confidence: 99%

“…This simply implies that if two agents are in the communication range of each other, e.g., in a wireless sensor network, both agents share their information. This is a typical assumption in the literature of networked estimation as in [2], [5]. This assumption changes the problem as in the following: Problem Formulation 5.…”

Section: Remark 5 For General (Directed) Communication Network the mentioning

confidence: 99%

On the Complexity of Minimum-Cost Networked Estimation of Self-Damped Dynamical Systems

Doostmohammadian

Khan

2020

IEEE Trans. Netw. Sci. Eng.

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In this paper, we consider the optimal design of networked estimators to minimize the communication/measurement cost under the networked observability constraint. This problem is known as the minimum-cost networked estimation problem, which is generally claimed to be NP-hard. The main contribution of this work is to provide a polynomial-order solution for this problem under the constraint that the underlying dynamical system is self-damped. Using structural analysis, we subdivide the main problem into two NP-hard subproblems known as (i) optimal sensor selection, and (ii) minimum-cost communication network. For self-damped dynamical systems, we provide a polynomial-order solution for subproblem (i). Further, we show that the subproblem (ii) is of polynomial-order complexity if the links in the communication network are bidirectional. We provide an illustrative example to explain the methodologies. . 1. In this paper, agent/sensor/estimator is used interchangeably. of measurements. This cost may represent sensor expenses, or utility/energy consumption by sensors [19]. On the other hand, the MCCN problem is to optimally design the communication network to minimize the communication cost at the agents, where the cost may represent communication reliability [20], communication energy/power [21], or distance (also referred to as capacity-infrastructure cost) [22], among others. Related literature: Optimal sensor selection [23], [24] and dual problem of optimal actuator placement [25], [26] is shown to be NP-hard 2 in the literature. The problem of optimal selection of sensors (information gatherers) is shown to be reducible to a minimum set covering problem [23].The problem of optimal input selection is shown to be reducible to r-hitting set problem in [25]. These references imply that the MCSS problem is NP-hard, in general. On the other hand, cost-optimal communication network design is considered in [18], [20]-[22], [27]-[29]. In [27], tradeoffs between optimal sensor placement and minimization of communication cost is claimed to be NP-hard and therefore a near-optimal solution is proposed. The near-optimal approximation 3 solution in [27] is of complexity O(n log(n)).In [22], communication to a central unit based on Poisson-Voronoi spanning tree with application to tracking in mobile communication systems is discussed. In the literature, a few references consider the optimal communication network design under observability constraints [18], [28], [29]; in these works, the main objective is to design the network such that the communication cost to a central base is minimized while satisfying observability constraint as a necessary condition 2. NP-hardness (Non-deterministic Polynomial-time hardness) is the defining property of a class of problems that has no solution in the time-complexity upperbounded by a polynomial function of the input parameters.3. For NP-hard problems, typically a ρ-approximation algorithm is provided with provable guarantees on the factor ρ of the returned solution to the optimal one.

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“…This is further used to determine the minimum number of measurements for observability. As compared to [12]- [15] on distributed estimation, we partition the agents (taking measurements) into Type-α and Type-β 1 and show that distributed inference only needs Type-α measurements directly at each agent, while Type-β measurements are needed over a path. This classification is significant as it provides the most general case based on matching properties of the social system and, further, it imposes less communication burden on the cyber-network as compared to, for example, [11].…”

Section: Introductionmentioning

confidence: 99%

“…• Distributed inference papers [12]- [15] (with partial observability of agents) in the literature assume that the underlying system is full-rank. This assumption significantly reduces the connectivity requirement in the cybernetwork of agents.…”

Section: Introductionmentioning

confidence: 99%

Cyber-Social Systems: Modeling, Inference, and Optimal Design

Doostmohammadian

Rabiee

Khan

2020

IEEE Systems Journal

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This paper models the cyber-social system as a cyber-network of agents monitoring states of individuals in a social network. The state of each individual is represented by a social node and the interactions among individuals are represented by a social link. In the cyber-network each node represents an agent and the links represent information sharing among agents. Agents make an observation of social states and perform distributed inference. In this direction, the contribution of this work is threefold: (i) A novel distributed inference protocol is proposed that makes no assumption on the rank of the underlying social system. This is significant as most protocols in the literature only work on full-rank systems. (ii) A novel agent classification is developed, where it is shown that connectivity requirement on the cyber-network differs for each type. This is particularly important in finding the minimal number of observations and minimal connectivity of the cyber-network as the next contribution. (iii) The cost-optimal design of cybernetwork constraint with distributed observability is addressed. This problem is subdivided into sensing cost optimization and networking cost optimization where both are claimed to be NPhard. We solve both problems for certain types of social networks and find polynomial-order solutions. Fig. 1. This figure shows a cyber-social system: a social system, represented by interaction of individuals over a social network, monitored by a cybernetwork of agents. In this figure, the social network may represent a consensus network or dynamics of opinions. The blue links from the social nodes to the cyber nodes represent the measurement or observation taken from the social states of individuals by the agents, and the intelligent units tracking and observing the state of individuals connected via, for example, a wireless network represent the cyber-network. Based on observed information, agents share sufficient information and perform distributed inference, and therefore, are able to globally track the state of all individuals in the social network.

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Necessary and sufficient conditions for the stabilizability of a class of LTI distributed observers

Cited by 53 publications

References 19 publications

A Distributed Observer for a Continuous-Time Linear System

A Distributed Observer for a Continuous-Time Linear System

On the Complexity of Minimum-Cost Networked Estimation of Self-Damped Dynamical Systems

Cyber-Social Systems: Modeling, Inference, and Optimal Design

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