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24
An overview of recent progress in the study of distributed multiagent coordination
, 2012
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Distributed Asynchronous Constrained Stochastic Optimization
, 2011
"... In this paper we study two problems which often occur in various applications arising in wireless sensor networks. These are the problem of reaching an agreement on the value of local variables in a network of computational agents and the problem of cooperative solution to a convex optimization prob ..."
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In this paper we study two problems which often occur in various applications arising in wireless sensor networks. These are the problem of reaching an agreement on the value of local variables in a network of computational agents and the problem of cooperative solution to a convex optimization problem, where the objective function is the aggregate sum of local convex objective functions. We incorporate the presence of a random communication graph between the agents in our model as a more realistic abstraction of the gossip and broadcast communication protocols of a wireless network. An added ingredient is the presence of local constraint sets to which the local variables of each agent is constrained. Our model allows for the objective functions to be nondifferentiable and accommodates the presence of noisy communication links and subgradient errors. For the consensus problem we provide a diminishing step size algorithm which guarantees asymptotic convergence. The distributed optimization algorithm uses two diminishing step size sequences to account for communication noise and subgradient errors. We establish conditions on these step sizes under which we can achieve the dual task of reaching consensus and convergence to the optimal set with probability one. In both cases we consider the constant step size behavior of the algorithm and establish asymptotic error bounds.
Consensus and products of random stochastic matrices: Exact rate for convergence in probability
 Carnegie Mellon University (CMU
, 2013
"... Abstract—We find the exact rate for convergence in probability of products of independent, identically distributed symmetric, stochastic matrices. It is wellknown that if the matrices have positive diagonals almost surely and the support graph of the mean or expected value of the random matrices ..."
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Abstract—We find the exact rate for convergence in probability of products of independent, identically distributed symmetric, stochastic matrices. It is wellknown that if the matrices have positive diagonals almost surely and the support graph of the mean or expected value of the random matrices is connected, the products of the matrices converge almost surely to the average consensus matrix, and thus in probability. In this paper, we show that the convergence in probability is exponentially fast, and we explicitly characterize the exponential rate of this convergence. Our analysis reveals that the exponential rate of convergence in probability depends only on the statistics of the support graphs of the randommatrices. Further, we show how to compute this rate for commonly used randommodels: gossip and link failure.With thesemodels, the rate is found by solving a mincut problem, and hence it is easily computable. Finally, as an illustration, we apply our results to solving power allocation among networked sensors in a consensus+innovations distributed detection problem. Index Terms—Consensus, consensus innovations, convergence in probability, exponential rate, performance analysis, random network. I.
Distributed Change Detection Based on a Consensus Algorithm
"... Abstract: In this paper a novel consensus based distributed recursive algorithm is proposed for real time change detection using sensor networks. Convergence of the algorithm to the optimal centralized solution defined by a weighted sum of the results of local signal processing is proved in the case ..."
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Abstract: In this paper a novel consensus based distributed recursive algorithm is proposed for real time change detection using sensor networks. Convergence of the algorithm to the optimal centralized solution defined by a weighted sum of the results of local signal processing is proved in the cases of constant and time varying forgetting factors of the underlying recursions, assuming correlated data and different local values of the parameter changes. Simulation results illustrate characteristic properties of the algorithms. 1.
Moving horizon state estimation of largescale constrained partitioned systems – Version 2
, 2009
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Distributed boundederror state estimation based on practical robust positive invariance
"... We propose a state estimator for linear discretetime systems composed by coupled subsystems affected by bounded disturbances. The architecture is distributed in the sense that each subsystem is equipped with a local state estimator that exploits suitable pieces of information from parent subsystems ..."
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We propose a state estimator for linear discretetime systems composed by coupled subsystems affected by bounded disturbances. The architecture is distributed in the sense that each subsystem is equipped with a local state estimator that exploits suitable pieces of information from parent subsystems. Furthermore, each local estimator reconstructs the state of the corresponding subsystem only. Differently from methods based on moving horizon estimation, our approach does not require the online solution to optimization problems. Our stateestimation scheme, which is based on the notion of practical robust positive invariance developed in (Raković, Kern, & Findeisen, 2011), also guarantees satisfaction of constraints on local estimation errors and it can be updated with a limited computational effort when subsystems are added or removed.
Plugandplay distributed state estimation for linear systems
 in Proceedings of the 52nd IEEE Conference on Decision and Control
"... This paper proposes a state estimator for largescale linear systems described by the interaction of statecoupled subsystems affected by bounded disturbances. We equip each subsystem with a Local State Estimator (LSE) for the reconstruction of the subsystem states using pieces of information from ..."
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This paper proposes a state estimator for largescale linear systems described by the interaction of statecoupled subsystems affected by bounded disturbances. We equip each subsystem with a Local State Estimator (LSE) for the reconstruction of the subsystem states using pieces of information from parent subsystems only. Moreover we provide conditions guaranteeing that the estimation errors are confined into prescribed polyhedral sets and converge to zero in absence of disturbances. Quite remarkably, the design of an LSE is recast into an optimization problem that requires data from the corresponding subsystem and its parents only. This allows one to synthesize LSEs in a PlugandPlay (PnP) fashion, i.e. when a subsystem gets added, the update of the whole estimator requires at most the design of an LSE for the subsystem and its parents. Theoretical results are backed up by numerical experiments on a mechanical system. ∗The research leading to these results has received funding from the European Union Seventh Framework Programme [FP7/20072013] under grant agreement n ◦ 257462 HYCON2 Network of excellence.
Distributed model predictive control: A tutorial review and future research directions
 Comput. Chem. Eng
"... AbstractIn this paper, we provide a tutorial review of recent results in the design of distributed model predictive control systems. Our goal is to not only conceptually review the results in this area but also to provide enough algorithmic details so that the advantages and disadvantages of the v ..."
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AbstractIn this paper, we provide a tutorial review of recent results in the design of distributed model predictive control systems. Our goal is to not only conceptually review the results in this area but also to provide enough algorithmic details so that the advantages and disadvantages of the various approaches can be become quite clear. In this sense, our hope is that this paper would complement a series of recent review papers and catalyze future research in this rapidlyevolving area.
Moving horizon estimation for distributed nonlinear systems with application to cascade river reaches
, 2010
"... This paper presents a Moving Horizon Estimation (MHE) method for discretetime nonlinear systems decomposed into coupled subsystems with nonoverlapping states. In the proposed algorithm, each subsystem solves a reducedorder MHE problem to estimate its own state based on the estimates computed by i ..."
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This paper presents a Moving Horizon Estimation (MHE) method for discretetime nonlinear systems decomposed into coupled subsystems with nonoverlapping states. In the proposed algorithm, each subsystem solves a reducedorder MHE problem to estimate its own state based on the estimates computed by its neighbors. Conditions for the convergence of the estimates are investigated. The algorithm is applied to a model of three river reaches.
Distributed Constrained Optimization over Noisy Networks
"... Abstract—In this paper we deal with two problems which are of great interest in the field of distributed decision making and control. The first problem we tackle is the problem of achieving consensus on a vector of local decision variables in a network of computational agents when the decision varia ..."
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Abstract—In this paper we deal with two problems which are of great interest in the field of distributed decision making and control. The first problem we tackle is the problem of achieving consensus on a vector of local decision variables in a network of computational agents when the decision variables of each node are constrained to lie in a subset of the Euclidean space. Such constraints arise out of consideration of local characteristics of each node. We assume that the constraint sets for the local variables are private information for each node. We provide a distributed algorithm for the case when there is communication noise present in the network. We show that we can achieve almost sure convergence under certain assumptions. The second problem we discuss is the problem of distributed constrained optimization when the constraint sets are distributed over the agents. Furthermore our model incorporates the presence of noisy communication links and the presence of stochastic errors in the evaluation of subgradients of the local objective function. We establish sufficient conditions and provide an analysis guaranteeing the convergence of the algorithm to the optimal set with probability one. I.