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Convergence speed in distributed consensus and averaging
 IN PROC. OF THE 45TH IEEE CDC
, 2006
"... We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove ..."
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Cited by 138 (4 self)
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We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worstcase convergence time for various classes of linear, timeinvariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a timevarying topology, and provide a polynomialtime averaging algorithm.
Distributed Kalman filtering based on consensus strategies
, 2007
"... In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman ..."
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Cited by 56 (1 self)
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In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalmanlike measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of exchanged messages per sampling time is small. Moreover, we showed that although the joint optimization of the consensus matrix and the Kalman gain is in general a nonconvex problem, it is possible to compute them under some important scenarios. We also provide some numerical examples to clarify some of the analytical results and compare them with alternative estimation strategies.
A distributed consensus protocol for clock synchronization in wireless sensor network
, 2007
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Consensusbased distributed sensor calibration and leastsquare parameter identification in wsns
 International Journal of Robust and Nonlinear Control
"... In this paper we study the problem of estimating the channel parameters for a generic wireless sensor network (WSN) in a completely distributed manner, using consensus algorithms. Specifically, we first propose a distributed strategy to minimize the effects of unknown constant offsets in the reading ..."
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Cited by 24 (8 self)
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In this paper we study the problem of estimating the channel parameters for a generic wireless sensor network (WSN) in a completely distributed manner, using consensus algorithms. Specifically, we first propose a distributed strategy to minimize the effects of unknown constant offsets in the reading of the Radio Strength Signal Indicator (RSSI) due to uncalibrated sensors. Then we show how the computation of the optimal wireless channels parameters, which are the solution of a global leastsquare optimization problem, can be obtained with a consensusbased algorithm. The proposed algorithms are general algorithms for sensor calibration and distributed leastsquare parameter identification, and do not require any knowledge on the global topology of the network nor the total number of nodes. Finally, we apply these algorithms to experimental data collected from an indoor wireless sensor network.
Secondorder consensus for multiagent systems with directed topologies and nonlinear dynamics
 IEEE Transactions on Automatic Control
"... Abstract—This paper considers a secondorder consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a timevarying asymptotic velocity. To describe the system’s ability for reaching co ..."
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Cited by 20 (4 self)
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Abstract—This paper considers a secondorder consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a timevarying asymptotic velocity. To describe the system’s ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching secondorder consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis. Index Terms—Algebraic connectivity, directed spanning tree, multiagent system, secondorder consensus, strongly connected network. I.
COORDINATED PATHFOLLOWING IN THE PRESENCE OF COMMUNICATION LOSSES AND TIME DELAYS ∗
"... Abstract. This paper addresses the problem of steering a group of vehicles along given paths while holding a desired formation pattern. The solution to this problem, henceforth referred to as the Coordinated PathFollowing problem, unfolds in two basic steps. First, a pathfollowing control law is u ..."
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Cited by 19 (9 self)
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Abstract. This paper addresses the problem of steering a group of vehicles along given paths while holding a desired formation pattern. The solution to this problem, henceforth referred to as the Coordinated PathFollowing problem, unfolds in two basic steps. First, a pathfollowing control law is used that drives each vehicle to its assigned path regardless of the temporal speed profile adopted. This is done by making each vehicle approach a conveniently defined virtual target that moves along the path. In the second step, the speeds of the vehicles are adjusted so as to synchronize the positions of the corresponding virtual targets (also called coordination states) thus achieving coordination along the paths. In the problem formulation, it is explicitly considered that each vehicle transmits its coordination state to only a subset of the other vehicles, as determined by the communications topology adopted. It is shown that the system that is obtained by putting together the path following and coordination strategies can be naturally viewed as a feedback interconnected system. Using this result and recent results from nonlinear system and graph theory, conditions are derived under which the path following and the coordination errors are driven to a neighborhood of zero in the presence of communication failures and time delays. Two different situations are considered. The first captures the case where the communication graph is alternately connected and disconnected (brief connectivity losses). The second reflects an operating scenario where the union of the communication graphs over uniform intervals of time remains connected (uniformly connected in mean). To better ground the paper on a nontrivial design example, a coordinated pathfollowing algorithm is derived for multiple underactuated Autonomous Underwater Vehicles (AUVs). Simulation results are presented and discussed. Key words. Coordination control, communication losses and time delays, pathfollowing, autonomous underwater vehicle AMS subject classifications. 1. Introduction. Increasingly
Opinion dynamics in heterogeneous networks: convergence conjectures and theorems
 SIAM Journal on Control and Optimization
, 2012
"... Abstract. Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors ’ opinions. The neighbors of each agent can be defined as either (1) those agent ..."
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Cited by 13 (3 self)
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Abstract. Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors ’ opinions. The neighbors of each agent can be defined as either (1) those agents whose opinions are in its “confidence range, ” or (2) those agents whose “influence range” contain the agent’s opinion. The former definition is employed in Hegselmann and Krause’s bounded confidence model, and the latter is novel here. As the confidence and influence ranges are distinct for each agent, the heterogeneous statedependent interconnection topology leads to a poorlyunderstood complex dynamic behavior. In both models, we classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. Then, we define a positive invariant set centered at each equilibrium opinion vector. We show that if a trajectory enters one such set, then it converges to a steady state with constant interconnection topology. This result gives us a novel sufficient condition for both models to establish convergence, and is consistent with our conjecture that all trajectories of the bounded confidence and influence models eventually converge to a steady state under fixed topology.
Attackresilient distributed formation control via online adaptation
 In IEEE Int. Conf. on Decision and Control
, 2011
"... Abstract. This paper tackles a distributed formation control problem where a group of vehicles is remotely controlled by a network of operators. Each operatorvehicle pair is attacked by an adversary, who corrupts the commands sent from the operator to the vehicle. From the point of view of operator ..."
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Cited by 12 (6 self)
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Abstract. This paper tackles a distributed formation control problem where a group of vehicles is remotely controlled by a network of operators. Each operatorvehicle pair is attacked by an adversary, who corrupts the commands sent from the operator to the vehicle. From the point of view of operators, each adversary follows an attacking strategy linearly parameterized by some (potentially timevarying) matrix which is unknown a priori. In particular, we consider two scenarios depending upon whether adversaries can adapt their attacking tactics online. To assure mission completion in such a hostile environment, we propose two novel attackresilient distributed control algorithms that allow operators to adjust their policies on the fly by exploiting the latest collected information about adversaries. Both algorithms enable vehicles to asymptotically achieve the desired formation from any initial configuration and initial estimate of the adversaries ’ strategies. It is further shown that the sequence of the distances to the desired formation is square summable for each proposed algorithm. In numerical examples, the convergence rates of our algorithms are exponential, outperforming the theoretic results.
Convergence speed of unsteady distributed consensus: decay estimate along the settling spanningtrees
, 2008
"... Results for estimating the convergence rate of nonstationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lowerbounds on the matrix entries). The results appear to be tight in a number of instances and ar ..."
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Cited by 12 (1 self)
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Results for estimating the convergence rate of nonstationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lowerbounds on the matrix entries). The results appear to be tight in a number of instances and are illustrated through simple as well as more sophisticated examples. The main idea is to follow propagation of information along certain spanning trees which arise in the communication graph.