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12
Information Consensus in Multivehicle Cooperative Control
, 2007
"... The abundance of embedded computational resources in autonomous vehicles enables enhanced operational effectiveness through cooperative teamwork in civilian and military applications. Compared to autonomous vehicles that perform solo missions, greater efficiency and operational capability can be rea ..."
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Cited by 228 (23 self)
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The abundance of embedded computational resources in autonomous vehicles enables enhanced operational effectiveness through cooperative teamwork in civilian and military applications. Compared to autonomous vehicles that perform solo missions, greater efficiency and operational capability can be realized from teams of autonomous vehicles operating in a coordinated fashion. Potential applications for multivehicle systems include spacebased interferometers, combat, surveillance, and reconnaissance systems, hazardous material handling, and distributed reconfigurable sensor networks. To enable these applications, various cooperative control capabilities need to be developed, including formation control, rendezvous, attitude alignment, flocking, foraging, task and role assign
Decentralized control of vehicle formations
, 2005
"... This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a prespecified communication digraph, G. A feedback control is designed using relative information between a vehicle an ..."
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Cited by 67 (0 self)
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This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a prespecified communication digraph, G. A feedback control is designed using relative information between a vehicle and its inneighbors in G. We prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that G has a rooted directed spanning tree. We show the direct relationship between the rate of convergence to formation and the eigenvalues of the (directed) Laplacian of G. Various special situations are discussed, including symmetric communication graphs and formations with leaders. Several numerical simulations are used to illustrate the results.
Effect of network structure on the stability margin of large vehicle formation with distributed control,” Mechanical and Aerospace Engineering
, 2010
"... Abstract — We study the problem of distributed control of a large network of doubleintegrator agents to maintain a rigid formation. A few lead vehicles are given information on the desired trajectory of the formation; while every other vehicle uses linear controller which only depends on relative p ..."
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Cited by 4 (1 self)
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Abstract — We study the problem of distributed control of a large network of doubleintegrator agents to maintain a rigid formation. A few lead vehicles are given information on the desired trajectory of the formation; while every other vehicle uses linear controller which only depends on relative position and velocity from a few other vehicles, which are called its neighbors. A predetermined information graph defines the neighbor relationships. We limit our attention to information graphs that are Ddimensional lattices, and examine the stability margin of the closed loop, which is measured by the real part of the least stable eigenvalue of the state matrix. The stability margin is shown to decay to 0 as O(1/N2/D) when the graph is “square”, where N is the number of agents. Therefore, increasing the dimension of the information graph can improve the stability margin by a significant amount. For a nonsquare information graph, the stability margin can be made independent of N by choosing the “aspect ratio ” appropriately. An information graph with large D may require nodes that are physically apart to exchange information. Similarly, choosing an aspect ratio to improve stability margin may entail an increase in the number of lead vehicles. These results are useful to the designer in making tradeoffs between performance and cost in designing information exchange architectures for decentralized control. I.
Modeling random flocks through generalized factor analysis
 In Proc. European Control Control Conference (ECC13), Zürich
"... Abstract — In this paper, we study modeling and identification of stochastic systems by Generalized Factor Analysis models. Although this class of models was originally introduced for econometric purposes, we present some possible applications of engineering interest. In particular, we show that the ..."
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Cited by 3 (3 self)
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Abstract — In this paper, we study modeling and identification of stochastic systems by Generalized Factor Analysis models. Although this class of models was originally introduced for econometric purposes, we present some possible applications of engineering interest. In particular, we show that there is a natural connection between Generalized Factor Analysis models and multiagents systems. The common factor component of the model has an interpretation as a flocking component of the system behavior. I.
Kernels of Directed Graph Laplacians
"... Abstract. Let G denote a directed graph with adjacency matrix Q and indegree matrix D. We consider the Kirchhoff matrix L = D − Q, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity of the eigenvalue 0 equals the numbe ..."
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Cited by 2 (0 self)
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Abstract. Let G denote a directed graph with adjacency matrix Q and indegree matrix D. We consider the Kirchhoff matrix L = D − Q, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity of the eigenvalue 0 equals the number of connected components of G. This fact has a meaningful generalization to directed graphs, as was observed by Chebotarev and Agaev in 2005. Since this result has many important applications in the sciences, we offer an independent and selfcontained proof of their theorem, showing in this paper that the algebraic and geometric multiplicities of 0 are equal, and that a graphtheoretic property determines the dimension of this eigenspace – namely, the number of reaches of the directed graph. We also extend their results by deriving a natural basis for the corresponding eigenspace. The results are proved in the general context of stochastic matrices, and apply equally well to directed graphs with nonnegative edge weights.
Cooperative Control of Unmanned Vehicle Formations
"... We review the enabling theory for the decentralized and cooperative control of formations of unmanned, autonomous vehicles. The decentralized and cooperative formation control approach combines recent results from dynamical system theory, control theory, and algebraic graph theory. The stability of ..."
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We review the enabling theory for the decentralized and cooperative control of formations of unmanned, autonomous vehicles. The decentralized and cooperative formation control approach combines recent results from dynamical system theory, control theory, and algebraic graph theory. The stability of vehicle formations is discussed, and the applicability of the technology concept to a variety of applications is demonstrated. 1
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"... Abstract — We investigate stable maneuvers for a group of autonomous vehicles while moving in formation. The allowed decentralized feedback laws are factored through the Laplacian matrix of the communication graph. We show that such laws allow for stable circular or elliptical motions for certain ve ..."
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Abstract — We investigate stable maneuvers for a group of autonomous vehicles while moving in formation. The allowed decentralized feedback laws are factored through the Laplacian matrix of the communication graph. We show that such laws allow for stable circular or elliptical motions for certain vehicle dynamics. We find necessary and sufficient conditions on the feedback gains and the dynamic parameters for convergence to formation. In particular, we prove that for undirected graphs there exist feedback gains that stabilize rotational (or elliptical) motions of arbitrary radius (or eccentricity). In the directed graph case we provide necessary and sufficient conditions on the curvature that guarantee stability for a given choice of feedback gains. We also investigate stable motions involving reorientation of the formation along the direction of motion.
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"... Analysis and identification of complex stochastic systems admitting a flocking structure ..."
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Analysis and identification of complex stochastic systems admitting a flocking structure
Modeling complex systems by Generalized Factor Analysis
"... Abstract—We propose a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The flocking component describes a sort of collective ..."
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Abstract—We propose a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The flocking component describes a sort of collective orderly motion which admits a much simpler mathematical description than the whole ensemble while the idiosyncratic component describes weakly correlated noise. We first discuss static GFA representations and characterize in a rigorous way the properties of the two components. The extraction of the dynamic flocking component is discussed for timestationary linear systems and for a simple classes of separable random fields. I.