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Information Centrality and Optimal Leader Selection in Noisy Networks
 IN: PROC. IEEE CONFERENCE ON DECISION AND CONTROL. IEEE
, 2013
"... We consider the leader selection problem in which a system of networked agents, subject to stochastic disturbances, uses a decentralized coordinated feedback law to track an unknown external signal, and only a limited number of agents, known as leaders, can measure the signal directly. The optima ..."
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Cited by 9 (2 self)
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We consider the leader selection problem in which a system of networked agents, subject to stochastic disturbances, uses a decentralized coordinated feedback law to track an unknown external signal, and only a limited number of agents, known as leaders, can measure the signal directly. The optimal leader selection minimizes the total system error by minimizing the steadystate variance about the external signal, equivalent to an H2 norm of the linear stochastic network dynamics. Efficient greedy algorithms have been proposed in the literature for similar optimal leader selection problems. In contrast, we seek systematic solutions. We prove that the single optimal leader is the node in the network graph with maximal information centrality. In the case of two leaders, we prove that the optimal pair maximizes a joint centrality, which depends on the information centrality of each leader and how well the pair covers the graph. We apply these results to solve explicitly for the optimal single leader and the optimal pair of leaders in special classes of network graphs. To generalize we compute joint centrality for m leaders.
On new characterizations of social influence in social networks
 in Proceedings of the 2013 American Control Conference, 2013
"... Abstract — We propose new characterizations of social influence, which quantify both the transient and the steadystate propagation of beliefs across society. These characterizations are used to optimally choose a desired number of agents in a social network to serve as social leaders with maximal ..."
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Cited by 4 (3 self)
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Abstract — We propose new characterizations of social influence, which quantify both the transient and the steadystate propagation of beliefs across society. These characterizations are used to optimally choose a desired number of agents in a social network to serve as social leaders with maximal social impact. We then consider a framework for optimally creating new social links subject to resource constraints, in order to improve the influence of designated agents or social leaders. We show that the formulated optimization problems are convex with respect to the individual elements of the optimization variables. This motivates the use of the coordinate descent method, a simple but efficient algorithm wellsuited to largescale optimization problems. Finally, using demonstrative examples, we compare the ability of our proposed characterizations of social influence in identifying the most influential agents with that of other measures of influence developed in the social networks literature. Index Terms — Betweenness centrality, consensus, convex relaxation, coordinate descent, leader selection, optimization,
Minimizing Convergence Error in MultiAgent Systems via Leader Selection: A Supermodular Optimization Approach
"... In a leaderfollower multiagent system (MAS), the leader agents act as control inputs and influence the states of the remaining follower agents. The rate at which the follower agents converge to their desired states, as well as the errors in the follower agent states prior to convergence, are dete ..."
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Cited by 3 (0 self)
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In a leaderfollower multiagent system (MAS), the leader agents act as control inputs and influence the states of the remaining follower agents. The rate at which the follower agents converge to their desired states, as well as the errors in the follower agent states prior to convergence, are determined by the choice of leader agents. In this paper, we study leader selection in order to minimize convergence errors experienced by the follower agents, which we define as a norm of the distance between the follower agents ’ intermediate states and the convex hull of the leader agent states. By introducing a novel connection to random walks on the network graph, we show that the convergence error has an inherent supermodular structure as a function of the leader set. Supermodularity enables development of efficient discrete optimization algorithms that directly approximate the optimal leader set, provide provable performance guarantees, and do not rely on continuous relaxations. We formulate two leader selection problems within the supermodular optimization framework, namely, the problem of selecting a fixed number of leader agents in order to minimize the convergence error, as well as the problem of selecting the minimumsize set of leader agents to achieve a given bound on the convergence error. We introduce algorithms for approximating the optimal solution to both problems in static networks, dynamic networks with known topology distributions, and dynamic networks with unknown and unpredictable topology distributions. Our approach is shown to provide significantly lower convergence errors than existing random and degreebased leader selection methods in a numerical study.
MultiAgent System Dynamics: Bifurcation and Behavior of Animal Groups
 In: Proc. 9th IFAC Symposium on Nonlinear Control Systems
, 2013
"... Abstract: Systematic design of decentralized feedback for coordinated control of multiagent systems has much to gain from the rigorous examination of the nonlinear dynamics of collective animal behavior. Animals in groups, from bird flocks to fish schools, employ decentralized strategies and have l ..."
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Cited by 1 (1 self)
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Abstract: Systematic design of decentralized feedback for coordinated control of multiagent systems has much to gain from the rigorous examination of the nonlinear dynamics of collective animal behavior. Animals in groups, from bird flocks to fish schools, employ decentralized strategies and have limitations on sensing, computation, and actuation. Yet, at the level of the group, they are known to manage a variety of challenging tasks quickly, accurately, robustly and adaptively in an uncertain and changing environment. In this paper we review recent work on models and methods for studying the mechanisms of collective migration and collective decisionmaking in highperforming animal groups. Through bifurcation analyses we prove systematically how behavior depends on parameters that model the system and the environment. These connections lay the foundations for proving systematic control design methodologies that endow engineered multiagent systems with the remarkable features of animal group dynamics. 1.
Minimum Cost Input/Output Design for LargeScale Linear Structural Systems
, 2015
"... In this paper, we provide optimal solutions to two different (but related) input/output design problems involving largescale linear dynamical systems, where the cost associated to each directly actuated/measured state variable can take different values, but is independent of the labeled input/outpu ..."
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In this paper, we provide optimal solutions to two different (but related) input/output design problems involving largescale linear dynamical systems, where the cost associated to each directly actuated/measured state variable can take different values, but is independent of the labeled input/output variable. Under these conditions, we first aim to determine and characterize the input/output placement that incurs in the minimum cost while ensuring that the resulting placement achieves structural controllability/observability. Further, we address a constrained variant of the above problem, in which we seek to determine the minimum cost placement configuration, among all possible input/output placement configurations that ensures structural controllability/observability, with the lowest number of directly actuated/measured state variables. We show that both problems can be solved efficiently, i.e., using algorithms with polynomial time complexity in the number of the state variables. Finally, we illustrate the obtained results with an example.
RESEARCH STATEMENT
"... My primary research interests in algebraic geometry lie in the Minimal Model Program and its applications, moduli spaces of stable maps (curves), and moduli spaces of branchvarieties. Recently I have also paid close attention to the new advances in computational algebraic geometry. 1 Minimal Model P ..."
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My primary research interests in algebraic geometry lie in the Minimal Model Program and its applications, moduli spaces of stable maps (curves), and moduli spaces of branchvarieties. Recently I have also paid close attention to the new advances in computational algebraic geometry. 1 Minimal Model Program and its applications In many branches of mathematics, classifications among objects up to certain relations are central themes. For example, topologists can classify topological spaces up to homeomorphism or up to the weaker relation of homotopy. Similarly, in algebraic geometry, we classify algebraic varieties up to either isomorphism or a weaker relation, birational equivalence (two varieties X and Y are birationally equivalent if there exist rational maps f: X − → Y and g: Y − → X such that g ◦f and f ◦ g are identity maps on some open subsets U ⊂ X and V ⊂ Y). Among algebraic varieties in the same birational equivalence class, we want to single out some “good ” representatives. Such good representatives are called minimal models. It is well known that every surface has a minimal model. Is there a minimal model for every higher dimensional algebraic variety? The answer was unknown for a long period of time even for threefolds. At first people tried to find a minimal model in the smooth category, but this turned out to be impossible. Gradually people realized that one can only
Sparse Sensing for Estimation with Correlated Observations
"... Abstract—We focus on discrete sparse sensing for nonlinear parameter estimation with colored Gaussian observations. In particular, we design offline sparse samplers to reduce the sensing cost as well as to reduce the storage and communications requirements, yet achieving a desired estimation accura ..."
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Abstract—We focus on discrete sparse sensing for nonlinear parameter estimation with colored Gaussian observations. In particular, we design offline sparse samplers to reduce the sensing cost as well as to reduce the storage and communications requirements, yet achieving a desired estimation accuracy. We optimize scalar functions of the CramérRao boundmatrix, which we use as the inference performance metric to design the sparse samplers of interest via a convex program. The sampler design does not require the actual measurements, however it needs the model parameters to be perfectly known. The proposed approach is illustrated with a sensor placement example. Index Terms—Sparse sensing, sensor selection, sensor placement, dependent observations, nonlinear least squares. I.
Sparse quadratic regulator
"... Abstract—We consider a control design problem aimed at balancing quadratic performance of linear systems with additional requirements on the control signal. These are introduced in order to obtain controls that are either sparse or infrequently changing in time. To achieve this objective, we augment ..."
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Abstract—We consider a control design problem aimed at balancing quadratic performance of linear systems with additional requirements on the control signal. These are introduced in order to obtain controls that are either sparse or infrequently changing in time. To achieve this objective, we augment a standard quadratic performance index with an additional term that penalizes either the `1 norm or the total variation of the control signal. We show that the minimizer of this convex optimization problem can be found by solving a two point boundary value problem (TPBVP) with nondifferentiable nonlinearities. Furthermore, we employ alternating direction method of multipliers to determine the optimal controller iteratively from a sequence of linear TPBVPs. Examples are provided to illustrate the developed method. Index Terms—Alternating direction method of multipliers, convex optimization, linear timeinvariant systems, quadratic performance, sparsity, total variation. I.
1Joint Centrality Distinguishes Optimal Leaders in Noisy Networks
"... We study the performance of a network of agents tasked with tracking an external unknown signal in the presence of stochastic disturbances and under the condition that only a limited subset of agents, known as leaders, can measure the signal directly. We investigate the optimal leader selection prob ..."
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We study the performance of a network of agents tasked with tracking an external unknown signal in the presence of stochastic disturbances and under the condition that only a limited subset of agents, known as leaders, can measure the signal directly. We investigate the optimal leader selection problem for a prescribed maximum number of leaders, where the optimal leader set minimizes total system error defined as steadystate variance about the external signal. In contrast to previously established greedy algorithms for optimal leader selection, our results rely on an expression of total system error in terms of properties of the underlying network graph. We demonstrate that the performance of any given set of leaders depends on their influence as determined by a new graph measure of centrality of a set. We define the joint centrality of a set of nodes in a network graph such that a leader set with maximal joint centrality is an optimal leader set. In the case of a single leader, we prove that the optimal leader is the node with maximal information centrality. In the case of multiple leaders, we show that the nodes in the optimal leader set balance high information centrality with a coverage of the graph. For special cases of graphs, we solve explicitly for optimal leader sets. We illustrate with examples. I.
1Topology Design for Optimal Network Coherence
"... Abstract—We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show that network coherence is a submodular function of ..."
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Abstract—We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show that network coherence is a submodular function of the network topology. As a consequence, a simple greedy algorithm is guaranteed to produce near optimal edge set selections. We also show that fast rank one updates of the Laplacian pseudoinverse using generalizations of the ShermanMorrison formula and an accelerated variant of the greedy algorithm can speed up the algorithm by several orders of magnitude in practice. These allow our algorithms to scale to network sizes far beyond those that can be handled by convex relaxation heuristics. I.