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Automatic Control, IEEE Transactions on

Issue 3 • Date March 2014

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Displaying Results 1 - 25 of 34
  • Table of Contents

    Publication Year: 2014 , Page(s): C1 - C4
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  • IEEE Transactions on Automatic Control publication information

    Publication Year: 2014 , Page(s): C2
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  • Scanning the issue

    Publication Year: 2014 , Page(s): 553 - 554
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  • Common Information Based Markov Perfect Equilibria for Stochastic Games With Asymmetric Information: Finite Games

    Publication Year: 2014 , Page(s): 555 - 570
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3263 KB) |  | HTML iconHTML  

    A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information among the controllers makes it difficult to compute or characterize Nash equilibria. Using the common information among the controllers, the game with asymmetric information is used to construct another game with symmetric information such that the equilibria of the new game can be transformed to equilibria of the original game. Further, under certain conditions, a Markov state is identified for the new symmetric information game and its Markov perfect equilibria are characterized. This characterization provides a backward induction algorithm to find Nash equilibria of the original game with asymmetric information in pure or behavioral strategies. Each step of this algorithm involves finding Bayesian Nash equilibria of a one-stage Bayesian game. The class of Nash equilibria of the original game that can be characterized in this backward manner are named common information based Markov perfect equilibria. View full abstract»

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  • Generalized Efficiency Bounds in Distributed Resource Allocation

    Publication Year: 2014 , Page(s): 571 - 584
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3603 KB) |  | HTML iconHTML  

    Game theory is emerging as a popular tool for distributed control of multiagent systems. To take advantage of these game theoretic tools, the interactions of the autonomous agents must be designed within a game-theoretic environment. A central component of this game-theoretic design is the assignment of a local utility function to each agent. One promising approach to utility design is assigning each agent a utility function according to the agent's Shapley value. This method frequently results in games that possess many desirable features, such as the existence of pure Nash equilibria with near-optimal efficiency. In this paper, we explore the relationship between the Shapley value utility design and the resulting efficiency of both pure Nash equilibria and coarse correlated equilibria. To study this relationship, we introduce a simple class of resource allocation problems. Within this class, we derive an explicit relationship between the structure of the resource allocation problem and the efficiency of the resulting equilibria. Lastly, we derive a bicriteria bound for this class of resource allocation problems-a bound on the value of the optimal allocation relative to the value of an equilibrium allocation with additional agents. View full abstract»

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  • Adaptive Projection-Based Observers and {\rm L}_{1} Adaptive Controllers for Infinite-Dimensional Systems With Full-State Measurement

    Publication Year: 2014 , Page(s): 585 - 598
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4739 KB) |  | HTML iconHTML  

    Adaptive observers using projection-operator-based parameter update laws are considered for a class of linear infinite-dimensional systems with bounded input operator and full state measurement and subject to time-varying matched uncertainties and disturbances. The L1 adaptive control architecture, introduced recently for finite-dimensional plants to provide guaranteed transient performance via fast adaptation, is then extended to this class using the proposed observers. Existence and uniqueness of solutions for the resulting closed loop system and uniform boundedness of the observation error are established first. Then, provided certain assumptions on the plant transfer function and the solution of a Lyapunov inequality hold, uniform guaranteed transient performance bounds on the plant state and control signal under the L1 architecture are derived. Two examples satisfying the assumptions-control of a heat equation and a wave equation-are presented. Reference input tracking simulation results for the heat equation under the L1 adaptive control subject to time-varying matched uncertainties and disturbances are presented in support of the theory. View full abstract»

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  • Energy-Aware Scheduling on Heterogeneous Processors

    Publication Year: 2014 , Page(s): 599 - 613
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3544 KB) |  | HTML iconHTML  

    We study a multiserver system where servers are heterogeneous in terms of both their speeds and their usage (energy) costs. We show that the optimal control policy is threshold type, and can be implemented in a decentralized manner through an individually optimal policy. When there are no arrivals, we also derive explicit expressions for the thresholds. We consider both the case with reassignment, where jobs can be moved from one server to another at any time, and the case where reassignment is not possible. When reassignment is possible, determining which server is preferred (i.e., the one that is used even if there are very few jobs waiting) is surprisingly difficult. With arrivals, for the reassignment and no-reassignment cases, determining server preference is also difficult, and depends on the arrival rate. View full abstract»

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  • A Differential Lyapunov Framework for Contraction Analysis

    Publication Year: 2014 , Page(s): 614 - 628
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    Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. View full abstract»

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  • Learning in Mean-Field Games

    Publication Year: 2014 , Page(s): 629 - 644
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4011 KB) |  | HTML iconHTML  

    The purpose of this paper is to show how insight obtained from a mean-field model can be used to create an architecture for approximate dynamic programming (ADP) for a certain class of games comprising of a large number of agents. The general technique is illustrated with the aid of a mean-field oscillator game model introduced in our prior work. The states of the model are interpreted as the phase angles for a collection of nonhomogeneous oscillators, and in this way the model may be regarded as an extension of the classical coupled oscillator model of Kuramoto. The paper introduces ADP techniques for design and adaptation (learning) of approximately optimal control laws for this model. For this purpose, a parameterization is proposed, based on an analysis of the mean-field PDE model for the game. In an offline setting, a Galerkin procedure is introduced to choose the optimal parameters while in an online setting, a steepest descent algorithm is proposed. The paper provides a detailed analysis of the optimal parameter values as well as the Bellman error with both the Galerkin approximation and the online algorithm. Finally, a phase transition result is described for the large population limit when each oscillator uses the approximately optimal control law. A critical value of the control penalty parameter is identified: above this value, the oscillators are incoherent; and below this value (when control is sufficiently cheap) the oscillators synchronize. These conclusions are illustrated with results from numerical experiments. View full abstract»

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  • Distributed Cardinality Estimation in Anonymous Networks

    Publication Year: 2014 , Page(s): 645 - 659
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3682 KB) |  | HTML iconHTML  

    We consider estimation of network cardinality by distributed anonymous strategies relying on statistical inference methods. In particular, we focus on the relative Mean Square Error (MSE) of Maximum Likelihood (ML) estimators based on either the maximum or the average of M-dimensional vectors randomly generated at each node. In the case of continuous probability distributions, we show that the relative MSE achieved by the max-based strategy decreases as 1/M, independently of the used distribution, while that of the average-based estimator scales approximately as 2/M. We then introduce a novel strategy based on the average of M-dimensional vectors locally generated from Bernoulli random variables. In this case, the ML estimator, which is the Least Common Multiple (LCM) of the denominators of the irreducible fractions corresponding to the M elements of the average vector, leads to an MSE which goes exponentially to zero as M increases. We then discuss the effects of finite-precision arithmetics in practical dynamic implementations. Numerical experiments reveal that the MSE of the strategy based on Bernoulli trials is two order of magnitude smaller than that based on continuous random variables, at a price of one order of magnitude slower convergence time. View full abstract»

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  • Time Synchronization in WSNs: A Maximum-Value-Based Consensus Approach

    Publication Year: 2014 , Page(s): 660 - 675
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4479 KB) |  | HTML iconHTML  

    This paper considers time synchronization in wireless sensor networks. When the communication delay is negligible, the maximum time synchronization (MTS) protocol is proposed by which the skew and offset of each node can be synchronized simultaneously. For a more practical case where the intercommunication delays between each connected node are positive random variables, we propose the weighted maximum time synchronization (WMTS), which is able to counteract the impact of random communication delays. Despite the clock offset that cannot be synchronized, WMTS can synchronize the clock skew completely in expectation and achieve acceptable synchronization accuracy. For both protocols, we provide rigorous proofs of global convergence as well as the upper bounds of their convergence time. Compared with existing consensus-based synchronization protocols, the main advantages of our protocols include: 1) a faster convergence speed so that the synchronization can be achieved in a finite time for MTS, and in a finite time in expectation for WMTS, respectively; 2) simultaneous synchronization of both skews and offsets; and 3) random communication delays can be handled effectively. Numerical examples are presented to demonstrate the effectiveness of the proposed protocols. View full abstract»

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  • Online Markov Decision Processes Under Bandit Feedback

    Publication Year: 2014 , Page(s): 676 - 691
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (6056 KB) |  | HTML iconHTML  

    We consider online learning in finite stochastic Markovian environments where in each time step a new reward function is chosen by an oblivious adversary. The goal of the learning agent is to compete with the best stationary policy in hindsight in terms of the total reward received. Specifically, in each time step the agent observes the current state and the reward associated with the last transition, however, the agent does not observe the rewards associated with other state-action pairs. The agent is assumed to know the transition probabilities. The state of the art result for this setting is an algorithm with an expected regret of O(T2/3lnT). In this paper, assuming that stationary policies mix uniformly fast, we show that after T time steps, the expected regret of this algorithm (more precisely, a slightly modified version thereof) is O(T1/2lnT), giving the first rigorously proven, essentially tight regret bound for the problem. View full abstract»

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  • On Passivity of a Class of Discrete-Time Switched Nonlinear Systems

    Publication Year: 2014 , Page(s): 692 - 702
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2877 KB) |  | HTML iconHTML  

    This paper analyzes the passivity and feedback passivity of discrete-time-switched nonlinear systems with passive and nonpassive modes that are affine in the control input. When a nonpassive mode is active, the increase in storage function is not necessarily bounded by the energy supplied to the switched system at every time step. Therefore, a switched system with at least one nonpassive mode is defined to be nonpassive in the classical passivity theory. In this paper, we propose a framework to analyze the passivity of such switched systems in a more general sense. We consider switched nonlinear systems which are affine in the control input and may consist of passive, feedback passive modes, and modes which cannot be rendered passive using feedback. In the proposed framework, we prove that a switched nonlinear system is locally feedback passive if and only if its zero dynamics are locally passive. A lower bound on the ratio of total activation time between (feedback) passive and nonfeedback passive modes is obtained to guarantee passive zero dynamics. Finally, we prove that two important properties of classical passivity still hold for the proposed passivity definition, that is: 1) output feedback control can be used to stabilize the switched system, and 2) parallel and negative feedback interconnections of two such passive systems are also passive. View full abstract»

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  • Cyclic Change of Server's Performance: Impacts and Applications

    Publication Year: 2014 , Page(s): 703 - 713
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2976 KB) |  | HTML iconHTML  

    This paper studies a stochastic system where the performance of the server changes stochastically and cyclically. We first investigate the performance measures of the system, including the queue length and the overall cost. In particular, we derive an exact expression for the expected length of the renewal cycle, and present closed matrix forms for the mean and variance of the queue length. We then develop an explicit method to tackle a workload control problem, based on an M/G/1 queue approximation. Numerical examples are presented to illustrate the effectiveness of the method. View full abstract»

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  • Stackelberg Routing on Parallel Networks With Horizontal Queues

    Publication Year: 2014 , Page(s): 714 - 727
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4359 KB) |  | HTML iconHTML  

    This paper presents a game theoretic framework for studying Stackelberg routing games on parallel networks with horizontal queues, such as transportation networks. First, we introduce a new class of latency functions that models congestion due to the formation of physical queues. For this new class, some results from the classical congestion games literature (in which latency is assumed to be a non-decreasing function of the flow) do not hold. In particular, we find that there may exist multiple Nash equilibria that have different total costs. We provide a simple polynomial-time algorithm for computing the best Nash equilibrium, i.e., the one which achieves minimal total cost. Then we study the Stackelberg routing game: assuming a central authority has control over a fraction of the flow on the network (compliant flow), and that the remaining flow (non-compliant) responds selfishly, what is the best way to route the compliant flow in order to minimize the total cost? We propose a simple Stackelberg strategy, the Non-Compliant First (NCF) strategy, that can be computed in polynomial time. We show that it is optimal for this new class of latency on parallel networks. This work is applied to modeling and simulating congestion relief on transportation networks, in which a coordinator (traffic management agency) can choose to route a fraction of compliant drivers, while the rest of the drivers choose their routes selfishly. View full abstract»

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  • Periodical Solutions in a Pulse-Modulated Model of Endocrine Regulation With Time-Delay

    Publication Year: 2014 , Page(s): 728 - 733
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (924 KB) |  | HTML iconHTML  

    A hybrid mathematical model of endocrine regulation obtained by augmenting the classical continuous Smith model with a pulse-modulated feedback to describe episodic (pulsatile) secretion is considered. Conditions for existence and local orbital stability of periodical solutions with m impulses in the least period ( m-cycles) are derived. An important implication of the performed analysis is that the nonlinear dynamics of the pulse-modulated system and not the delay itself cause the sustained closed-loop oscillations. Furthermore, simulation and bifurcation analysis indicate that increasing the time delay in the system in hand typically, but not always, leads to less complex dynamic pattern in the closed-loop system by giving rise to stable cycles of lower periodicity. View full abstract»

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  • Minimum-Time Quantum Transport With Bounded Trap Velocity

    Publication Year: 2014 , Page(s): 733 - 738
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1074 KB) |  | HTML iconHTML  

    We formulate the problem of efficient transport of a quantum particle trapped in a harmonic potential which can move with a bounded velocity, as a minimum-time problem on a linear system with bounded input. We completely solve the corresponding optimal control problem and obtain an interesting bang-bang solution, where the switching times are obtained from a transcendental equation. These results are expected to find applications in quantum information processing and atom interferometry. View full abstract»

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  • Reach Controllability of Single Input Affine Systems on a Simplex

    Publication Year: 2014 , Page(s): 738 - 744
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1757 KB) |  | HTML iconHTML  

    We study the reach control problem (RCP) for a single input affine system with a simplicial state space. We extend previous results by exploring arbitrary triangulations of the state space; particularly allowing the set of possible equilibria to intersect the interior of simplices. In the studied setting, it is shown that closed-loop equilibria, nevertheless, only arise on the boundary of simplices. This allows to define a notion of reach controllability which quantifies the effect of the control input on boundary equilibria. Using reach controllability we obtain necessary and sufficient conditions for solvability of RCP by affine feedback. View full abstract»

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  • Upper and Lower Bounds for Controllable Subspaces of Networks of Diffusively Coupled Agents

    Publication Year: 2014 , Page(s): 745 - 750
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1202 KB) |  | HTML iconHTML  

    This technical note studies the controllability of diffusively coupled networks where some agents, called leaders, are under the influence of external control inputs. First, we consider networks where agents have general linear dynamics. Then, we turn our attention to infer network controllability from its underlying graph topology. To do this, we consider networks with agents having single-integrator dynamics. For such networks, we provide lower and upper bounds for the controllable subspaces in terms of the distance partitions and the maximal almost equitable partitions, respectively. We also provide an algorithm for computing the maximal almost equitable partition for a given graph and a set of leaders. View full abstract»

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  • Output Synchronization of Networked Passive Systems With Event-Driven Communication

    Publication Year: 2014 , Page(s): 750 - 756
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1502 KB) |  | HTML iconHTML  

    In this note, we study the output synchronization problem of networked passive systems with event-driven communication, in which the information exchange among the coupled agents are event-based rather than pre-scheduled periodically. We propose a setup for the interconnected agents to achieve output synchronization with event-driven communication in the presence of constant communication delays. The results presented here are important extensions of applying event-driven communication to control of multi-agent systems, especially when it is difficult to derive a common upper bound on the admissible network induced delays, or when the network induced delays between coupled agents are larger than the inter-event time implicitly determined by the event-triggering condition. View full abstract»

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  • Finite-Time Consensus in Networks of Integrator-Like Dynamic Agents With Directional Link Failure

    Publication Year: 2014 , Page(s): 756 - 762
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1518 KB) |  | HTML iconHTML  

    This technical note proposes a general class of nonlinear protocols in the form of continuous state feedbacks for finite-time consensus in networks of integrator-like dynamic agents with directional link failure. These protocols, with adjustable terms, are applicable in a wide range of situations, such as with input saturation restrictions and with convergence rate constraints. Based on the assumption of a common positive dwell time for all active information links, it is shown that if the union of the interaction topology over some fixed length of time always contains a spanning tree, then the system will solve an asymptotical consensus problem; in addition, if the length sum of time intervals, over which the interaction topology contains a spanning tree, is larger than a threshold, determined by the state differences between agents, then the system will solve a finite-time consensus problem. The validity of the protocols is proven in the case with external reference inputs. Finally, simulations are presented to demonstrate the effectiveness of the theoretical results. View full abstract»

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  • Average Consensus in the Presence of Delays in Directed Graph Topologies

    Publication Year: 2014 , Page(s): 763 - 768
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1161 KB) |  | HTML iconHTML  

    Classical distributed algorithms for asymptotic average consensus typically assume timely and reliable exchange of information between neighboring components of a given multi-component system. These assumptions are not necessarily valid in practice due to varying delays that might affect computations at different nodes and/or transmissions at different links. In this work, we propose a protocol that overcomes this limitation and, unlike existing consensus protocols in the presence of delays, ensures asymptotic consensus to the exact average, despite the presence of arbitrary (but bounded) delays in the communication links. The protocol requires that each component has knowledge of the number of its out-neighbors (i.e., the number of components to which it can send information) and its proof of correctness relies on the weak convergence of a backward product of column stochastic matrices. The proposed algorithm is demonstrated via illustrative examples. View full abstract»

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  • Cooperative Optimal Control for Multi-Agent Systems on Directed Graph Topologies

    Publication Year: 2014 , Page(s): 769 - 774
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1239 KB) |  | HTML iconHTML  

    This note brings together stability and optimality theory to design distributed cooperative control protocols that guarantee consensus and are globally optimal with respect to a positive semi-definite quadratic performance criterion. A common problem in cooperative optimal control is that global optimization problems generally require global information, which is not available to distributed controllers. Optimal control for multi-agent systems is complicated by the fact that the communication graph topology interplays with the agent system dynamics. In the note we use an inverse optimality approach together with partial stability to consider the cooperative consensus and pinning control. Agents with identical linear time-invariant dynamics are considered. Communication graphs are assumed directed and having fixed topology. Structured quadratic performance indices are derived that capture the topology of the graph, which allows for global optimal control that is implemented using local distributed protocols. A new class of digraphs is defined that admits a distributed solution to the global optimal control problem, namely those with simple graph Laplacian matrices. View full abstract»

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  • Constrained Consensus in Unbalanced Networks With Communication Delays

    Publication Year: 2014 , Page(s): 775 - 781
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2180 KB) |  | HTML iconHTML  

    In this note, a constrained consensus problem is studied for multi-agent systems in unbalanced networks in the presence of communication delays. Here each agent needs to lie in a closed convex constraint set while reaching a consensus. The communication graphs are directed, dynamically changing, and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of a certain bounded length. The analysis is performed based on an undelayed equivalent system that is composed of a linear main body and an error auxiliary. To tackle the loss of symmetry caused by unbalanced graphs and communication delays, a novel approach is proposed. The idea is to estimate the distance from each agent to the intersection set of all agents' constraint sets based on the properties of the projection on convex sets so as to show consensus convergence by contradiction. It is shown that the error auxiliary vanishes as time evolves and the linear main body converges to a vector with an exponential rate as a separate system. It is also shown that the communication delays do not affect the consensus stability and constrained consensus is reached even if the communication delays are arbitrarily bounded. Finally, a numerical example is included to illustrate the obtained theoretical results. View full abstract»

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  • Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs

    Publication Year: 2014 , Page(s): 781 - 786
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1730 KB) |  | HTML iconHTML  

    This technical note studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed scenarios, we show that the consensus-based dynamics that solves the continuous-time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting. This study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge, on any strongly connected weight-balanced digraph, to the set of minimizers of a sum of convex differentiable functions with globally Lipschitz gradients. Our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results. View full abstract»

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Aims & Scope

In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering.  Two types of contributions are regularly considered

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Meet Our Editors

Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame