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33
SYNCHRONIZATION VIA PINNING CONTROL ON GENERAL COMPLEX NETWORKS
, 2013
"... This paper studies synchronization via pinning control on general complex dynamical networks, such as strongly connected networks, networks with a directed spanning tree, weakly connected networks, and directed forests. A criterion for ensuring network synchronization on strongly connected network ..."
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This paper studies synchronization via pinning control on general complex dynamical networks, such as strongly connected networks, networks with a directed spanning tree, weakly connected networks, and directed forests. A criterion for ensuring network synchronization on strongly connected networks is given. It is found that the vertices with very small indegrees should be pinned first. In addition, it is shown that the original condition with controllers can be reformulated such that it does not depend on the form of the chosen controllers, which implies that the vertices with very large outdegrees may be pinned. Then, a criterion for achieving synchronization on networks with a directed spanning tree, which can be composed of many strongly connected components, is derived. It is found that the strongly connected components with very few connections from other components should be controlled and the components with many connections from other components can achieve synchronization even without controls. Moreover, a simple but effective pinning algorithm for reaching synchronization on a general complex dynamical network is proposed. Finally, some simulation examples are given to verify the proposed pinning scheme.
Optimal decentralized statefeedback control with sparsity and delays
, 2015
"... This work presents the solution to a class of decentralized linear quadratic statefeedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition of the noise history, the control problem is split into ind ..."
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This work presents the solution to a class of decentralized linear quadratic statefeedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition of the noise history, the control problem is split into independent subproblems that are solved using dynamic programming. The approach presented herein both unifies and generalizes many existing results.
On the convergence of decentralized gradient descent
, 2013
"... Consider the consensus problem of minimizing f(x) = ∑n i=1 fi(x) where each fi is only known to one individual agent i belonging to a connected network of n agents. All the agents shall collaboratively solve this problem and obtain the solution via data exchanges only between neighboring agents. Suc ..."
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Consider the consensus problem of minimizing f(x) = ∑n i=1 fi(x) where each fi is only known to one individual agent i belonging to a connected network of n agents. All the agents shall collaboratively solve this problem and obtain the solution via data exchanges only between neighboring agents. Such algorithms avoid the need of a fusion center, offer better network load balance, and improve data privacy. We study the decentralized gradient descent method in which each agent i updates its variable x(i), which is a local approximate to the unknown variable x, by taking the average of its neighbors ’ followed by making a local negative gradient step −α∇fi(x(i)). The iteration is x(i)(k + 1)←
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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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.
Modeling a multirobot system with fractionalorder differential equations
 In Proceedings of the 2014 IEEE International Conference on Robotics and Automation
, 2014
"... Abstract—This paper shows that a fractionalorder differential equation may be used to accurately model the dynamic relationship between the first and last generations in a fleet of coordinating robots, even when the individual robots and interconnections have the usual integerorder dynamics. Such ..."
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Abstract—This paper shows that a fractionalorder differential equation may be used to accurately model the dynamic relationship between the first and last generations in a fleet of coordinating robots, even when the individual robots and interconnections have the usual integerorder dynamics. Such a fractionalorder model offers the possibility of general applicability, particularly in the case of heterogeneous fleets of robots. Such systems tend to be very high order, and therefore model reduction is useful in modeling, simulation and control. Results are presented for the system considered illustrating that the fractionalorder model achieves significant computational savings compared to simulating the full system. I.
Design and Analysis of Distributed Averaging with Quantized Communication. Research Report RR8501, INRIA,
, 2014
"... AbstractConsider a network whose nodes have some initial values, and it is desired to design an algorithm that builds on neighbor to neighbor interactions with the ultimate goal of convergence to the average of all initial node values or to some value close to that average. Such an algorithm is ca ..."
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AbstractConsider a network whose nodes have some initial values, and it is desired to design an algorithm that builds on neighbor to neighbor interactions with the ultimate goal of convergence to the average of all initial node values or to some value close to that average. Such an algorithm is called generically "distributed averaging", and our goal in this paper is to study the performance of a subclass of distributed averaging algorithms where the information exchange between neighboring nodes (agents) is subject to deterministic uniform quantization. With such quantization, the precise average cannot be achieved (except in exceptional cases), but some value close to it, called quantized consensus. It is shown in this paper that in finite time, the algorithm will either cause all agents to reach a quantized consensus where the consensus value is the largest integer not greater than the average of their initial values, or will lead all variables to cycle in a small neighborhood around the average, depending on initial conditions. In the latter case, tight bounds for the size of the neighborhood are given, and it is further shown that the error can be made arbitrarily small by adjusting the algorithm's parameters in a distributed manner.
Obstacle Avoidance in Formation Using Navigationlike Functions and Constraint Based Programming
 in Intelligent Robots and Systems (IROS), 2013 IEEE/RSJ International Conference on, Nov 2013
"... AbstractIn this paper, we combine navigation functionlike potential fields and constraint based programming to achieve obstacle avoidance in formation. Constraint based programming was developed in robotic manipulation as a technique to take several constraints into account when controlling redund ..."
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AbstractIn this paper, we combine navigation functionlike potential fields and constraint based programming to achieve obstacle avoidance in formation. Constraint based programming was developed in robotic manipulation as a technique to take several constraints into account when controlling redundant manipulators. The approach has also been generalized, and applied to other control systems such as dual arm manipulators and unmanned aerial vehicles. Navigation functions are an elegant way to design controllers with provable properties for navigation problems. By combining these tools, we take advantage of the redundancy inherent in a multiagent control problem and are able to concurrently address features such as formation maintenance and goal convergence, even in the presence of moving obstacles. We show how the user can decide a priority ordering of the objectives, as well as a clear way of seeing what objectives are currently addressed and what are postponed. We also analyze the theoretical properties of the proposed controller. Finally, we use a set of simulations to illustrate the approach.
FractionalOrder Dynamics in a Random, Approximately ScaleFree Network of Agents
"... Abstract—Differential equations with fractionalorder derivatives, e.g., the “onehalf ” derivative, have a long history in mathematics, but have not yet attained mainstream use in engineering and applied science. While applications do exist in modeling specific phenomena such as viscoelasticity a ..."
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Abstract—Differential equations with fractionalorder derivatives, e.g., the “onehalf ” derivative, have a long history in mathematics, but have not yet attained mainstream use in engineering and applied science. While applications do exist in modeling specific phenomena such as viscoelasticity and other types of difficulttomodel phenomena, and extensions to control such as in fractionalorder PID do exist, everyday use of fractional order modeling is uncommon. A subset of complex systems called CyberPhysical Systems (CPS) is receiving much emphasis in the research community. In this paper we show examples of networked system models which exhibit fractionalorder dynamic responses. This suggests that fractionalorder dynamics may be prevalent in CPS and hence may be an important and useful modeling tool in that area. We particularly focus on a scale free networked system. I.
Consensus of multiagent systems with nonuniform nondifferentiable timevarying delays
"... Abstract—In this paper the consensus problem for continuous time multiagent systems in the presence of timedelay is addressed. A novel sufficient condition for the case of nonuniform nondifferentiable timevarying delays with minimum value greater than zero and a method to compute an estimate o ..."
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Abstract—In this paper the consensus problem for continuous time multiagent systems in the presence of timedelay is addressed. A novel sufficient condition for the case of nonuniform nondifferentiable timevarying delays with minimum value greater than zero and a method to compute an estimate of the convergence rate are given. Simulation examples are given to show the performance of the proposed method. I.
Distributed Tracking Control for MultiAgent Systems Under Two Types of Attacks ⋆
"... Abstract: This paper studies a distributed consensus tracking control problem for a class of stochastic linear multiagent systems subject to two types of attacks. The problem boils down to how to achieve robust consensus tracking of multiagent systems with switching connected and disconnected dire ..."
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Abstract: This paper studies a distributed consensus tracking control problem for a class of stochastic linear multiagent systems subject to two types of attacks. The problem boils down to how to achieve robust consensus tracking of multiagent systems with switching connected and disconnected directed topologies under attacks. The attacks on the edges instead of nodes lead to the loss of consensus tracking security. Based on a multistep design procedure for designing a distributed secure algorithm, sufficient conditions on robust meansquare exponential consensus tracking are derived via the idea of average dwell time switching between some stable and unstable subsystems obtained from graph theory analysis. An applicaton to a practical power system is considered. It is proved that each distributed generator (DG) modeled as an agent in a microgrid can successfully synchronize their terminal voltage amplitude to a prespecified reference value under these two types of attacks.