Consensus of high-order continuous-time multi-agent systems with time-delays and switching topologies

Consensus problems of high-order continuous-time multi-agent systems with time-delays and switching topologies are studied.The motivation of this work is to extend second-order continuous-time multi-agent systems from the literature.It is shown that consensus can be reached with arbitrarily bounded time-delays even though the communication topology might not have spanning trees.A numerical example is included to show the theoretical results.     

Containment Control for First-Order Multi-Agent Systems with Time-Varying Delays and Uncertain Topologies

Containment control of first-order multi-agent systems with uncertain topologies and communication time-delays is studied. Suppose system topologies are dynamically changed, a containment control algorithm with time-varying delays is presented. The stability of the control algorithm is studied under the assumption that communication topologies are jointly-connected, and constraint condition of distributed containment control for delayed multi-agent systems is derived with the aid of Lyapunov-Krasovskii function. Simulation results are provided to prove the correctness and effectiveness of the conclusion.     

Impulsive synchronization of networked nonlinear dynamical systems

In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.     

Consensus problems of first-order dynamic multi-agent systems with multiple time delays

Consensus problems of first-order multi-agent systems with multiple time delays are investigated in this paper. We discuss three cases: 1) continuous, 2) discrete, and 3) a continuous system with a proportional plus derivative controller. In each case, the system contains simultaneous communication and input time delays. Supposing a dynamic multi-agent system with directed topology that contains a globally reachable node, the sufficient convergence condition of the system is discussed with respect to each of the three cases based on the generalized Nyquist criterion and the frequency-domain analysis approach, yielding conclusions that are either less conservative than or agree with previously published results. We know that the convergence condition of the system depends mainly on each agent’s input time delay and the adjacent weights but is independent of the communication delay between agents, whether the system is continuous or discrete. Finally, simulation examples are given to verify the theoretical analysis.     

Agreement dynamics on interaction networks with diverse topologies

We review the behavior of a recently introduced model of agreement dynamics, called the "Naming Game." This model describes the self-organized emergence of linguistic conventions and the establishment of simple communication systems in a population of agents with pairwise local interactions. The mechanisms of convergence towards agreement strongly depend on the network of possible interactions between the agents. In particular, the mean-field case in which all agents communicate with all the others is not efficient, since a large temporary memory is requested for the agents. On the other hand, regular lattice topologies lead to a fast local convergence but to a slow global dynamics similar to coarsening phenomena. The embedding of the agents in a small-world network represents an interesting tradeoff: a local consensus is easily reached, while the long-range links allow to bypass coarsening-like convergence. We also consider alternative adaptive strategies which can lead to faster global convergence.     

The value of less connected agents in Boolean networks

In multiagent systems, agents often face binary decisions where one seeks to take either the minority or the majority side. Examples are minority and congestion games in general, i.e., situations that require coordination among the agents in order to depict efficient decisions. In minority games such as the El Farol Bar Problem, previous works have shown that agents may reach appropriate levels of coordination, mostly by looking at the history of past decisions. Not many works consider any kind of structure of the social network, i.e., how agents are connected. Moreover, when structure is indeed considered, it assumes some kind of random network with a given, fixed connectivity degree. The present paper departs from the conventional approach in some ways. First, it considers more realistic network topologies, based on preferential attachments. This is especially useful in social networks. Second, the formalism of random Boolean networks is used to help agents to make decisions given their attachments (for example acquaintances). This is coupled with a reinforcement learning mechanism that allows agents to select strategies that are locally and globally efficient. Third, we use agent-based modeling and simulation, a microscopic approach, which allows us to draw conclusions about individuals and/or classes of individuals. Finally, for the sake of illustration we use two different scenarios, namely the El Farol Bar Problem and a binary route choice scenario. With this approach we target systems that adapt dynamically to changes in the environment, including other adaptive decision-makers. Our results using preferential attachments and random Boolean networks are threefold. First we show that an efficient equilibrium can be achieved, provided agents do experimentation. Second, microscopic analysis show that influential agents tend to consider few inputs in their Boolean functions. Third, we have also conducted measurements related to network clustering and centrality that help to see how agents are organized.     

Distributed optimization for discrete-time multiagent systems with nonconvex control input constraints and switching topologies

This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies. We introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point, while their control inputs are constrained in their own nonconvex region. It is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term. Based on the dynamic transformation technique, the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error term. By utilizing the nonnegative matrix theory, it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly connected. Finally, a numerical simulation example is used to demonstrate the acquired theoretical results.     

Average consensus of multi-agent systems with communication time delays and noisy links

In this paper,we consider the average-consensus problem with communication time delays and noisy links.We analyze two different cases of coupling topologies:fixed and switching topologies.By utilizing the stability theory of the stochastic differential equations,we analytically show that the average consensus could be achieved almost surely with the perturbation of noise and the communication time delays even if the time delay is time-varying.The theoretical results show that multi-agent systems can tolerate relatively large time delays if the noise is weak,and they can tolerate relatively strong noise if the time delays are low.The simulation results show that systems with strong noise intensities yield slow convergence.     

Tracking of a third-order maneuvering target under an arbitrary topology

We explore the tracking problem of a maneuvering target. Tracking agents with third-order kinematics can communicate with each other via wireless network. The communication network topology is arbitrary rather than switches among several fixed topologies. The information sharing and interaction among agents are position, velocity, and acceleration. Some sufficient conditions of tracking strategy have been proposed. Finally, a numerical example is employed to demonstrate the effectiveness of proposed tracking strategy.     

Emergence and evolution of multiple clusters of attracting agents

We investigate a multi-agent system with a behavior akin to the cluster formation in systems of coupled oscillators. The saturating attractive interactions between an infinite number of non-identical agents, characterized by a multimodal distribution of their natural velocities, lead to the emergence of clusters. We derive expressions that characterize the clusters, and calculate the asymptotic velocities of the agents and the critical value for the coupling strength under which no clustering can occur. The results are supported by mathematical analysis.For the particular case of a symmetric and unimodal distribution of the natural velocities, the relationship with the Kuramoto model of coupled oscillators is highlighted. While in the generic case the emergence of a cluster corresponds to a second-order phase transition, for a specific choice of the natural velocity distribution a first-order phase transition may occur, a phenomenon recently observed in the Kuramoto model. We also present an example for which the clustering behavior is quantitatively described in terms of the coupling strength.As an illustration of the potential of the model, we discuss how it applies to the dynamic process of opinion formation.     

Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction

Nonlinear consensus protocols for dynamic directed networks of multi-agent systems with fixed and switching topologies are investigated separately in this paper. Based on the centre manifold reduction technique, nonlinear consensus protocols are presented. We prove that a group of agents can reach a β-consensus, the value of which is the group decision value varying from the minimum and the maximum values of the initial states of the agents. Moreover, we derive the conditions to guarantee that all the agents reach a β--consensus on a desired group decision value. Finally, a simulation study concerning the vertical alignment manoeuvere of a team of unmanned air vehicles is performed. Simulation results show that the nonlinear consensus protocols proposed are more effective than the linear protocols for the formation control of the agents and they are an improvement over existing protocols.     

Consensus of leader-followers system of multi-missile with time-delays and switching topologies

The consensus problem in directed networks with arbitrary finite time-varying communication delays under both fixed topology and switching topologies is investigated in this article. The dynamics of each missile in this leader-followers system is with linear form. Feedback linearization is used here to attain linear guidance law for each missile, which is the base law for cooperative. Based on graph theory, the consensus problem can be converted to the stability of corresponding error system. Then Lyapunov function method is used to analyze the stability of the error system. Consensus of networks with time-delays under switching topologies is proved using common Lyapunov function method. Simulations indicate the excellent performances of the algorithms in terms of accuracy and efficiency.     

Output regulation for linear multi-agent systems with unmeasurable nodes

The output regulation of linear multi-agent systems with partial unmeasurable agents is investigated in this paper. All the agents except the exosystem can be classified into two groups. Agents in the first group can be measured by themselves and their neighbors. State variables are not fully accessible for direct communication and full order Luenberger observers are constructed for the unmeasurable agents. We give a state feedback control law to solve the output regulation problem under the communication topologies based on both measurable and unmeasurable agents. The heterogeneous agents’ synchronization problem is a general case of our results. Finally, examples are utilized to show the effectiveness of the obtained results.     

Synchronization of networks

We study the synchronization of coupled dynamical systems on networks. The dynamics is governed by a local nonlinear oscillator for each node of the network and interactions connecting different nodes via the links of the network. We consider existence and stability conditions for both single- and multi-cluster synchronization. For networks with time-varying topology we compare the synchronization properties of these networks with the corresponding time-average network. We find that if the different coupling matrices corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand, for non-commuting coupling matrices the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.      

Leader-following formation control of multi-agent networks based on distributed observers

To investigate the leader-following formation control, in this paper we present the design problem of control protocols and distributed observers under which the agents can achieve and maintain the desired formation from any initial states, while the velocity converges to that of the virtual leader whose velocity cannot be measured by agents in real time. The two cases of switching topologies without communication delay and fixed topology with time-varying communication delay are both considered for multi-agent networks. By using the Lyapunov stability theory, the issue of stability is analysed for multi-agent systems with switching topologies. Then, by considering the time-varying communication delay, the sufficient condition is proposed for the multi-agent systems with fixed topology. Finally, two numerical examples are given to illustrate the effectiveness of the proposed leader-following formation control protocols.     

Leader-following consensus criteria for multi-agent systems with time-varying delays and switching interconnection topologies

We consider multi-agent systems with time-varying delays and switching interconnection topologies.By constructing a suitable Lyapunov-Krasovskii functional and using the reciprocally convex approach,new delay-dependent consensus criteria for the systems are established in terms of linear matrix inequalities(LMIs),which can be easily solved by using various effective optimization algorithms.Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Graded and filtrated topological 1-algebras I. graded normal topologies

We consider locally convex topologies on graded and filtrated 1-algebras for which the wedge of all finite sums of squares is normal. Some rather general conditions for this are given and applied to tensor algebras and symmetrized tensor algebras. For the tensor algebra over an involutive locally convex space all graded normal topologies formed by ε- or σ-crossnorms in each component are described.     

Onsager Relations and Eulerian Hydrodynamic Limit for Systems with Several Conservation Laws

We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in case of more than one conservation laws, in order that the system exhibit hydrodynamic behaviour, some particular identities reminiscent of Onsager's reciprocity relations must hold. We check validity of these identities whenever a stationary measure with product structure exists. It also follows that, as a general rule, the equilibrium thermodynamic entropy (as function of the densities of the conserved variables) is a globally convex Lax entropy of the hyperbolic systems of conservation laws arising as hydrodynamic limit. As concrete examples we also present a number of models modeling deposition (or domain growth) phenomena. The Onsager relations arising in the context of hydrodynamic limits under hyperbolic scaling seem to be novel. The fact that equilibrium thermodynamic entropy is Lax entropy for the arising Euler equations was noticed earlier in the context of Hamiltonian systems with weak noise, see ref. 7.     

The effect of distributed time-delays on the synchronization of neuronal networks

Here we investigate the synchronization of networks of FitzHugh-Nagumo neurons coupled in scale-free, small-world and random topologies, in the presence of distributed time delays in the coupling of neurons. We explore how the synchronization transition is affected when the time delays in the interactions between pairs of interacting neurons are non-uniform. We find that the presence of distributed time-delays does not change the behavior of the synchronization transition significantly, vis-a-vis networks with constant time-delay, where the value of the constant time-delay is the mean of the distributed delays. We also notice that a normal distribution of delays gives rise to a transition at marginally lower coupling strengths, vis-a-vis uniformly distributed delays. These trends hold across classes of networks and for varying standard deviations of the delay distribution, indicating the generality of these results. So we conclude that distributed delays, which may be typically expected in real-world situations, do not have a notable effect on synchronization. This allows results obtained with constant delays to remain relevant even in the case of randomly distributed delays.     

Order preservation in a generalized version of Krause’s opinion dynamics model

Krause’s model of opinion dynamics has recently been the subject of several studies, partly because it is one of the simplest multi-agent systems involving position-dependent changing topologies. In this model, agents have an opinion represented by a real number and they update it by averaging those agent opinions distant from their opinion by less than a certain interaction radius. Some results obtained on this model rely on the fact that the opinion orders remain unchanged under iteration, a property that is consistent with the intuition in models with simultaneous updating on a fully connected communication topology.Several variations of this model have been proposed. We show that some natural variations are not order preserving and therefore cause potential problems with the theoretical analysis and the consistence with the intuition. We consider a generic version of Krause’s model parameterized by an “influence function” that encapsulates most of the variations proposed in the literature. We then derive a necessary and sufficient condition on this function for the opinion order to be preserved.