Communication Digraph Research Articles

Event-triggered learning synchronization of coupled heterogeneous recurrent neural networks

This paper investigates the synchronization of coupled heterogeneous recurrent neural networks. Based on the assumption of the existence of a spanning tree in the communication digraph, an effective event-triggered iterative learning control applicable to continuous nonlinear dynamical systems is proposed, under which some sufficient criteria for guaranteeing the synchronization of coupled heterogeneous recurrent neural networks are rigorously derived in virtue of contracting mapping principle. Moreover, the exclusion of the Zeno behaviors is analyzed. In contrast with relevant existing results, the control presented herein is applicable to both continuous and nonlinear dynamical systems, and the designed control involves the directed topology with a spanning tree, which includes the existing controls that based on the strongly connected topologies as special cases. Finally, the validity of theoretical results is substantiated by a numerical example.

Event-Triggered Synchronization of Multiple Fractional-Order Recurrent Neural Networks With Time-Varying Delays.

This paper addresses the synchronization of multiple fractional-order recurrent neural networks (RNNs) with time-varying delays under event-triggered communications. Based on the assumption of the existence of strong connectivity or a spanning tree in the communication digraph, two sets of sufficient conditions are derived for achieving event-triggered synchronization. Moreover, an additional condition is derived to preclude Zeno behaviors. As a generalization of existing results, the criteria herein are also applicable to the event-triggered synchronization of multiple integer-order RNNs with or without delays. Two numerical examples are elaborated to illustrate the new results.

Hierarchical Hybrid Control for Scaled Consensus and Its Application to Secondary Control for DC Microgrid.

This article addresses the scaled consensus problem for a class of heterogeneous multiagent systems (MASs) with a cascade-type two-layer structure. It is assumed that the information of the upper layer state components is intermittently exchangeable through a strongly connected communication network among the agents. A distributed hierarchical hybrid control framework is proposed, which consists of a lower layer controller and an upper layer one. The lower layer controller is a decentralized continuous feedback controller, which makes the lower layer state components converge to their target values. The upper layer controller is a distributed impulsive controller, which enforces a scaled consensus for the upper layer state components. It is proved that the two layer controllers can be designed separately. By considering the dwell-time condition of impulses and the feature of the strongly connected Laplacian matrix, a novel weighted discontinuous function is constructed for scaled consensus analysis. By using the Lyapunov function, a sufficient condition for scaled consensus of the MAS is derived in terms of linear matrix inequalities. As an application of the proposed distributed hybrid control strategy, a relaxed distributed hybrid secondary control algorithm for dc microgrid is obtained, by which the balance requirement on the communication digraph is removed, and an improved current sharing condition is obtained.

Cooperative Following of Multiple Autonomous Robots Based on Consensus Estimation

When performing a specific task, a Multi-Agent System (MAS) not only needs to coordinate the whole formation but also needs to coordinate the dynamic relationship among all the agents, which means judging and adjusting their positions in the formation according to their location, velocity, surrounding obstacles and other information to accomplish specific tasks. This paper devises an integral separation feedback method for a single-agent control with a developed robot motion model; then, an enhanced strategy incorporating the dynamic information of the leader robot is proposed for further improvement. On this basis, a method of combining second-order formation control with path planning is proposed for multiple-agents following control, which uses the system dynamic of one agent and the Laplacian matrix to generate the consensus protocol. Due to a second-order consensus, the agents exchange information according to a pre-specified communication digraph and keep in a certain following formation. Moreover, an improved path planning method using an artificial potential field is developed to guide the MAS to reach the destination and avoid collisions. The effectiveness of the proposed approach is verified with simulation results in different scenarios.

Stochastic Synchronization of Nonlinear Networks With Directed Graphs and Degenerate Noise

Noise is ubiquitous in network systems and has profound impacts on network dynamics. Despite substantial progress in stochastic synchronization of complex networks, most studies limit their focus to nondegenerate noise. However, the influence of degenerate noise on synchronization has not been studied properly. Here, we tackle this challenging problem by introducing a network of nonlinear units with a deterministic communication digraph and a noisy communication digraph. The communication links in the noisy communication digraph are affected by degenerate noise in a relative-dependent manner. Two types of deterministic communication digraphs are considered: 1) the case of strongly connected graphs and 2) the case of graphs containing a spanning tree. By using the algebraic graph theory and the stability theory of stochastic differential equations, algebraic sufficient conditions for both cases are derived, which depend on node dynamics, network structure, and coupling strengths. These criteria demonstrate that strong deterministic communication can compensate for the detrimental effect of degenerate noise, thus ensuring the stochastic synchronization in the almost sure sense. Numerical simulations support and illustrate the proposed theoretical results.

Global Optimal Cooperative Control of Multiple DC–DC Converter Systems for Dynamic Consensus

To improve the poor dynamic consensus in multiple dc-dc converter systems caused by parameter differences, this article proposes a global optimal cooperative control strategy. The proposed control strategy achieves dynamic consensus of output currents by minimizing a global performance index, which consists of local errors and neighbor synchronization errors. In this system, each converter is regarded as an agent in the communication digraph, so as to construct a cyber-physical model. Accordingly, a cooperative control method based on the linear quadratic regulator (LQR) is proposed, with the help of nonlinear coordinate transformation techniques. Different from conventional LQR, integral action is introduced to eliminate steady-state errors and improve coordinated performance. Meanwhile, the proof of the stability and consensus of the closed-loop system is given using Lyapunov approach. Moreover, the design guidelines to tune the dynamic response are provided through simulations. The experimental results further demonstrate the effectiveness and superiority of the proposed control method in a multiconverter prototype.

Topology-induced containment for general linear systems on weakly connected digraphs

The paper deals with topology-induced containment output feedback for ensuring multi-consensus of homogeneous linear systems evolving over a weakly connected communication digraph. Starting from the extension of a recent characterization of multi-consensus, a decentralized static feedback enforcing multi-consensus is designed based on a suitable network-induced decomposition; a neighborhood state-observer is proposed for completing the design. The results are finally illustrated over a simple simulated example.

Asymptotic behavior of second-order multiagent systems with fixed configuration

Second-order protocols for consensus and convergence of agent’s trajectories to a fixed configuration are investigated. It is proved that the asymptotic behavior of the second-order system is uniquely determined by the eigenprojection of the Laplacian matrix of the communication digraph. The presented protocol and the corresponding expression for the asymptotic behavior are generalizations of the protocols for simpler cases.

Structural Controllability of Directed Signed Networks

In this article, the structural controllability of multiagent networks defined over directed signed graphs is investigated, where the agents are divided into leaders and followers, and only leaders are manipulated by the external control input directly. The communication digraph contains positive and negative edges, which represent cooperative and antagonistic interactions between agents, respectively. First, a graph-theoretic necessary and sufficient condition for structural controllability of multiagent networks is derived, that is, a multiagent network is structurally controllable if and only if the communication digraph is leader–follower connected. Next, the minimal controllability problem is studied. It is shown that the minimal controllability problem is solvable, and a method of polynomial complexity to accomplish minimal structural controllability is developed. In addition, the structural controllability of specified Cartesian product networks is discussed and a necessary and sufficient condition concerning the factor networks for the structural controllability is established. The application of the theoretical results is demonstrated by several practical examples.

Nash Equilibrium Seeking with Non-doubly Stochastic Communication Weight Matrix

A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players' actions. The players communicate over a strongly connected digraph to send/receive the estimates of the other players' actions to/from the other local players according to a gossip communication protocol. Due to asymmetric information exchange between the players, a non-doubly (row) stochastic weight matrix is defined. We show that, due to the non-doubly stochastic property, the total average of all players' estimates is not preserved for the next iteration which results in having no exact convergence. We present an almost sure convergence proof of the algorithm to a Nash equilibrium of the game. Then, we extend the algorithm for graphical games in which all players' cost functions are only dependent on the local neighboring players over an interference digraph. We design an assumption on the communication digraph such that the players are able to update all the estimates of the players who interfere with their cost functions. It is shown that the communication digraph needs to be a superset of a transitive reduction of the interference digraph. Finally, we verify the efficacy of the algorithm via a simulation on a social media behavioral case.

Delay tolerant containment control for second-order multi-agent systems based on communication topology design

In this paper, a delay tolerant containment control problem for second-order multi-agent systems (MASs) is studied. Considering the disturbance caused by the time-varying delays between agents, we utilize the delay tolerant character of MASs with multiple leaders to redesign the topology of concerned MASs and solve the containment control problem. Corresponding sufficient and necessary conditions on the communication digraph of the MAS are developed to ensure the followers converging to interior points of a convex hull formed by the leaders. Furthermore, considering the inevitable delays between the communications of agents, we present the topology design algorithm in light of the proposed conditions to solve the delay tolerant containment control problem for the second-order MAS. In this case, we focus on how to redesign the communication topology structure instead of constructing a proper distributed cooperative controller. Finally, some examples are given to illustrate the effectiveness of the obtained results.

Distributed Containment Control of Multi-agent Systems with General Linear Dynamics and Time-delays

Containment control problems for high-order linear time-invariant multi-agent systems with fixed communication time-delays are investigated. Based on Lyapunov-Krasovskii functional method and the linear matrix inequality (LMI) method, sufcient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control of the multi-agent systems under the different containment control algorithms are given. Finally, numerical simulations are presented to demonstrate theoretical results.

Coordination of multi-agent systems on interacting physical and communication topologies

A new framework is given for coordination of multi-agent systems that are interconnected by a physical coupling digraph. The edges of this graph represent physical couplings between agents that are fixed due to dynamical interactions. On top of the physical graph, distributed control protocols are designed where the allowed communications between agents for control purposes are prescribed by a second fixed communication digraph. The physical and communication digraphs are generally different and the combination of these two graphs forms a cyber-physical system. The interactions between physical and communication graphs are the focus of this paper. We consider different interactions between two graphs, including the case when their pinned Laplacian commutes, the case of the communication graph with diagonalizable pinned Laplacian, and the case of two general graphs. Moreover, within each graph, the relations between the agents can be either collaborative or antagonistic. To capture this, the theory of bipartite consensus is used. Coordination protocols for different cases are designed that are distributed with respect to the communication graph, and overcome the detrimental effects of the signed physical graph. The proposed control methods are illustrated by simulation examples.

The Forest Consensus Theorem

We show that the limiting state vector in the differential model of consensus seeking with an arbitrary communication digraph is obtained by multiplying the eigenprojection of the Laplacian matrix of the model by the vector of initial states. Furthermore, the eige nprojection coincides with the stochastic matrix of maximum out-forests of the weighted communication digraph. These statements make the

Containment control for second-order multi-agent systems with time-varying delays

This paper considers the containment control problem for second-order multi-agent systems with time-varying delays. Both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated. Sufficient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control are given. In the case that the leaders are stationary, the Lyapunov–Razumikhin function method is used. In the case that the leaders are dynamic, the Lyapunov–Krasovskii functional method and the linear matrix inequality (LMI) method are jointly used. A novel discretized Lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is, which leads to a better result on the allowed upper bound of the delays to ensure containment control. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

Secondary control of microgrids based on distributed cooperative control of multi‐agent systems

This study proposes a secondary voltage and frequency control scheme based on the distributed cooperative control of multi-agent systems. The proposed secondary control is implemented through a communication network with one-way communication links. The required communication network is modelled by a directed graph (digraph). The proposed secondary control is fully distributed such that each distributed generator only requires its own information and the information of its neighbours on the communication digraph. Thus, the requirements for a central controller and complex communication network are obviated, and the system reliability is improved. The simulation results verify the effectiveness of the proposed secondary control for a microgrid test system.

The forest consensus theorem and asymptotic properties of coordination protocols

We show that the final state vector of the continuous-time consensus protocol with an arbitrary communication digraph is obtained by multiplying the eigenprojection of the Laplacian matrix of the model by the vector of initial states. Furthermore, the eigenprojection coincides with the stochastic matrix of maximum out-forests of the weighted communication digraph. These statements make the forest consensus theorem. A similar result for DeGroot's iterative pooling model requires the Cesàro (time-average) limit in the general case. The forest consensus theorem generalizes the well-known spanning arborescence criterion of achieving consensus. Its field of application is the analysis of consensus algorithms.

The Projection Method for Reaching Consensus in Discrete-time Multiagent Systems

In the coordination problems for multi-agent systems, a well-known condition of achieving consensus is the presence of a spanning arborescence in the communication digraph. The paper deals with the discrete consensus problem in the case where this condition is not satisfied. Let P be a row stochastic influence matrix, whereas TP is the subspace of initial opinions that ensure consensus in DeGroot's iterative pooling model. We propose a method of coordination that consists of: (1) transformation of the vector of initial opinions into the closest vector in TP and (2) subsequent DeGroot process with the matrix P.

Coordination of networked systems on digraphs with multiple leaders via pinning control

It is well known that achieving consensus among a group of multi-vehicle systems by local distributed control is feasible if and only if all nodes in the communication digraph are reachable from a single (root) node. In this article, we take into account a more general case that the communication digraph of the networked multi-vehicle systems is weakly connected and has two or more zero-in-degree and strongly connected subgraphs, i.e. there are two or more leader groups. Based on the pinning control strategy, the feasibility problem of achieving second-order controlled consensus is studied. At first, a necessary and sufficient condition is given when the topology is fixed. Then the method to design the controller and the rule to choose the pinned vehicles are discussed. The proposed approach allows us to extend several existing results for undirected graphs to directed balanced graphs. A sufficient condition is proposed in the case where the coupling topology is variable. As an illustrative example, a second-order controlled consensus scheme is applied to coordinate the movement of networked multiple mobile robots.

A cyclic representation of discrete coordination procedures

We show that any discrete opinion pooling procedure with positive weights can be asymptotically approximated by DeGroot's procedure whose communication digraph is a Hamiltonian cycle with loops. In this cycle, the weight of each arc (which is not a loop) is inversely proportional to the influence of the agent the arc leads to.