M-matrix strategies for pinning-controlled leader-following consensus in multiagent systems with nonlinear dynamics

Bipartite synchronization of Lur'e network with signed graphs based on intermittent control

In this paper, the bipartite synchronization of signed Lur'e network is studied under intermittent control, where the communication relationship of these adjacent nodes in the network can be either cooperative or competitive. Assuming that the network is structurally balanced, bipartite synchronization can be reached with some conditions and coordinate transform criterion. Then, Based on Lyapunov stability theory, some important norms are established. Ultimately, the simulation results can illustrate validness of theoretical analysis.

Aperiodically intermittent saturation consensus on multi-agent systems with discontinuous dynamics

This paper mainly investigates the exponential consensus problem for the multi-agent systems (MASs) with nonlinear discontinuous dynamics and time-varying delay. A novel aperiodically intermittent distributed control strategy is proposed to force the state of each agent to the common trajectory, where the configuration of control width and rest width can be aperiodic. Meanwhile, in order to limit the control effects into certain reasonable ranges, an improved saturation algorithm is proposed, which effectively reduces the non-smoothness of the control signal. Sufficient conditions for the exponential consensus on the discontinuous MASs are obtained through the Filippov differential inclusion (FDI), the Lie derivative method (LDM) and the measurement selection theorem (MST). Finally, the validity and feasibility of the main theories is demonstrated by numerical simulations.

Fully Distributed Synchronization of Complex Networks With Adaptive Coupling Strengths

This article considers the fully distributed leaderless synchronization in a complex network by only utilizing local neighboring information to design and tune the coupling strength of each node such that the synchronization problem can be solved without involving any global information of the network. For an undirected network, a fully distributed synchronization algorithm is presented to adjust the coupling strength of each node based on a simple adaptive law. When the topology of a network is directed, two different types of adaptive algorithms are developed to achieve synchronization in a fully distributed manner, where the coupling strength of each node is designed to be either the sum or product of two non-negative scalar functions. The fully distributed leaderless synchronization of a directed network is investigated in a leader-follower framework, where the leader subnetwork is analyzed by using the techniques from constrained Rayleigh quotients and the follower subnetwork is addressed by employing the properties of nonsingular M -matrices. Simulations are given to illustrate the theoretical results.

A Distributed Lyapunov-Based Redesign Approach for Heterogeneous Uncertain Agents With Cooperation-Competition Interactions

A swarming behavior problem is investigated in this article for heterogeneous uncertain agents with cooperation-competition interactions. In such a problem, the agents are described by second-order continuous systems with different intrinsic nonlinear terms, which satisfies the "linearity-in-parameters" condition, and the agents' models are coupled together through a distributed protocol containing the information of competitive neighbors. Then, for four different types of cooperation-competition networks, a distributed Lyapunov-based redesign approach is proposed for the heterogeneous uncertain agents, where the distributed controller and the estimation laws of unknown parameters are obtained. Under their joint actions, the heterogeneous uncertain multiagent system can achieve distributed stabilization for structurally unbalanced networks and output bipartite consensus for structurally balanced networks. In particular, the concept of coherent networks is proposed for structurally unbalanced directed networks, which is beneficial to the design of distributed controllers. Finally, four illustrative examples are given to show the effectiveness of the designed distributed controller.

Cross-dimensional formation control of second-order heterogeneous multi-agent systems

This paper is concerned with the cross-dimensional formation control of a second-order multi-dimensional heterogeneous multi-agent system. Agents are first separated into several groups according to their position/velocity vector dimensions. Then the cross-dimensional formation control problem is formulated such that agents in the same group form a time-varying formation in their own dimension and agents in different groups cooperatively move in multiple dimensions. This can make follower agents in different dimensions cooperatively track a leader. Moreover, a cross-dimensional formation protocol is designed based on full or partial information of neighboring agents. For higher-dimensional agents, full information of lower-dimensional neighbors is adopted. For lower-dimensional ones, only partial information of higher-dimensional neighbors is used. Furthermore, a necessary and sufficient condition for the second-order heterogeneous multi-agent system to achieve cross-dimensional formation is provided. Accordingly, a criterion for designing cross-dimensional formation protocol is further derived. Finally, under an undirected graph, a lower-dimensional protocol design criterion is obtained if there is no data exchange between lower- and higher-dimensional followers. The effectiveness of the obtained results is demonstrated through cross-dimensional target enclosing performance analysis for multiple robots and quadrotors.

Couple-Group Consensus of Cooperative-Competitive Heterogeneous Multiagent Systems: A Fully Distributed Event-Triggered and Pinning Control Method

This article discusses the couple-group consensus for heterogeneous multiagent systems via event-triggered and pinning control methods. Considering cooperative-competitive interaction among the agents, a novel group consensus protocol is designed. As inducing the time-correlation threshold function, a class of fully distributed event-triggered conditions without depending on any global information is proposed. Utilizing the Lyapunov stability theory, some sufficient conditions are obtained. Under hybrid event triggered and pinning control, pinning control strategies are first introduced. It is shown that under the proposed strategies, all agents can asymptotically achieve pinning couple-group consensus with discontinuous communication in a fully distributed way. Furthermore, the Zeno behavior for each agent is overcome. Finally, the reduction of the systems' controller update frequency and the correctness of our conclusions are illustrated by some simulations.

Distributed Control of Time-Varying Signed Networks: Theories and Applications

Signed networks admitting antagonistic interactions among agents may polarize, cluster, or fluctuate in the presence of time-varying communication topologies. Whether and how signed networks can be stabilized regardless of their sign patterns is one of the fundamental problems in the network system control areas. To address this problem, this paper targets at presenting a self-appraisal mechanism in the protocol of each agent, for which a notion of diagonal dominance degree is proposed to represent the dominant role of agent's self-appraisal over external impacts from all other agents. Selection conditions on diagonal dominance degrees are explored such that signed networks in the presence of directed time-varying topologies can be ensured to achieve the uniform asymptotic stability despite any sign patterns. Further, the established stability results can be applied to achieve bipartite consensus tracking of time-varying signed networks and realize state-feedback stabilization of time-varying systems. Simulations are implemented to verify our uniform asymptotic stability results for directed time-varying signed networks.

Further Results for Edge Convergence of Directed Signed Networks

The edge convergence problems have been explored for directed signed networks recently in 2019 by Du, Ma, and Meng, of which the analysis results, however, depend heavily on the strong connectivity of the network topologies. The question asked in this article is: whether and how can the edge convergence be achieved when the strong connectivity is not satisfied? The answer for the case of spanning tree is given. It is shown that if a signed network is either structurally balanced or r-structurally unbalanced, then the edge state can be ensured to converge to a constant vector. In contrast, if a signed network is both structurally unbalanced and r-structurally balanced, then its edge state does not converge to a constant vector any longer, but to a time-varying vector trajectory with a constant speed. Further, the dynamic behavior results of edges can be derived to address the node convergence problems of signed networks. The simulation examples are provided to illustrate the validity of the established edge convergence results.

Cluster Consensus of Multiagent Systems With Weighted Antagonistic Interactions

This article addresses the problem of cluster consensus for multiagent systems (MASs) associated with weighted antagonistic interactions. Compared with some existing results, a general communication topology among agents is introduced in this article, where there is no need to confine directed cycles to the root of a spanning tree. By taking into consideration the structures of directed cycles and multiple paths, the judgment of structural balance is simplified significantly. A novel cluster consensus protocol is also proposed for structurally unbalanced digraphs. Moreover, two necessary and sufficient conditions are derived, by which cluster consensus can be achieved in an MAS if and only if its communication topology contains a directed spanning tree. Then, by employing an algebra theorem, a sufficient criterion for the unstable system under a directed cycle is obtained, whether the number of agents on this cycle is odd or even. Some illustrative examples are given to demonstrate the effectiveness of theoretical results.

Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons

An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is formulated by means of linear matrix inequalities via the stochastic version of the Razumikhin functional. The recovery and the adaptation variables are also synchronized; this is demonstrated with the help of the minimum-phase property of the Hindmarsh–Rose neuron. The results are illustrated by an example.

Fully Distributed Anti-Windup Consensus Protocols for Linear MASs With Input Saturation: The Case With Directed Topology

We aim to solve the consensus problem of linear multiagent systems (MASs) with input saturation under directed interaction graphs in this article, where only local output information of neighbors is available for each agent. By introducing the multilevel saturation feedback control approach, a fully distributed adaptive anti-windup protocol is proposed, where a local observer, a distributed observer, as well as an anti-windup observer are separately constructed for each agent to estimate consensus error, achieve consensus for a certain internal state, and provide anti-windup compensator, respectively. A dual protocol is further presented with the distributed observer designed based on the input matrix, which gives a thorough view on the connection between the distributed observer and the anti-windup observer, and provides the opportunity to reduce the order of the controller by designing the integrated distributed anti-windup observer. Then, three types of distributed anti-windup protocols are proposed based on the integrated distributed anti-windup observer, which requires different assumptions. Specifically, the first protocol needs two-hop relay information to generate the local observer to estimate consensus error; the second protocol designs the local observer with absolute output information to estimate the state instead; while the last protocol introduces certain assumption on transmission zero of agents' dynamics to design the unknown input observer to estimate consensus error. All of the protocols are validated by strictly theoretical proof, and are illustrated by performing simulation examples.

Distributed Optimization of Multiagent Systems Subject to Inequality Constraints

In this paper, we study a distributed convex optimization problem with inequality constraints. Each agent is associated with its cost function, and can only exchange information with its neighbors. It is assumed that each cost function is convex and the optimization variable is subject to an inequality constraint. The objective is to make all the agents reach consensus, and meanwhile converge to the minimum point of the sum of local cost functions. A distributed protocol is proposed to guarantee that all agents can reach consensus in finite time and converge to the optimal point within the inequality constraints. Based on the ideas of parameter projection, the protocol includes two decent directions. One makes the cost function decrease, and the other makes agents step forward to the constraint set. It is shown that the proposed protocol solves the problem under connected undirected graphs without using a Lagrange multiplier technique. Especially, all of the agents could reach the constraint sets in finite time and stay in there after. The method could also be used in the centralized optimization problems.

Edge-Based Finite-Time Protocol Analysis With Final Consensus Value and Settling Time Estimations

The objective of this paper is to design the protocols with a final consensus value and settling time estimations for finite-time consensus of multiagent systems. A couple of new edge-based protocols are developed for multiple second-order nonlinear agents under bounded or Lipschitz-type nonlinear functions, respectively. The final consensus value of the multiagent system is obtained as an average expression. Further, to obtain the estimation of the finite settling time, a special Lyapunov function is constructed. Through the construction processes, both the final consensus value and the settling time are obtained. Finally, as applications, a finite-time formation controller based on the first protocol is designed for multiple mini-spacecraft, verified by simulations.

Impulsive Consensus of Multiagent Systems With Limited Bandwidth Based on Encoding-Decoding

Energy constrains are always significant to be considered in control of multiagent systems. Besides, nonlinear phenomena are often involved into such systems. In this paper, we discuss the impulsive consensus problem of nonlinear multiagent systems via impulsive protocol with limited bandwidth communication based on encoding-decoding. The scheme based on encoding-decoding with impulsive protocol is introduced to multiagent systems in general directed networks topology of which the graph is strongly connected. The impulsive protocols and limited bandwidth communication enhance the performance on energy saving and the involvement of nonlinear dynamics could suit more real-world cases. The design of encoders and decoders is presented, which is the key to achieve the goal that the information exchanged is subject to limited bandwidth communication. The conditions to guarantee the impulsive consensus and the conditions to avoid quantizer saturation are obtained. Moreover, the convergence rate of such multiagent systems are also characterized by the analysis of the exponential consensus. The numerical simulations are presented to support the theoretical results.

Adaptive Fault-Tolerant Consensus Protocols for Multiagent Systems With Directed Graphs

This paper investigates the problem of adaptive fault-tolerant tracking control for the multiagent systems (MASs) under the time-varying actuator faults and bounded unknown control input of the leader. On the basis of the local state information of neighboring agents, an adaptive fault-tolerant control protocol, which consists of the adaptive estimation of faults, is constructed to compensate for the loss of actuator effectiveness in the leader-follower consensus of MASs. Moreover, the modification term in the adaptive estimation can avoid high-frequency oscillations. It is shown that the tracking errors converge to a neighborhood around the origin in the presence of actuator faults, and the performance of the tracking problem is improved. Furthermore, the protocol is distributed in the sense that the coupling gains are independent. Finally, two examples are given to show the effectiveness of the proposed control protocol.

Pinning Synchronization of Multiplex Delayed Networks With Stochastic Perturbations

As the monoplex network has its limitations in describing the real world, a new framework called the multiplex network is put forward and has received much attention in recent years. This paper focuses on synchronization of the multiplex network with multiple delays and stochastic perturbations. Due to the complexity, pinning control of the multiplex network is of particular interest. Based on the LaSalle-type invariance principle for stochastic differential delay equations and the Lyapunov stability theory, some control schemes and synchronization criteria are obtained. It is concluded that under some mild conditions, one can determine which nodes should be pinned in a multiplex network. In addition, it is found that the number of pinned nodes increases with the varying interval of noise and time delay, and decreases with the varying interval of intralayer coupling strength. Some two-layer and three-layer networks are employed to validate the effectiveness of the proposed algorithm.

Some Necessary and Sufficient Conditions for Synchronization of Second-Order Interconnected Networks

This paper presents some necessary and sufficient conditions for the synchronization of second-order interconnected networks, where fixed inner-linked connections with information communication exist. First, a novel derivation of the conditions for a second-order polynomial with complex coefficients to be Hurwitz is provided. Based on this, a sufficient and necessary condition is proposed for the synchronization of the coupled complex network. Next, the design method of the synchronization protocol is constructively given, where the upper and lower bounds of the control gains are obtained through the properties of the polynomial. In addition, we consider some special cases where the second-order model is a double integrator, or general multiagent model without fixed interactions. Finally, the simulation result is given to verify the theoretical analysis.

Synchronization Control for Network Systems With Communication Constraints

A novel control strategy for synchronization control for network systems with communication constraints is presented in this paper. The dynamics of nodes in the network are nonidentical. The communication topology of network is weakly connected with communication constraints. The designed distributed controller for each node has two parts: reference generator (RG) and regulator. All RGs adopt the communication channels to exchange local information and track the target trajectory. Meanwhile, regulator can ensure that nonidentical node achieves synchronization with its RG. In order to reduce the communication frequency between node and its regulator, a sampled-date control strategy is utilized. The upper bound of the aperiodic sampling instants is calculated through the small-gain theorem, where the closed-loop system is equivalently formulated as the feedback interconnection of a linear time-invariant system and an integral sampled-data operator. Finally, some simulation results are given to demonstrate the effectiveness of the controller design strategy.

Data-Driven Distributed Output Consensus Control for Partially Observable Multiagent Systems

This paper is concerned with a class of optimal output consensus control problems for discrete linear multiagent systems with the partially observable system state. Since the optimal control policy depends on the full system state which is not accessible for a partially observable system, traditionally, distributed observers are employed to recover the system state. However, in many situations, the accurate model of a real-world dynamical system might be difficult to obtain, which makes the observer design infeasible. Furthermore, the optimal consensus control policy cannot be analytically solved without system functions. To overcome these challenges, we propose a data-driven adaptive dynamic programming approach that does not require the complete system inner state. The key idea is to use the input and output sequence as an equivalent representation of the underlying state. Based on this representation, an adaptive dynamic programming algorithm is developed to generate the optimal control policy. For the implementation of this algorithm, we design a neural network-based actor-critic structure to approximate the local performance indices and the control polices. Two numerical simulations are used to demonstrate the effectiveness of our method.

Finite-Time Synchronization of Networks via Quantized Intermittent Pinning Control

This technical correspondence considers finite-time synchronization of dynamical networks by designing aperiodically intermittent pinning controllers with logarithmic quantization. The control scheme can greatly reduce control cost and save both communication channels and bandwidth. By using multiple Lyapunov functions and convex combination techniques, sufficient conditions formulated by a set of linear matrix inequalities are derived to guarantee that all the node systems are synchronized with an isolated trajectory in a finite settling time. Compared with existing results, the main characteristics of this paper are twofold: 1) quantized controller is used for finite-time synchronization and 2) the designed multiple Lyapunov functions are strictly decreasing. An optimal algorithm is proposed for the estimation of settling time. Numerical simulations are provided to demonstrate the effectiveness of the theoretical analysis.

Reaching Non-Negative Edge Consensus of Networked Dynamical Systems

In this paper, the problem of non-negative edge consensus of undirected networked linear time-invariant systems is addressed by associating each edge of the network with a state variable, for which a distributed algorithm is constructed. Sufficient conditions referring only to the number of edges are derived for non-negative edge consensus of the networked systems. Subsequently, the linear programming method and a low-gain feedback technique are introduced to simplify the design of the feedback gain matrix for achieving the non-negative edge consensus. It is found that the low-gain feedback technique has a good effect on the non-negative edge consensus of the networked systems subject to input saturation. Numerical simulations are presented to verify the effectiveness of the theoretical results.

Fully Distributed Adaptive Consensus Control of a Class of High-Order Nonlinear Systems With a Directed Topology and Unknown Control Directions

In this paper, we investigate the adaptive consensus control for a class of high-order nonlinear systems with different unknown control directions where communications among the agents are represented by a directed graph. Based on backstepping technique, a fully distributed adaptive control approach is proposed without using global information of the topology. Meanwhile, a novel Nussbaum-type function is proposed to address the consensus control with unknown control directions. It is proved that boundedness of all closed-loop signals and asymptotically consensus tracking for all the agents' outputs are ensured. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme.

Event-Triggered Communication for Leader-Following Consensus of Second-Order Multiagent Systems

This paper is concerned with leader-following consensus of second-order multiagent systems with nonlinear dynamics. First, to save the limited communication resources, a new event-triggered control protocol is delicately developed without requiring continuous communication among the follower agents. Then, by employing the Lyapunov functional method and the Kronecker product technique, a novel sufficient criterion with less conservation is derived to guarantee the leader-following consensus while excluding the Zeno behavior. Furthermore, for the first time, an algorithm to actively adjust the leader adjacency matrix is presented, which efficiently expands the application range of some existing criteria. An example is finally given to illustrate the effectiveness of theoretical results.

Analysis and Design of Synchronization for Heterogeneous Network

In this paper, we investigate the synchronization for heterogeneous network subject to event-triggering communication. The designed controller for each node includes reference generator (RG) and regulator. The predicted value of relative information between intermittent communication can significantly reduce the transmitted information. Based on the event triggering strategy and time-dependent threshold, all RGs can exponentially track the target trajectory. Then by the action of regulator, each node synchronizes with its RG. Meanwhile, a positive lower bound is obtained for the interevent intervals. Numerical example is given to demonstrate the effectiveness of the proposed event triggering strategy.

Finite-Time and Fixed-Time Cluster Synchronization With or Without Pinning Control

In this paper, the finite-time and fixed-time cluster synchronization problem for complex networks with or without pinning control are discussed. Finite-time (or fixed-time) synchronization has been a hot topic in recent years, which means that the network can achieve synchronization in finite-time, and the settling time depends on the initial values for finite-time synchronization (or the settling time is bounded by a constant for any initial values for fixed-time synchronization). To realize the finite-time and fixed-time cluster synchronization, some simple distributed protocols with or without pinning control are designed and the effectiveness is rigorously proved. Several sufficient criteria are also obtained to clarify the effects of coupling terms for finite-time and fixed-time cluster synchronization. Especially, when the cluster number is one, the cluster synchronization becomes the complete synchronization problem; when the network has only one node, the coupling term between nodes will disappear, and the synchronization problem becomes the simplest master-slave case, which also includes the stability problem for nonlinear systems like neural networks. All these cases are also discussed. Finally, numerical simulations are presented to demonstrate the correctness of obtained theoretical results.

Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks

This paper investigates the controllability and synchronization problems for identical-hierarchy mixed-valued logical control networks. The logical network considered is hierarchical, and Boolean network is a special case of logical network. Here, identical-hierarchy means that there are identical number of nodes in each layer of logical network and corresponding nodes have the same dimension for any two layers of logical networks. Meanwhile, in each layer of logical networks, the dimensions of nodes are distinct, and it is called a mixed-valued logical network. First, the controllability problem is investigated and two notions of controllability are presented, i.e., group-controllability and simultaneously-controllability. By resorting to Perron-Frobenius theorem, some necessary and sufficient criteria are obtained to guarantee group-controllability and simultaneously-controllability, respectively. Second, based on the algebraic representation of the studied model, synchronization problems are analytically discussed for two types of controls, i.e., free control sequences and state-output feedback control. Finally, two numerical examples are presented to show the validness of our main results.

Observer-Based Consensus Tracking of Nonlinear Agents in Hybrid Varying Directed Topology

The problem of leader-following consensus of nonlinear agents in hybrid varying directed topology is considering not only the agent but also that the directed edges can have a time-varying nonlinear dynamics with jump discontinuity, which contains the switching topology as its special case. This paper has the following contributions toward this problem. The leader-following consensus problem in hybrid varying directed topology is first addressed, and an online leader switching method is proposed, which reduces the dependence on some global conditions and the connectivity assumptions on the selection of leaders. Second, we generalize the Lipschitz condition and the combined condition of one-sided Lipschitz and quadratically inner-boundedness conditions to a new generalized linear incremental condition, which gives us a more generalized result in the Lyapunov proof and better performance in simulation. Third, an observer-based consensus protocol is constructed with two sufficient observability and controllability conditions and two optimal control design algorithms. Finally, an example of teleoperating multirobotic manipulator joint network is provided to illustrate the performance improvement by comparing with the existing results.

Network-Based Practical Consensus of Heterogeneous Nonlinear Multiagent Systems

This paper studies network-based practical leader-following consensus problem of heterogeneous multiagent systems with Lipschitz nonlinear dynamics under both fixed and switching topologies. Considering the effect of network-induced delay, a network-based leader-following consensus protocol with heterogeneous gain matrix is proposed for each follower agent. By employing Lyapunov-Krasovskii method, a sufficient condition for designing the network-based consensus controller gain is derived such that the leader-following consensus error exponentially converges to a bounded region under a fixed topology. Correspondingly, the proposed design approach is then extended to the case of switching topology. Two numerical examples with networked Chua's circuits are given to show the efficiency of the design method proposed in this paper.

Pinning Control of Lag-Consensus for Second-Order Nonlinear Multiagent Systems

Lag consensus means that the corresponding state vectors of the followers are behind the leader with a lag time. In this paper, Lyapunov functional and matrix theory are applied to analyze pinning-controlled lag consensus of second-order nonlinear multiagent systems. The focus is twofold: 1) to find out which agents should be pinned and 2) to determine what the coupling strength should be, so that the multiagent systems can reach lag consensus. Moreover, the practical problem in a noisy environment is considered. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed pinning control protocol.

Distributed Bounds on the Algebraic Connectivity of Graphs With Application to Agent Networks

This paper establishes several bounds on the algebraic connectivity and spectral radius of graphs. Before deriving these bounds, a directed graph with a leader node is first investigated, for which some bounds on the spectral radius and the smallest real part of all the eigenvalues of M = L + D are obtained using the properties of M-matrix and non-negative matrix under a mild assumption, where L is the Laplacian matrix of the graph and D = diag{d1, d2, ..., dN} with di > 0 if node i can access the information of the leader node and 0 otherwise. Subsequently, by virtue of the results on directed graphs, the bounds on the algebraic connectivity and spectral radius of an undirected connected graph are provided. Besides establishing these bounds, another important feature is that all these bounds are distributed in the sense of only knowing the information of edge weights' bounds and the number of nodes in a graph, without using any information of inherent structures of the graph. Therefore, these bounds can be in some sense applied to agent networks for reducing the conservatism where control gains in control protocols depend on the eigenvalues of matrices M or L, which are global information. Also some examples are provided for corroborating the feasibility of the theoretical results.

A Layered Event-Triggered Consensus Scheme

This paper studies the dynamics of multiagent systems with a multilayer structure, proposing a novel layered event-triggered scheme (LETS) for consensus. This LETS emphasizes on synchronous information transmission in the same layer but asynchronous message update between different layers, which differs from the existing centralized or distributed event-triggered schemes. Moreover, under the LETS, agents in different layers achieve asymptotical consensus eventually and the Zeno behavior is successfully eliminated. Furthermore, an algorithm is provided to avoid continuous event detection, verified by a numerical example.

Distributed Position-Based Consensus of Second-Order Multiagent Systems With Continuous/Intermittent Communication

This paper considers the position-based consensus in a network of agents with double-integrator dynamics and directed topology. Two types of distributed observer algorithms are proposed to solve the consensus problem by utilizing continuous and intermittent position measurements, respectively, where each observer does not interact with any other observers. For the case of continuous communication between network agents, some convergence conditions are derived for reaching consensus in the network with a single constant delay or multiple time-varying delays on the basis of the eigenvalue analysis and the descriptor method. When the network agents can only obtain intermittent position data from local neighbors at discrete time instants, the consensus in the network without time delay or with nonuniform delays is investigated by using the Wirtinger's inequality and the delayed-input approach. Numerical examples are given to illustrate the theoretical analysis.

Necessary and Sufficient Conditions for Consensus of Fractional-Order Multiagent Systems via Sampled-Data Control

In this paper, the consensus of fractional-order multiagent systems (FOMASs) is considered via sampled-data control over directed communication topology with the order 0 <; α <; 1. Two cases are considered. One is FOMASs without leader, and the other is FOMASs with a leader. For each case, by applying matrix theory and algebraic graph theory, some algebraic-type necessary and sufficient conditions based on the sampling period, the fractional-order, the coupling gain, and the structure of the network are established for achieving consensus of the system. Moreover, for the network with a dynamic leader, the sampling period, the coupling gain, and the spectrum of the Laplacian matrix are carefully devised, respectively. Finally, several simulation examples are employed to validate the effectiveness of the theoretical results.

Consensus Problem Over High-Order Multiagent Systems With Uncertain Nonlinearities Under Deterministic and Stochastic Topologies

The leaderless consensus problem over a class of high-order nonlinear multiagent systems (MASs) is studied. A robust protocol is proposed which guarantees achieving consensus in the network in the presences of uncertainties in agents models. Achieving consensus in the case of stochastic links failure is studied as well. Based on the concept super-martingales, it is shown that if the probability of the network connectivity is not zero, under some conditions, achieving almost sure consensus in the network can be guaranteed. Despite existing consensus protocols for high-order stochastic networks, the proposed consensus protocol in this paper is robust to uncertain nonlinearities in the agents models, and it can be designed independent of knowledge on the set of feasible topologies (topologies with nonzero probabilities). Numerical examples for a team of single-link flexible joint manipulators with fourth-order models verify the accuracy of the proposed strategy for consensus control of high-order MASs with uncertain nonlinearities.

Distributed Consensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized Communication

This paper considers solving a class of optimization problems which are modeled as the sum of all agents' convex cost functions and each agent is only accessible to its individual function. Communication between agents in multiagent networks is assumed to be limited: each agent can only interact information with its neighbors by using time-varying communication channels with limited capacities. A technique which overcomes the limitation is to implement a quantization process to the interacted information. The quantized information is first encoded as a binary sequence at the side of each agent before sending. After the binary sequence is received by the neighboring agent, corresponding decoding scheme is utilized to resume the original information with a certain degree of error which is caused by the quantization process. With the availability of each agent's encoding states (associated with its out-channels) and decoding states (associated with its in-channels), we devise a set of distributed optimization algorithms that generate two iterative sequences, one of which converges to the optimal solution and the other of which reaches to the optimal value. We prove that if the parameters satisfy some mild conditions, the quantization errors are bounded and the consensus optimization can be achieved. How to minimize the number of quantization level of each connected communication channel in fixed networks is also explored thoroughly. It is found that, by properly choosing system parameters, one bit information exchange suffices to ensure consensus optimization. Finally, we present two numerical simulation experiments to illustrate the efficacy of the algorithms as well as to validate the theoretical findings.

Neuro-Adaptive Consensus Tracking of Multiagent Systems With a High-Dimensional Leader

This paper is concerned with the distributed consensus tracking problem of uncertain multiagent systems with directed communication topology and a single high-dimensional leader. Compared with existing related works, the dynamics of each follower in the present framework are subject to unmodeled dynamics and unknown external disturbances, which is more practical in various applications. Furthermore, the dimensions of leader's dynamics may be different with those of the followers' dynamics. Under the mild assumption that each follower can directly or indirectly sense the output information of the leader, a distributed robust adaptive neural network controller together with a local observer are designed to each follower to ensure that the states of each follower ultimately synchronize to the leader's output with bounded residual errors under a fixed topology. By appropriately constructing some multiple Lyapunov functions, the derived results are further extended to consensus tracking with switching directed communication topologies. The effectiveness of the analytical results is demonstrated via numerical simulations.

Sampled-Data-Based Consensus and $L_{2}$ -Gain Analysis for Heterogeneous Multiagent Systems

This paper is concerned with the sampled-data-based consensus problem of heterogeneous multiagent systems under directed graph topology with communication failure. The heterogeneous multiagent system consists of first-order and second-order integrators. Consensus of the heterogeneous multiagent system may not be guaranteed if the communication failure always happens. However, if the frequency and the length of the communication failure satisfy certain conditions, consensus of the considered system can be reached. In particular, we introduce the concepts of communication failure frequency and communication failure length. Then, with the help of the switching technique and the Lyapunov stability theory, sufficient conditions are derived in terms of linear matrix inequalities, which guarantees that the heterogeneous multiagent system not only achieves consensus but also maintains a desired L₂ -gain performance. A simulation example is given to show the effectiveness of the proposed method in this paper.

Finite-Time Control for Robust Tracking Consensus in MASs With an Uncertain Leader

This paper investigates the finite-time control for robust tracking consensus problems of multiagent systems with an uncertain leader for situations where the state of the considered active leader may not be measured and the directed network topology is time-varying. Based on the neighbor-based state-estimation rule and a new Lyapunov stability analysis method, a continuous and nonlinear distributed tracking protocol using only relative position information is designed, under which each agent can follow the leader in finite time if the input (acceleration) of the leader is known, and the tracking errors can converge to a bounded region in finite time if the input of the leader is unknown. In particular, a special continuous distributed tracking protocol with bounded control inputs is introduced to track the active leader in finite time. Numerical simulations are also given to illustrate the effectiveness of the theoretic results.