Semi‐global bipartite output consensus of heterogeneous multi‐agent systems subject to input saturation by finite‐time observer

In this paper, the semi‐global bipartite output consensus problem of heterogeneous linear multi‐agent systems is studied. Compared with related works, both cooperative interactions and antagonistic interactions between agents are considered, and the input saturation on each follower is taken into account. First, two distributed finite‐time observers are designed to recover the leader's state. Particularly, the setting time can be independent of any initial states. Due to the antagonistic interactions, estimation values are the same as the leader's state in modulus but may not in sign. Then, the low‐gain feedback technique is used to develop the distributed control law for each follower. Moreover, we summarize a framework for solving the semi‐global bipartite output consensus problem of heterogeneous multi‐agent systems subject to input saturation. Finally, examples are given to illustrate the results.     

Fully distributed bipartite output consensus of heterogeneous linear multiagent systems based on event‐triggered transmission mechanism

This study investigates the fully distributed bipartite output consensus issue of heterogeneous linear multiagent systems (HLMASs) based on event‐triggered transmission mechanism. Both the cooperative interaction and the antagonistic interaction between neighbor agents are considered. A fully distributed bipartite compensator consisting of time‐varying coupling gain and dynamic event‐triggered mechanism is first proposed to estimate the leader's states. Different from the existing schemes, the proposed compensator is independent of any global information of the network topology, is capable of achieving intermittent communication between neighbors, and is applicable for the signed communication topology. Then the distributed output feedback control protocol is developed such that the fully distributed bipartite event‐triggered output consensus problem can be achieved. Moreover, we extend the results in HLMASs without external disturbances to HLMASs with disturbances, which is more challenging in three cases (a) the disturbances are not available for measurement, (b) the disturbances suffered by each agent are heterogeneous, and (c) the disturbances are not required to be stable or bounded. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, two examples are provided to illustrate the feasibility of the theoretical results.     

Consensus analysis of continuous‐time second‐order multi‐agent systems with nonuniform time‐delays and switching topologies

In this study, consensus problems for second‐order multi‐agent systems with nonuniform and switching topologies are investigated. Each agent has a self‐delay, and each delay is independent of the others. As a measure of the disagreement dynamics, a class of positive semi‐definite Lyapunov–Krasovskii functions are introduced. Using algebraic graph theory and these Lyapunov–Krasovskii functions, sufficient conditions are derived by contradiction under which all agents asymptotically reach consensus. Finally, the effectiveness of the obtained theoretical results is demonstrated through numerical simulations.     

Suboptimal Output Consensus for Time‐Delayed Singular Multi‐Agent Systems

The current paper investigates guaranteed‐cost output consensus analysis and design problems for high‐order linear time‐invariant singular multi‐agent systems with constant time delays, which can realize suboptimal output consensus control. Firstly, a new output consensus protocol with a suboptimal index and a single delay is proposed to realize the tradeoff design between output consensus regulation performances and control energy consumptions. Then, sufficient conditions for guaranteed‐cost output consensus and consensualization are derived in terms of linear matrix inequalities by a combined tool from the Lyapunov‐Krasovskii approach and the free‐weighting matrix technique, respectively, and the output consensus function is determined on the basis of the First Equivalent Form. Finally, a numerical example is performed to demonstrate the effectiveness and conservativeness of theoretical results.     

Distributed consensus of delayed multi‐agent systems with nonlinear dynamics via intermittent control

In this paper, a distributed consensus of delayed multi‐agent systems with a leader is investigated, and a nonlinear protocol is proposed based on intermittent control. A notable feature of this protocol is to address second‐order consensus problems for delayed nonlinear multi‐agent systems, where agents can only communicate with each other over some disconnected time intervals. Some sufficient conditions to guarantee the consensus over fixed and switching topologies are derived. It is shown that second‐order consensus for delayed multi‐agent system with intermittent control can be achieved if the time delay is less than a critical value and the communication time duration is larger than a threshold value. In addition, some numerical examples are given to illustrate the effectiveness and feasibility of the theoretical results.     

Leader‐Following Consensus of Multi‐Agent System with Diffusion

This paper is concerned with the leader‐following consensus problem for multi‐agent systems consisting of one stationary leader and multiple cooperative followers, where the controlling effect of each follower depends on its own state. It is noted that the influence of diffusion among followers is taken into account and the system is modeled by reaction‐diffusion equations. With the assumption of the followers' initial states, a linear control protocol is designed. Based on algebraic graph theory, the method of energy estimates, and Sobolev embedding theorem, the sufficient conditions guaranteeing the leader‐following consensus under the proposed control protocol are provided. Numerical examples illustrate the effectiveness of the theoretical results.     

Consensus of linear multi‐agent systems with stochastic noises and binary‐valued communications

This article studies consensus problems of discrete‐time linear multi‐agent systems with stochastic noises and binary‐valued communications. Different from quantized consensus of first‐order systems with binary‐valued observations, the quantized consensus of linear multi‐agent systems requires that each agent observes its neighbors' states dynamically. Unlike the existing quantized consensus of linear multi‐agent systems, the information that each agent in this article gets from its neighbors is only binary‐valued. To estimate its neighbors' states dynamically by using the binary‐valued observations, we construct a two‐step estimation algorithm. Based on the estimates, a stochastic approximation‐based distributed control is proposed. The estimation and control are analyzed together in the closed‐loop system, since they are strongly coupled. Finally, it is proved that the estimates can converge to the true states in mean square sense and the states can achieve consensus at the same time by properly selecting the coefficient in the estimation algorithm. Moreover, the convergence rate of the estimation and the consensus speed are both given by O(1/t). The theoretical results are illustrated by simulations.     

Modulus consensus in a network of singularly perturbed systems with collaborative and antagonistic interactions

This paper addresses the modulus consensus in a network of singularly perturbed systems, all of which own multi-time scales characteristics. The interactions among the agents are collaborative and antagonistic interactions, and it can been modelled by a signed directed graph. Also, the effect of time-varying delay has been taken into account when modelling the agent dynamics. Based on singularly perturbed decomposition method, Kronecker product technique and the comparison principle, several sufficient conditions are presented under which networked singularly perturbed time-varying delay systems with collaborative and antagonistic interactions achieve modulus consensus. Moreover, the upper bound of singular perturbation parameter is deduced explicitly. Two simulation examples are presented to illustrate the validity of the proposed results.     

Output sign‐consensus of heterogeneous multiagent systems over fixed and switching signed graphs

This paper investigates output sign‐consensus of multiagent systems over directed signed graphs. In signed graphs, the sign of each edge stands for either hostile interaction (associated with positive sign) or antagonistic interactions (associated with negative sign) among agents. Agent dynamics are heterogeneous, allowing coexistence of distinct agent dynamics in one group. Heterogeneity in this paper also implies that the states of different agents may have different dimensions, but their outputs should have the same dimension. Distributed control laws are designed for both fixed and switching graph topologies. For fixed topology, the graph is assumed to be eventually positive. For switching topology, the graph needs to be jointly eventually positive, which extends the well‐known concept of joint connectivity by taking dwell time into consideration.     

Exponential synchronization of nonlinear multi‐agent systems with time delays and impulsive disturbances

The problem of cooperative synchronization of nonlinear multi‐agent systems with time delays is investigated in this paper. Compared with the existing works about synchronization (or consensus) of multi‐agent systems, the method in this paper provides a more general framework by considering nonlinear multi‐agent systems with time delays and impulsive disturbances. The model in this paper is sufficiently general to include a class of delayed chaotic systems. Based on the Lyapunov stability theory and algebraic graph theory, sufficient conditions are presented to guarantee the cooperative exponential synchronization for these multi‐agent delayed nonlinear systems. These conditions are expressed in terms of linear matrix inequalities, which can easily be checked by existing software tools. It is seen that the Lyapunov functions must be constructed based on the graph topology to prove synchronization. The well‐known master–slave (drive‐response) synchronization of two chaotic delayed systems is a special case of this paper, and therefore, the results in this paper are also useful for practical applications in secure communication. Simulation results verify the effectiveness of the proposed synchronization control algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Semi‐global output consensus of a group of linear systems in the presence of external disturbances and actuator saturation: An output regulation approach

This paper studies the problem of semi‐global leader‐following output consensus of a multi‐agent system. The output of each follower agent in the system, described by a same general linear system subject to external disturbances and actuator saturation, is to track the output of the leader, described by a linear system, which also generates disturbances as the exosystem does in the classical output regulation problem. Conditions on the agent dynamics are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the output consensus is achieved when the communication topology among the agents is a digraph containing no loop, and the leader is reachable from any follower agent. We also extend the results to the non‐identical disturbance case. In this case, conditions based on both the agent dynamics and the communication topology are identified, under which a low‐gain feedback‐based linear state‐control algorithm is constructed for each follower agent such that the leader‐following output consensus is achieved when the communication topology among the follower agents is a strongly connected and detailed balanced digraph, and the leader is a neighbor of at least one follower. In addition, under some further conditions on the agent dynamics, the control algorithm is adapted so as to achieve semi‐global leader‐following output consensus for a jointly connected undirected graph and the leader reachable from at least one follower. Copyright © 2015 John Wiley & Sons, Ltd.     

Leaderless and leader‐following fixed‐time consensus for multiagent systems via impulsive control

This article addresses the leaderless fixed‐time consensus (LLFTC) and leader‐following fixed‐time consensus (LFFTC) problems for multiagent systems (MASs) via impulsive control. First, a novel fixed‐time stability for impulsive dynamical system is developed. Then the novel fixed‐time impulsive control protocols are designed to achieve leaderless and leader‐following consensus for MASs. Based on the impulsive control theory, fixed‐time stability theory and algebraic graph theory, some sufficient conditions are derived for each agent to achieve LLFTC and LFFTC under the proposed control protocols. Finally, numerical simulations are put forward to validate the theoretical results.     

A novel consensus algorithm for second‐order multi‐agent systems without velocity measurements

In this paper, a novel consensus protocol for second‐order multi‐agent systems is elegantly designed, and it relaxes the common requirement of the velocity information of the agents. An interesting consensus criterion is explicitly derived in terms of the proposed cooperation law provided that the dynamical equation for each agent is linear. As an extension, the proposed cooperation rule is further extended to a general scenario, where the coupling weights characterizing the relationships among the neighboring agents are time‐varying. Accordingly, two distributed cooperative algorithms (node/edge‐based scheme) are explicitly designed. Moreover, we study the case of network with switching communication setting. It shows that edge‐based law is capable with the time‐varying topology, while the node‐based scheme is not. In addition, the proposed coordination strategies are applied to the tracking problem as well. Finally, these obtained consensus results are well supported in the light of the pendulum models. Copyright © 2016 John Wiley & Sons, Ltd.     

Event-based consensus of multi-agent systems with general linear models

In this paper, the event-based consensus problem of general linear multi-agent systems is considered. Two sufficient conditions with or without continuous communication between neighboring agents are presented to guarantee the consensus. The advantage of the event-based strategy is the significant decrease of the number of controller updates for cooperative tasks of multi-agent systems involving embedded microprocessors with limited on-board resources. The controller updates of each agent are driven by properly defined events, which depend on the measurement error, the states of its neighboring agents and an arbitrarily small threshold. It is shown that the controller updates for each agent only trigger at its own event time instants. A simulation example is presented to illustrate the theoretical results.     

Event‐Triggered Consensus of Nonlinear Multi‐Agent Systems with Unknown External Disturbance

This paper addresses the consensus problem of nonlinear multi‐agent systems with unknown external disturbance. First, a distributed observer is proposed to estimate the state and unknown disturbance of each agent simultaneously. Then, a novel event‐triggered control scheme based on the agent state estimation and disturbance estimation is proposed. Unlike the existing strategies, our event‐triggered conditions depend on agent state estimation and disturbance estimation, which are more effective and practical. Under this observer and control strategy, some sufficient conditions are derived to ensure the consensus of the multi‐agent system with unknown external disturbance. Moreover, the Zeno‐behavior of triggering time sequences is also excluded. Finally, a simulation example is given to verify the theoretical analysis.     

Event‐Triggered Control for Multi‐Agent Systems with General Directed Topology and Time Delays

Recent years have witnessed a growing interest in event‐triggered strategies for coordination and cooperative control of multi‐agent systems. However, the most previous works and developments focus on the interactive network that has no communication delays. This paper deals with the consensus problem of an agent system with event‐triggered control strategy under communication time delays. We first propose a time delays system model, then present a novel event triggering function that not only avoids continuous communication but also excludes the Zeno behavior. Furthermore, we provide the consensus analysis using an inequality technique instead of the traditional linear matrix inequality method, and we demonstrate that the inter‐event times for each agent are strictly positive, which implies that the Zeno behavior can be excluded. Finally, simulation results show the effectiveness of the proposed approach and illustrate the correctness of the theoretical results.     

Distributed model‐independent consensus of Euler–Lagrange agents on directed networks

This paper proposes a distributed model‐independent algorithm to achieve leaderless consensus on a directed network where each fully‐actuated agent has self‐dynamics described by Euler–Lagrange equations of motion. Specifically, we aim to achieve consensus of the generalised coordinates with zero generalised velocity. We show that on a strongly connected graph, a model‐independent algorithm can achieve the consensus objective at an exponential rate if an upper bound on the initial conditions is known a priori. By model‐independent, we mean that each agent can execute the algorithm with no knowledge of the equations describing the self‐dynamics of any agent. For design of the control laws which achieve consensus, a control gain scalar and a control gain matrix are required to satisfy several inequalities involving bounds on the matrices of the agent dynamic model, bounds on the Laplacian matrix describing the network topology and the set of initial conditions; design of the algorithm therefore requires some knowledge on the bounds of the agent dynamical parameters. Because only bounds are required, the proposed algorithm offers robustness to uncertainty in the parameters of the multiagent system. We systematically show that additional relative velocity information improves the performance of the controller. Numerical simulations are provided to show the effectiveness of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Reach a nonlinear consensus for MAS via doubly stochastic quadratic operators

This technical note addresses the new nonlinear protocol class of doubly stochastic quadratic operators (DSQOs) for coordination of consensus problem in multi-agent systems (MAS). We derive the conditions for ensuring that every agent reaches consensus on a desired rate of the group's decision where the group decision value in its agent's initial statuses varies. Besides that, we investigate a nonlinear protocol sub-class of extreme DSQO (EDSQO) to reach a consensus for MAS to a common value with nonlinear low-complexity rules and fast time convergence if the interactions for each agent are not selfish. In addition, to extend the results to reach a consensus and to avoid the selfish case we specify a general class of DSQO for reaching a consensus under any given case of initial states. The case that MAS reach a consensus by DSQO is if each member of the agent group has positive interactions of DSQO (PDSQO) with the others. The convergence of both EDSQO and PDSQO classes is found to be directed towards the centre point. Finally, experimental simulations are given to support the analysis from theoretical aspect.     

Admissible Consensus of Multi‐Agent Singular Systems

Consensus problems are studied for both continuous‐time and discrete‐time multi‐agent singular systems with time‐invariant and directed communication topologies. Under restricted system equivalence of singular agents, sufficient and necessary conditions are obtained for admissible consensus ability with static protocols, which are based on both the relative information of the dynamic states and the absolute information of the static states. For a network of continuous‐time singular systems, the existence of admissible consensualization can be cast into strong stabilizability of the agent dynamics. Once discrete‐time multi‐agent singular systems satisfy the condition of reaching nontrivial final consensus states, strong stabilizability is a sufficient condition to achieve admissible consensualization. Two algorithms are proposed to construct two protocols, which are based on a linear matrix inequality and a modified Riccati equation, respectively. Finally, the algorithms are illustrated by two simulation examples.