Fixed‐Time Consensus of Multi‐Agent Systems with Directed and Intermittent Communications

This paper proposes a new class of nonlinear protocols for fixed‐time consensus in networked agents with directed and intermittent communications. First of all, based on the assumption of a common positive dwell time for all successful links, it is theoretically shown that the asymptotical consensus can be achieved if the interaction topology with some fixed length of time has a spanning tree. Then, if the length sum of time intervals, over which the directed interaction topology contains a spanning tree, is larger that a threshold value, which is independent of initial conditions, the system will solve a fixed‐time consensus problem. Furthermore, in light of the mirror operation principle of graph theory, the proposed protocol is extended to solve the fixed‐time consensus problem if a common positive dwell time for all active links is strongly connected without the detailed balanced condition. Finally, the effectiveness of the theoretical results is illustrated by simulation results.     

Fixed‐Time Synchronization of a Class of Second‐Order Nonlinear Leader‐Following Multi‐Agent Systems

The fixed‐time synchronization problem for a class of second‐order nonlinear multi‐agent systems with a leader‐follower architecture is investigated in this paper. To achieve the fixed‐time tracking task, the design procedure is divided into two steps. At the first step, a distributed fixed‐time observer is designed for each agent to estimate the leader's state in a fixed time. Then, at the second step, based on the technique of adding a power integrator, a fixed‐time tracking controller for each agent is proposed such that the estimate leader's state can be tracked in a fixed time. Finally, an observer‐based fixed‐time controller is developed such that the leader can be tracked by all the followers in a fixed time, which can be predetermined. Simulations are presented to verify the effectiveness of the proposed approach.     

Observer‐Based Consensus Tracking for Nonlinear Multi‐Agent Systems With Intermittent Communications

This paper addresses the observer‐based consensus tracking problem of multi‐agent systems with intermittent communications. The agent dynamics are modeled as general linear systems with Lipschitz nonlinearity. Under the assumption that each agent can intermittently share its relative output with neighbors, a class of an observer‐type protocol is proposed, and the consensus tracking problem can be converted further into the stability problem of the nonlinear switching systems. Using a combined tool from M matrix theory, switching theory and the averaging approach, a multi‐step algorithm is presented to construct the observer gains and protocol parameters, and the sufficient criteria established not only can ensure the state estimates convergence to the real values but also can guarantee the follower states synchronize to those of the leader. The obtained results reveal the relationships among the communication rate, the convergence rate, and the dwell time of switching topologies. Finally, the theoretical findings are validated by a numerical example.     

Distributed Containment Control for Nonlinear Multi‐Agent Systems with Time‐Delayed Protocol

In this paper, the containment control problem is considered for nonlinear multi‐agent systems with directed communication topology. Under the guidance of designed distributed communication protocols with/without previous state information, the followers are expected to converge to a dynamic convex hull spanned by multiple leaders. Two multi‐step algorithms are proposed to construct the corresponding protocols, the state feedback protocol and the delay‐coupled protocol, under which the containment control can be achieved asymptotically. Furthermore, it is found that the delay‐coupled protocol is rather sensitive to time delays. That is, real‐time tracking will become impossible by only using long‐dated previous state information. Finally, a numerical example is given to demonstrate the applicability and efficiency of the proposed schemes.     

Finite‐Time Consensus Problem for Second‐Order Multi‐Agent Systems Under Switching Topologies

This paper investigates the finite‐time consensus problem for multi‐agent systems with second‐order individual dynamics under switching topologies. A distributed continuous‐time protocol is designed to guarantee finite‐time consensus for homogeneous agents without predetermined leaders, i.e., it ensures agents asymptotically converge to an average consensus within finite time, even if the interaction topology among them is time‐varying but stepwise jointly‐connected. In particular, it introduces a distributed continuous‐time protocol to reach consensus in finite time and reduce the chattering together. Finally, the simulation results are also given to validate the proposed approach.     

Adaptive Leader‐Following Consensus for Uncertain Nonlinear Multi‐Agent Systems

This paper is concerned with the adaptive leader‐following consensus for first‐ and second‐order uncertain nonlinear multi‐agent systems (NMASs) with single‐ and double‐integrator leader, respectively. Remarkably, the control coefficients of the followers need not belong to any known finite interval, which makes the systems in question essentially different from those in the related works. Moreover, parameterized unknowns exist in the nonlinearities of the followers, and unknown control input is imposed on the leader, which make the problems difficult to solve. To compensate for these uncertainties/unknowns, the leader‐following consensus protocols are constructed by employing adaptive technique for the first‐order and the second‐order NMASs. Under the designed adaptive consensus protocols and the connected graph, the leader‐following consensus is achieved. Finally, two examples are given to show the effectiveness of the proposed leader‐following consensus protocols.     

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.     

Bounded Consensus Algorithms for Multi‐Agent Systems in Directed Networks

In this paper, the consensus problem is investigated via bounded controls for the multi‐agent systems with or without communication. Based on the nested saturation method, the saturated control laws are designed to solve the consensus problem. Under the designed saturated control laws, the transient performance of the closed‐loop system can be improved by tuning the saturation level. First of all, asymptotical consensus algorithms with bounded control inputs are proposed for the multi‐agent systems with or without communication delays. Under these consensus algorithms, the states’ consensus can be achieved asymptotically. Then, based on a kind of novel nonlinear saturation functions, bounded finite‐time consensus algorithms are further developed. It is shown that the states’ consensus can be achieved in finite time. Finally, two examples are given to verify the efficiency of the proposed methods.     

Distributed Adaptive Event‐Triggered Control for Leader‐Following Consensus of Multi‐Agent Systems

This paper studies the leader‐following consensus problem for Lipschitz nonlinear multi‐agent systems using novel event‐triggered controllers. A distributed adaptive law is introduced for the event‐based control strategy design such that the proposed controllers are independent of system parameters and only use the relative states of neighboring agents, and hence are fully distributed. Due to the introduction of an event‐triggered control scheme, the controller of the agent is only triggered at it's own event times, and thus reduces the amount of communication between controller and actuator and lowers the frequency of controller updates in practice. Based on a quadratic Lyapunov function, the event condition which uses only neighbor information and local computation at trigger instants is established. Infinite triggers within a finite time are also verified to be impossible. The effectiveness of the theoretical results are illustrated through simulation examples.     

NNs‐Based Event‐Triggered Consensus Control of a Class of Uncertain Nonlinear Multi‐Agent Systems

We are concerned with the consensus problem for a class of uncertain nonlinear multi‐agent systems (MASs) connected through an undirected communication topology via event‐triggered approaches in this paper. Two distributed control strategies, the adaptive centralized event‐triggered control one and adaptive distributed event‐triggered control one, are presented utilizing neural networks (NNs) and event‐driven mechanisms, where the advantages of the proposed control laws lie that they remove the requirement for exact priori knowledge about parameters of individual agents by taking advantage of NNs approximators and they save computing and communication resources since control tasks only execute at certain instants with respect to predefined threshold functions. Also, the trigger coefficient can be regulated adaptively with dependence on state errors to ensure not only the control performance but also the efficiency of the network interactions. It is proven that all signals in the closed‐loop system are bounded and the Zeno behavior is excluded. Finally, simulation examples are presented for illustration of the theoretical claims.     

Consensus of Fractional Multi‐Agent Systems Using Distributed Adaptive Protocols

This paper is concerned with the adaptive consensus problem of fractional multi‐agent systems for both the linear and nonlinear cases. Distributed adaptive protocols are designed, respectively, for linear and nonlinear fractional multi‐agent systems, under which consensus is achieved for any undirected connected communication graph without using any global information. Furthermore, the leader‐following problem is studied as an extension. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.     

Exponential Consensus for Nonlinear Multi‐Agent Systems with Communication and Input Delays via Hybrid Control

This paper aims to investigate the exponential leader‐following consensus for nonlinear multi‐agent systems with time‐varying communication and input delays by using hybrid control. Based on the Lyapunov functional method, impulsive differential equation theory and matrix analysis, we show that all the followers can achieve leader‐following consensus with the virtual leader exponentially even if only a fraction of followers can obtain the leader's information. Two classes of exponential consensus criteria as well as the convergence rates for the controlled multi‐agent systems are presented under very relaxed interaction topology conditions, i.e., the directed interaction topology among the followers is only required to have p(p>1) disjoint strong components. Finally, two numerical examples are given to validate the proposed theoretical results.     

Multi‐Tracking of First Order Multi‐Agent Networks Via Self‐Triggered Control

A multi‐tracking problem of multi‐agent networks is investigated in this paper where multi‐tracking refers to that the states of multiple agents in each subnetwork asymptotically converge to the same desired trajectory in the presence of information exchanges among subnetworks. The multi‐tracking of first order multi‐agent networks with directed topologies was studied. Self‐triggered protocols were proposed along with triggering functions to solve the stationary multi‐tracking and bounded dynamic multi‐tracking. The self‐triggered scheduling is obtained, and the system does not exhibit Zeno behavior. Numerical examples are provided to illustrate the effectiveness of the obtained criteria.     

“Kronecker Basis” Based Average Consensus Analyses for High‐Order Linear Multi‐Agent Systems with Multiple Time Delays

This paper investigates the average consensus for multi‐agent systems governed by high‐order linear dynamics with multiple time delays. Necessary and sufficient conditions for high‐order average consensus under balanced communication topology are provided by using a newly defined mathematical concept – the Kronecker basis. Furthermore, previous studies for average consensus governed by first‐order, or high‐order integrator can be regarded as special cases of our results. Simulation results are employed to demonstrate the effectiveness of our results for high‐order average consensus.     

Event‐Based Semiglobal Consensus of Homogenous Linear Multi‐Agent Systems Subject to Input Saturation

In this paper, we consider the semiglobal leader‐following consensus of general linear multi‐agent systems subject to input saturation. First, an event‐triggered control protocol is provided to ensure semiglobal consensus of the multi‐agent systems, in which the agents should continuously monitor the information of their neighbors. Second, a self‐triggered control protocol is proposed to guarantee the semiglobal consensus of the multi‐agent systems, in which the agents only have access to the information of their neighbors in discrete time instants. Moreover, both event‐triggered control protocol and self‐triggered control protocol are proved to be Zeno‐free, that is, the inter‐event times for such two protocols have positive lower bounds. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed event‐based semiglobal consensus protocols.     

Tracking Control for Stochastic Multi‐Agent Systems Based on Hybrid Event‐Triggered Mechanism

This paper deals with the leader‐following consensus for nonlinear stochastic multi‐agent systems. To save communication resources, a new centralized/distributed hybrid event‐triggered mechanism (HETM) is proposed for nonlinear multi‐agent systems. HETMs can be regarded as a synthesis of continuous event‐triggered mechanism and time‐driven mechanism, which can effectively avoid Zeno behavior. To model the multi‐agent systems under centralized HETM, the switched system method is applied. By utilizing the property of communication topology, low‐dimensional consensus conditions are obtained. For the distributed hybrid event‐triggered mechanism, due to the asynchronous event‐triggered instants, the time‐varying system method is applied. Meanwhile, the effect of network‐induced time‐delay on the consensus is also considered. To further reduce the computational resources by constantly testing whether the broadcast condition has been violated, self‐triggered implementations of the proposed event‐triggered communication protocols are also derived. A numerical example is given to show the effectiveness of the proposed method.     

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.     

Asynchronous Distributed Algorithms for Heading Consensus of Multi‐Agent Systems with Communication Delay

In this paper, we propose two asynchronous distributed protocols for the heading consensus of a multi‐agent group which cannot access a global coordinate system and a global time. Both the leaderless and leader‐following cases are addressed, and inter‐agent communication delay is taken into account. It is proved, under some standard connectivity assumptions, that our leaderless algorithm ensures the heading consensus provided the initial headings are not balanced; and the leader‐based algorithm guarantees the global heading consensus.     

Distributed Consensus of Multi‐Agent Networks Via Event‐Triggered Pinning Control

This paper is concerned with distributed consensus between two multi‐agent networks with the same topology structure. Considering one network as the leaders' network and the other one as the followers' network, a new event‐triggered pinning control scheme is proposed to realize distributed consensus between these two networks. By utilizing the graph theory and Lyapunov functional method, consensus criteria are derived in the form of linear matrix inequalities. Moreover, distributed consensus of multi‐agent networks with Lipschitz nonlinear dynamics is also discussed. Numerical simulations are provided to demonstrate the effectiveness of the theoretical analysis.     

Consensus Problem with a Reference State for Fractional‐Order Multi‐Agent Systems

In this paper, the consensus problem of fractional‐order multi‐agent systems with a reference state is studied under fixed directed communication graph. At the beginning, the convergence speeds of fractional‐order multi‐agent systems are investigated based on the Mittag‐Leffler function. Then, a common consensus control law and a consensus control law based on error predictor are proposed, and it is shown that the consensus tracking can be achieved using the above control laws when a communication graph has a directed spanning tree. Finally, the convergence speeds of fractional‐order systems are compared, and it is discovered that the convergence of systems is faster using the control law based on error predictor than using the common one.