具有时延的多个体系统的一致性问题综述

考察了具有时延的多个体系统的一致性问题．根据不同的分析方法,介绍了关于具有通信时延的多个体系统一致性问题的结果,并对各种分析方法的特点进行了比较．此外,对具有输入时延的多个体系统的现有一致性结果也作了介绍．最后评述了该研究领域存在的问题以及今后的研究方向．     

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.     

Leader-following fixed-time output feedback consensus for second-order multi-agent systems with input saturation

This paper investigates the leader-following fixed-time output feedback consensus problem for second-order multi-agent systems with input saturation. By combing fixed-time control technique and bi-limit homogeneous systems theory, a class of bounded fixed-time consensus protocols are developed for leader-following multi-agent systems. The protocol design is divided into two parts. First, when all the state information of the followers are measurable, a state feedback consensus protocol is designed to achieve fixed-time consensus. Then, when the velocity information is unmeasurable, an observer-based fixed-time consensus protocol is proposed. With the help of Lyapunov stability theorem and the property of a homogeneous function, it is theoretically shown that the states of all followers can track that of the leader in fixed-time in the presence of input saturation. Finally, numerical simulation is carried out to illustrate the effectiveness of theoretical results.     

A note on connectivity of multi-agent systems with proximity graphs and linear feedback protocol

In this note, we investigate the possibility of simplifying the connectivity verification for multi-agent systems with proximity graphs and the linear feedback protocol. A Lyapunov-like approach is developed for analyzing the monotonicity of the largest edge length in the network. Based on this approach, we provide an initial-connectivity-based sufficient condition for dynamic connectivity. In particular, when each initial node degree is not less than three fourth of the graph order, initial network connectivity implies dynamic connectivity.     

Decentralized event-triggered consensus with general linear dynamics

The consensus problem with general linear dynamics and undirected graphs is studied in this paper by means of event-triggered control strategies. A novel consensus protocol is proposed, where each agent implements a model of the decoupled dynamics of its neighbors. Under this control strategy, transmission of information does not occur continuously but only at discrete points in time. The approach presented in this paper provides both a decentralized control law and a decentralized communication policy. We are able to design thresholds that only depend on local information and guarantee asymptotic consensus. Positive inter-event times are guaranteed for particular cases of the linear dynamics. In an extension, a positive constant is added to the thresholds in order to exclude Zeno behavior for general linear dynamics. The difference between agents trajectories can be bounded in this case and bounds on the state disagreement are derived.     

Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties

This paper considers the distributed consensus problem of linear multi-agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input. Due to the existence of nonidentical uncertainties, the multi-agent systems discussed in this paper are essentially heterogeneous. For the case where the communication graph is undirected and connected, based on the local state information of neighboring agents, a fully distributed continuous adaptive consensus protocol is designed, under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable bounded set. For the case where there exists a leader whose control input is unknown and bounded, a distributed adaptive consensus protocol is proposed to ensure the boundedness of the consensus error. A sufficient condition for the existence of the proposed protocols is that each agent is stabilizable.     

Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations

The consensus problem of second-order multi-agent systems with diverse input delays is investigated. Based on the frequency-domain analysis, decentralized consensus conditions are obtained for the multi-agent system with symmetric coupling weights. Then, the robustness of the symmetric system with asymmetric perturbation is studied. A bound of the largest singular value of the perturbation matrix is obtained as the robust consensus condition. Simulation examples illustrate the design procedure of consensus protocols and validate the correctness of the results.     

Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics

The objective of this paper is to analyze the finite-time convergence of a nonlinear but continuous consensus algorithm for multi-agent networks with unknown inherent nonlinear dynamics. Due to the existence of the unknown inherent nonlinear dynamics, the stability analysis and the finite-time convergence analysis are more challenging than those under the well-studied consensus algorithms for known linear systems. For this purpose, we propose a novel comparison based tool. By using this tool, it is shown that the proposed nonlinear consensus algorithm can guarantee finite-time convergence if the directed switching interaction graph has a directed spanning tree at each time interval. Specifically, the finite-time convergence is shown by comparing the closed-loop system under the proposed consensus algorithm with some well-designed closed-loop system whose stability properties are easier to obtain. Moreover, the stability and the finite-time convergence of the closed-loop system using the proposed consensus algorithm under a (general) directed switching interaction graph can even be guaranteed by the stability and the finite-time convergence of some well-designed nonlinear closed-loop system under some special directed switching interaction graph. This provides a stimulating example for the potential applications of the proposed comparison based tool in the stability analysis of linear/nonlinear closed-loop systems by making use of known results in linear/nonlinear systems.     

Distributed adaptive consensus for linear multi-agent systems with quantised information

This paper considers the distributed adaptive consensus problem for linear multi-agent systems with quantised relative information. By using a lemma in algebraic graph theory and introducing a projection operator in adaptive law, a novel distributed adaptive state feedback controller is designed with quantised relative state information. It is shown that the practical consensus for multi-agent systems with a uniform quantiser is achieved via the Lyapunov theory and the non-smooth analysis. In contrast with the existing quantised controllers, which rely on the minimum nonzero eigenvalue of the Laplacian matrix, the developed controller is only dependent on the number of nodes. Furthermore, a dynamic output feedback controller based on quantised relative output information is proposed. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.     

Adaptive output feedback consensus tracking for linear multi-agent systems with unknown dynamics

In this paper, the consensus tracking problem with unknown dynamics in the leader for the linear multi-agent systems is addressed. Based on the relative output information among the agents, decentralised adaptive consensus protocols with static coupling gains are designed to guarantee that the consensus tracking errors converge to a small neighbourhood around the origin and all the signals in the closed-loop dynamics are uniformly ultimately bounded. Moreover, the result is extended to the case with dynamic coupling gains which are independent of the eigenvalues of the Laplacian matrix. Both of the protocols with static and dynamic coupling gains are designed by using the relative outputs, which are more practical than the state-feedback ones. Finally, the theoretical results are verified through an example.     

Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach

In this paper, we study the consensus (and synchronization) problem for multi-agent linear dynamic systems. All the agents have identical MIMO linear dynamics which can be of any order, and only the output information of each agents is delivered throughout the communication network. It is shown that consensus is reached if there exists a stable compensator which simultaneously stabilizes N−1 systems in a special form, where N is the number of agents. We show that there exists such a compensator under a very general condition. Finally, the consensus value is characterized as a function of initial conditions with stable compensators in place.     

Robust cooperative control for multi-agent systems via distributed output regulation

Robust cooperative control for multi-agent systems is considered in this paper, under the framework of the distributed output regulation problem. With some fundamental assumptions, two necessary and sufficient conditions are given for the distributed output regulation problem to be solvable. The algorithm of designing the robust distributed control law is provided, with the help of internal models. It is shown that this robust controller is effective in a neighborhood of the nominal system, which is tolerant of system uncertainties.     

Leader-following consensus of nonlinear fractional-order multi-agent systems via event-triggered control

This paper investigates the consensus problem of leader-following multi-agent systems with fractional-order nonlinear dynamics. A typical event is defined as some error signals exceeding a given threshold. By applying Lyapunov functional approach and skills of computing function limit, consensus of the controlled multi-agent systems can be reached asymptotically. Meanwhile, the event-triggered algorithm can exclude Zeno behaviours. Finally, a numerical simulation is exploited to verify the effectiveness of the theoretical result.     

Leader-follower consensus control of Lipschitz nonlinear systems by output feedback

This paper deals with the leader-follower consensus problem of Lipschitz nonlinear systems under fixed directed communication networks. Both state and output feedback control are proposed based on state and output measurements of neighbouring agents, respectively. Laplacian matrix features are explored for the stability analysis, and the sufficient conditions are derived to solve the consensus problem. Finally, simulation results are included to demonstrate the effectiveness of the output-based consensus controller.     

Distributed event-triggered output consensus control for heterogeneous multi-agent system with general linear dynamics

This paper studies the distributed event-triggered output consensus problem of heterogeneous multi-agent system with general linear dynamics under an undirected connected graph. With the state-dependent triggering function, we design a novel distributed event-triggered output consensus controller for each agent to reach consensus with zero final consensus error. This strategy has several distinguishing features, including the fact that individual agent does not require continuous, or even periodic, communication with their neighbours to update the controller or monitor the triggering condition, and all parameters required by its implementation can be locally determined by the agent. We also prove that events cannot be triggered infinitely in finite time (i.e. no Zeno behaviour). Furthermore, the simulation examples are given to illustrate the theoretical analysis.     

Consensus of linear multi-agent systems with reduced-order observer-based protocols

This paper considers the consensus problems for both continuous- and discrete-time linear multi-agent systems with directed communication topologies. Distributed reduced-order observer-based consensus protocols are proposed, based on the relative outputs of neighboring agents. A multi-step algorithm is presented to construct a reduced-order protocol, under which a continuous-time multi-agent system whose communication topology contains a directed spanning tree can reach consensus. This algorithm is further modified to achieve consensus with a prescribed convergence rate. These two algorithms have a favorable decoupling property. In light of the modified algebraic Riccati equation, an algorithm is then given to construct a reduced-order protocol for the discrete-time case.     

Robust homogenization and consensus of nonlinear multi-agent systems

In this paper, we consider consensus of a group of heterogeneous agents with nonlinear dynamics in the presence of system uncertainties. It requires that all agent states reach an agreement which is governed by specified reference dynamics. However, the reference dynamics do not generate a specific reference trajectory for feedback regulation for any agent. For this purpose, the proposed controller integrates two fundamental actions, homogenization and consensus, concurrently. On one hand, it asymptotically regulates each individual (heterogeneous, nonlinear, and uncertain) agent dynamics to the common reference dynamics using a robust homogenization technique; on the other hand, it aligns agent trajectories, asymptotically governed by the common reference dynamics, to consensus through network cooperation. The effectiveness of the controller is verified in the rigorous proof and numerical simulation.     

Tracking control for multi-agent consensus with an active leader and variable topology

In this paper, we consider a multi-agent consensus problem with an active leader and variable interconnection topology. The state of the considered leader not only keeps changing but also may not be measured. To track such a leader, a neighbor-based local controller together with a neighbor-based state-estimation rule is given for each autonomous agent. Then we prove that, with the proposed control scheme, each agent can follow the leader if the (acceleration) input of the active leader is known, and the tracking error is estimated if the input of the leader is unknown.     

On the cluster consensus of discrete-time multi-agent systems

Nowadays, multi-agent systems (MAS) are ubiquitous in the real world. Consensus is a fundamental natural phenomenon. Over the past decade, consensus of MAS has received increasing attention from various disciplines. This paper aims to further investigate a novel kind of cluster consensus of MAS with several different subgroups. Based on Markov chains and nonnegative matrix analysis, two novel cluster consensus criteria are obtained for MAS with fixed and switching topology, respectively. Furthermore, numerical simulations are also given to validate the effectiveness of these proposed criteria. The proposed cluster consensus criteria have some potential applications in real world engineering systems.     

A new framework of consensus protocol design for complex multi-agent systems

This paper aims to find a simple but efficient method for consensus protocol design. This paper presents two consensus protocols to solve the consensus problem of complex multi-agent systems that consist of inhomogeneous subsystems. The limitations of current studies are analyzed, and a novel model based on transfer functions is presented. This model can be used to describe both homogeneous and inhomogeneous multi-agent systems in a unified framework. Based on this model, two sufficient and necessary conditions for the consensus of complex multi-agent systems have been obtained. One is for the systems without any external input, and the other is for the systems with the same external input. Then, two corresponding distributed consensus protocols are presented. Considering that the complex multi-agent systems may require different outputs sometimes, the relationship between inputs and outputs is analyzed. Finally, some simulations are given to demonstrate the performance and effectiveness of the proposed approaches.