Consensus Problem Of Multi-agent Systems Research Articles

Observer-based event-triggered consensus of leader-following linear multi-agent systems with input saturation and switching topologies

In this paper, the observer-based leader-following consensus problem for multi-agent systems with input saturation is studied under fixed and switching topology. Firstly, based on the measurable output information of systems, we construct an auxiliary observation system to estimate the real state information of systems. At the same time, the centralized event-triggered control is considered in the fixed and switching topology, and the Lyapunov function and Cauchy’s convergence criterion are used to prove that the consensus of systems can be achieved. Secondly, the sufficient conditions of the event-triggered function are given, and it is proved that the constructed centralized event-triggered function can exclude the Zeno behavior. Then, the group case is considered in the fixed topology, and it is emphasized that the group event-triggered mechanism has the idea of event-triggered and decentralized control. Finally, the validity and feasibility of the theoretical results are illustrated by numerical examples.

Adaptive Consensus of Nonlinearly Parameterized Multi-Agent Systems

This letter studies the distributed adaptive consensus problem for multi-agent systems (MASs) subject to nonlinearly parameterized uncertainties. In the existing research, an adaptive consensus scheme was developed for the same scenario but under the assumption that the uncertainties must be linearly parameterized in their unknown parameters. In this letter, the assumption is removed by using a novel distributed adaptive update law, which makes the scheme applicable for more general nonlinear MASs. This letter contains a general design paradigm using the certainty equivalence principle and specific implementation of it on nonlinear second-order MASs. The results are supported by rigorous mathematical analysis and numerical simulation.

Consensus of multi-agent systems with impulsive perturbations and time-varying delays by dynamic delay interval method

In this paper, the consensus problem of multi-agent systems (MASs) with impulsive perturbations and time-varying delays is investigated. To reduce the conservative in consensus analysis of the MAS with impulsive perturbations and time-varying delays, the dynamic delay interval (DDI) method is used. It changes the fixed delay interval into a dynamic one so that a bigger allowed maximum upper bound (AMUB) of delay is derived. It is shown that the consensus of the MAS can be reached. Finally, two examples are given to illustrate the effectiveness of the proposed method.

A binary cooperative bat algorithm based optimal topology design of leader–follower consensus

In this paper, a binary cooperative bat searching algorithm(BCBA) is developed to tackle binary optimization problems. Different from the original bat searching algorithm, a consensus term was added into the velocity equation of the original bat searching algorithm in the cooperative bat searching algorithm(CBA). To develop the binary algorithm, the velocity value is mapped into a probability value between zero and one, and then the position will update to one or zero depending on the comparison between the mapped velocity and a random number. In this paper, four different mapping functions are investigated to determine the best transfer function for the binary CBA. The numerical illustrations are provided to demonstrate the superior performance of BCBA by comparing with the four binary algorithms in the literature. Moreover, the leader–follower consensus problem of multi-agent systems is studied. The condition of the communication topologies of the leader–follower protocol is relaxed so that the different topologies can be used to share different state information. In order to find the trade-off between the convergence rate and communication cost, a binary variable optimal topology design problem is formulated, and then the BCBA is used to tackle the proposed design problem. The numerical evaluation is conducted to show the competitive performance of the BCBA.

Analysis of linear asynchronous hybrid stochastic systems and its application to multi-agent systems with Markovian switching topologies

ABSTRACTThis paper studies the stability and stabilisation of a class of asynchronous hybrid stochastic systems described by linear Markov jump systems with asynchronous parameters induced by hysteretic mode and input delay. By exploring the essential properties of the Markov chain and developing novel Lyapunov function/functional based approaches, we derive sufficient conditions in terms of sizes of the delays ensuring the mean square asymptotical stability of the systems. Interestingly, the Lyapunov functional based approach further leads to the mean square stability criteria that depend only on the drift part and allow an arbitrary large delay for the diffusion part, which is different from the Lyapunov-Razumikhin based results. The theoretical results are applied to solve the consensus problems of multi-agent systems with Markovian switching topologies and input delay. Numerical examples demonstrate the established results.

T–S fuzzy model-based adaptive repetitive consensus control for multi-agent systems with imprecise communication topology structure

ABSTRACTThis paper studies the consensus problem of multi-agent systems (MAS) with imprecise communication topology structure (ICTS). T–S fuzzy model is used to express the ICTS. Through repeated learning techniques, this paper designs a distributed learning protocol that enables all agents reach consensus with periodic uncertainty parameters. The periodic uncertainty parameters are compensated based on a repetitive learning design method. With the information of leader agent is known to a small portion of following agents, an auxiliary control term is presented for each follower agent to handle leader's dynamic. Under the condition that the ICTS is fuzzy union connected, the learning control protocol proposed in this paper makes all the agents reach an agreement. In addition, the proposed consensus learning protocol is further promoted to solve the formation control problem. Sufficient conditions are given for the consensus and formation problems of the MAS by constructing a composite energy function, respectively. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed control protocol.

Distributed Consensus Over Markovian Packet Loss Channels

This paper studies the consensusability problem of multiagent systems (MASs), where agents communicate with each other through Markovian packet loss channels. We try to determine conditions under which there exists a linear distributed consensus controller such that the MAS can achieve mean square consensus. We first provide a necessary and sufficient consensus condition for MASs with single input and independent and identically distributed channel losses, which complements existing results. Then, we proceed to study the case with identical Markovian packet losses. A necessary and sufficient consensus condition is first derived based on the stability of Markov jump linear systems. Then, a numerically verifiable consensus criterion in terms of the feasibility of linear matrix inequalities (LMIs) is proposed. Furthermore, analytic sufficient conditions and necessary conditions for mean square consensusability are provided for general MASs. The case with nonidentical packet loss is studied subsequently. The necessary and sufficient consensus condition and a sufficient consensus condition in terms of LMIs are proposed. In the end, numerical simulations are conducted to verify the derived results.

Distributed Event-Triggered Consensus of Multiagent Systems With Communication Delays: A Hybrid System Approach.

This paper investigates the leader-following consensus problem for multiagent systems (MASs) with communication delays. A novel hybrid event-triggered control scheme is developed and a hybrid system approach is proposed to design the event-triggering condition. Meanwhile, by means of temporal regularization, a strictly positive lower bound on the interevent times can be guaranteed, that is, Zeno-freeness can be guaranteed. The MASs are first described as a closed-loop system with both flow dynamics and jump dynamics, where the jump dynamics is induced from the triggering events and communication delays. Then, a hybrid model of the MASs is constructed under a hybrid systems framework. Based on this hybrid model, how to construct the Lyapunov function is given and the event-triggering condition design is also developed, such that the asymptotic consensus is achieved. Finally, an example is provided to show the effectiveness of the proposed approach.

Leader-following consensus of multi-agent systems with randomly varying nonlinearities and stochastic disturbances under directed switching topologies

This paper investigates leader-following consensus problem of multi-agent systems with randomly varying nonlinearities and stochastic disturbances under switching topologies. The randomly varying nonlinearities and stochastic disturbances are introduced to reflect more realistic dynamical behaviors that are caused by the noisy environment. The communication topology is molded by a directed graph will fall into two categories, i.e., one satisfies that contains a spanning tree whereas the other does not. Thus, the communication topology is time-varying. By using tools from M-matrix theory and multiple Lyapunov methods, some sufficient criteria are derived to achieve leader-following consensus. Finally, a numerical example is given to show the effectiveness of the proposed method.

Finite-time Asymmetric Bipartite Consensus for Signed Networks of Dynamic Agents

This paper addresses the finite-time asymmetric bipartite consensus problem for multi-agent systems (MAS) associated with signed graphs. Different from bipartite consensus in the previous literatures, asymmetric bipartite consensus means that the states of all agents will converge to two values with different signs and modulus. Two distinct nonlinear consensus control protocols are constructed for the considered system to achieve the finite-time asymmetric bipartite consensus and the fixed-time asymmetric bipartite consensus, respectively. Under the first proposed protocol, it is shown that within a finite time, the considered system can realize asymmetric bipartite consensus. To strengthen the obtained result, the second protocol is proposed, which guarantees that all agents could achieve the asymmetric bipartite consensus in fixed time, that is, the finite-time consensus can be reached before a settling time which is irrelevant with the initial states of the agents. Finally, numerical simulations are given to verify effectiveness of the proposed consensus control protocols.

Event-triggered and quantized self-triggered control for multi-agent systems based on relative state measurements

This paper studies the consensus problem of multi-agent systems by event- and self-triggered control. An event-triggered algorithm with periodic event detection and relative state measurements is designed to determine all event times. Furthermore, a self-triggered control algorithm with periodic event detection and quantization is proposed to further reduce resource consumption. In the proposed control strategies, only relative state information, or called edge information, is utilized by controllers, and all edge state information incident to each agent is processed together. The results are illustrated by two numerical experiments.

Consensus of Multiagent System in the Sense of Curvature and Torsion

In this paper, the consensus problem is investigated for a distributed multiagent system (MAS), where the consensus is characterized by curvature function and torsion function. According to the Frenet-Serret formulas, a distributed consensus protocol is designed for the tangent, normal, and binormal unit vectors of trajectory of each agent, and then it gets a closed-loop system. Based on the Lyapunov function, several sufficient conditions for consensus are derived for the closed-loop system. Also the consensus problem of multiagent system on a surface is studied. Finally, the numerical examples show the reliability of the proposed methods.

Predictive Pinning Control with Communication Delays for Consensus of Multi-Agent Systems

In this paper, based on the policy of model predictive control (MPC), a new method of predictive pinning control is proposed for the consensus problem of multi-agent systems. Pinning control is a method that the external control input is added to some agents (pinning nodes), e.g., leaders. By the external control input, consensus to a certain target value (not the average of the initial states) and faster consensus are achieved. In the proposed method, the external control input is calculated by the controller node connected to pinning nodes. Since all states of agents are required in calculation of the external control input, communication delays must be considered. The proposed algorithm includes not only calculation of the external control input but also delay compensation. The effectiveness of the proposed method is presented by two numerical examples.

Bipartite Consensus of Multi-Agent Systems With Intermittent Interaction

This paper studies the bipartite consensus problem of multi-agent systems with intermittent interaction under signed directed graph. It is assumed that each agent receives its states information relative to its neighbors at the sampling time and updates the control input by using the states information, and the period of each agent updates control input is equal to a positive integer multiple of its sampling period. Cooperation and competition between agents are represented by positive and negative weights of edge respectively in the signed topology. The sufficient condition for achieving bipartite consensus is obtained by Shure-Cohen stability criterion, which reveals the relationship among sampling period, update control input period and controller gain of system. Finally, simulation tests show the bipartite consensus performances of agents under intermittent protocol and signed topology.

Event-Triggered Finite-Time Integral Sliding Mode Controller for Consensus-Based Formation of Multirobot Systems With Disturbances

This paper deals with the distributed fast and finite-time consensus problem of multiagent systems with bounded disturbances in a leader-follower-based frame work. A novel integral sliding mode-based robust finite-time event-triggered control strategy has been proposed. A fast reaching law is also utilized to improve the speed of convergence. The triggering condition is derived based on the defined novel measurement error, suited for systems with model uncertainties/disturbances. The expression for the lower bound for the interexecution time has been derived to ensure that the zeno behavior is avoided. The proposed nonlinear consensus protocol is such that the desired relative state deviation between the agents can be achieved with a directed graph topology. The theoretical results are validated through real-time experimentations done using Pioneer P3-DX as well as FireBird VI robots.

Event-Triggered Consensus Control for Linear Multi-Agent Systems

For the consensus problem of multi-agent systems with linear dynamics, distributed event-triggered control strategies are put forward, which can decrease the frequency of information transmissions between agents and the number of control inputs of each agent. In the case that the agent states can be obtained or outputs can be obtained, distributed consensus protocols are designed based on event-triggered state information and event-triggered observer information, respectively. The consensus problem is converted into the stability problem by model transformation. Sufficient conditions for multi-agent systems to achieve consensus are obtained. Meanwhile, it is theoretically proved that the event-triggering conditions will exclude Zeno behavior. Simulation examples verify the effectiveness of obtained results.

固定拓扑下带有时延的二阶多智能体系统的一致性问题

固定拓扑下带有时延的二阶多智能体系统的一致性问题

Consensus analysis of multi-agent systems with general linear dynamics and switching topologies by non-monotonically decreasing Lyapunov function

This paper investigates consensus problems for multi-agent systems with general linear dynamics and switching topologies. In order to deal with the intricate interaction between dynamics of isolated agents and switching-disconnected topologies, the consensus analysis is performed by non-monotonically decreasing Lyapunov function. Particularly, the design of consensus laws is explored from the perspective of fast time-varying systems with two time scales. Sufficient conditions for achieving consensus are derived, which depend on not only feedback gains and connectivity of network topologies but also the speed of topology switching and the stability of individual agent. Therefore consensus laws are generalized in the sense that the dynamics of linear agents are allowed to be unstable and switching topologies are allowed to be jointly weakly connected and balanced. Finally, numerical simulations are provided to demonstrate the effectiveness of theoretical results.

Weighted Consensus Problem for Multiagent Systems with Edge‐ and Node‐Weighted Directed Graphs

In this paper, the concept of consensus is generalized to weighted consensus, by which the conventional consensus, the bipartite consensus, and the cluster consensus problems can be unified in the proposed weighted consensus frame. The dynamics of agents are modeled by the general linear time‐invariant systems. The interaction topology is modeled by edge‐ and node‐weighted directed graphs. Under both state feedback and output feedback control strategies, the weighted consensus problems are transformed into the equivalent conventional consensus problems. Then, some distributed state feedback and output feedback protocols are proposed to solve the weighted consensus problems. For output feedback case, a unified frame to construct the state‐observer‐based weighted consensus protocols is proposed, and different design approaches are discussed. As special cases, some related results for bipartite consensus and cluster consensus can be obtained directly. Finally, a simple example is given to illustrate the effectiveness of our proposed approaches.

H∞ Output Consensus for Markov Jump Multiagent Systems With Uncertainties.

This paper investigates the H∞ output consensus problem for multiagent systems with Markov jump and external disturbance in both continuous-time and discrete-time domains. The communication network is directed and fixed with uncertainties. Based on the hidden Markov model, an output feedback controller is constructed. Then, the original system is transformed into a reduced-order system, which features the error dynamics. By using a Lyapunov function, sufficient conditions are developed to ensure that all agents can reach the consensus with the desired H∞ performance in the mean-square sense. Finally, simulation results are presented to illustrate the efficiency of the proposed approaches.