Bipartite Consensus Of Multi-agent Systems Research Articles

Event-triggered bipartite consensus of multi-agent systems in signed networks

<abstract><p>This paper focuses on the event-triggered bipartite consensus of multi-agent systems in signed networks, where the dynamics of each agent is assumed to be Lur'e system, and both the cooperative interaction and antagonistic interaction are allowed among neighbor agents. A novel event-triggered communication scheme is presented to save limited network resources, and distributed bipartite control techniques are raised to address the bipartite leaderless consensus and bipartite leader-following consensus respectively. By virtue of the Lyapunov stability theory and algebraic graph theory, bipartite consensus conditions are derived, which can be easily solved by MATLAB. In addition, the upper bounds of the sampling period and triggered parameter can be estimated. Finally, two examples are employed to show the validity and advantage of the proposed transmission scheme.</p></abstract>

H-infinity bipartite consensus of multi-agent systems with external disturbance and probabilistic actuator faults in signed networks

<abstract><p>The H-infinity bipartite consensus problem is addressed for a class of linear multi-agent systems with external disturbance, where the positive and negative links are allowed in communication topology. A novel event-triggered communication scheme is presented to save limited network resources, which dependents on information from neighboring agents at event-triggered instants, the given event-triggered condition is detected only at discrete sampling times, thus Zeno behavior can be excluded, two types of event-triggered matrices have been introduced in our event-triggered communication scheme, which can further reduce the sampled-data transmission compared with some existed results. Considering the probabilistic actuator faults, the reliable controller is designed based on sampled-data, then a new distribution-based fault model is constructed by using coordinate transform. Some H-infinity bipartite consensus criteria can be derived by the Lyapunov stability theory and algebraic graph theory, at the same time, the feedback matrices and event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, a numerical example is employed to show the validity and advantage of the proposed transmission scheme.</p></abstract>

Mean Square Bipartite Consensus for Multi-agent Systems with Measurement Noises and Communication Time-delays

Mean Square Bipartite Consensus for Multi-agent Systems with Measurement Noises and Communication Time-delays

High-Order Bipartite Consensus for Multiagent Systems Over Signed Networks Subject to Asynchronous Communications

Bipartite consensus is a common collective behavior emerging from multiagent systems (MASs) when cooperative and hostile relationships are present simultaneously in the interaction network. The main focus of this study is the problem of bipartite consensus for high-order MASs subject to asynchronous communications, where the instants for each agent to derive the information from neighboring agents and adjust its state are determined by the exclusive clock. Through the construction of the augmented system, we establish algebraic graph conditions for achieving bipartite consensus in the context of various communication constraints. Moreover, an effective strategy for how to select feasible gain parameters in high-order MASs is developed. At last, an illustrative example, which demonstrates the achievement of asynchronous bipartite consensus, is given.

Resilient dynamic output feedback control for bipartite consensus of multiagent systems with Markov switching topologies

AbstractThis study is systematically devoted to the problem of dynamic output feedback control for bipartite consensus of multiagent systems in the presence of Markov switching topologies. The main purpose of this study is to develop a dynamic output feedback controller with gain fluctuations such that the considered multiagent system achieves bipartite consensus. Notably, the interaction among agents of the considered system is depicted by a signed undirected Markovian switching network topologies. Pursuant to Lyapunov stability theory and algebraic graph theory, sufficient conditions will be derived in terms of linear matrix inequalities to obtain the bipartite consensus of the concerned problem. At last, superiority of the designed dynamic output feedback control technique and developed theoretical results are conferred through two numerical examples.

Bipartite consensus of multi-agent systems with reduced-order observer-based distributed control protocols

This paper considers the bipartite consensus problem for multi-agent systems, in which both bipartite leaderless consensus and bipartite tracking problems are investigated under signed digraph. Two distributed output feedback control laws are proposed based on reduced-order observer design, respectively, for solving the bipartite leaderless consensus and bipartite tracking consensus problems. Some sufficient conditions are obtained for achieving the bipartite consensus of the multi-agent systems, by using the algebraic Riccati equation design and Jordan decomposition technique. Finally, two simulation examples are presented to illustrate the effectiveness of the obtained theoretical results.

A Unified Framework Design for Finite-Time Bipartite Consensus of Multi-Agent Systems

In this paper, the finite-time bipartite consensus (FTBC) problem is investigated for the multi-agent system (MAS) with detail balanced structure. To realize FTBC of MAS, a unified protocol framework is developed. Some criteria are established for realizing FTBC. It is worth noticing that estimations of settling time can be given in form of mathematical expression. The unified framework can bring in various protocols by choosing different parameters, which extends previous results. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of corresponding theoretical results.

Distributed Prescribed-Time Interval Bipartite Consensus of Multi-Agent Systems on Directed Graphs: Theory and Experiment

This work deals with the analysis and protocol design problems of the prescribed-time interval bipartite consensus of multi-agent systems on signed and directed graphs. A new distributed protocol with hybrid constant and time-varying feedbacks of local signed error is proposed, whose consensus time period is independent of the specific topology among agents and initial states of all agents. By introducing a series of well-structured Lyapunov functions, the technical difficulties arising from the asymmetrical Laplacian matrices of directed graphs are circumvented. The effectiveness of this prescribed-time protocol for multi-agent systems on signed digraphs with a spanning tree is proven both on structurally balanced digraphs and structurally unbalanced ones with a positive root subgraph. An illustrative simulation example and a prescribed-time bipartite formation experiment on a swarm of nano-quadcopters are implemented to show the validity and practicability of these proposed protocols.

Mean Square Bipartite Consensus for Multiagent Systems With Antagonistic Information and Time-Varying Topologies

We consider the discrete-time distributed bipartite-consensus problem for multiagent systems subject to measurement noises and time-varying random networks, where the information exchange among the agents can be antagonistic and disturbed by both multiplicative and additive noises. The antagonistic information is characterized by a signed random graph. The main challenge is that the coexistence of multiplicative noise and antagonistic information does not allow the multiplicative noise term to be converted into an error equation. Based on the semi-decomposition method and Lyapunov-based technique, we derive sufficient conditions for stochastic approximation step size to assure the mean square bipartite consensus. Moreover, the convergence rate of the consensus error is explicitly formulated, which is tightly linked to the step size and the eigenvalues of the Laplacian matrix. Finally, we verify the main results via a numerical example.

Bipartite consensus for multi-agent systems with noises over Markovian switching topologies

In this paper, we investigate the distributed control problem for multi-agent systems (MASs) subject to multiplicative and additive noises over switching networks, where both cooperative and antagonistic interactions coexist. The communication topology is governed by a continuous-time Markovian chain. A stochastic approximation technique is utilized to handle stochastic bipartite consensus with communication noises. The major challenge, due to the fact that the intensity of the multiplicative noise is nonlinearly coupled with the distance between agents, is that the coexistence of antagonistic information and multiplicative noise makes the multiplicative noise term impossible to be converted into an error form. This leads to the inapplicability of the Lyapunov-based method. To cope with this, we first show the boundedness of agents’ states where the second moment approach is employed. Based on it, the mean square and almost surely bipartite consensus are achieved under some mild requirements. The efficiency of the proposed method is supported by an example.

Prescribed-Time Event-Triggered Bipartite Consensus of Multiagent Systems.

This article studies event-triggered control for the prescribed-time bipartite consensus of first-order multiagent systems. For each agent, the new event-triggered control law and triggering condition are constructed without continuous interneighboring communication. Based on the Lyapunov stability theory and the algebraic graph theory, permissible value ranges of the designed parameters are established to guarantee that all agents reach bipartite consensus in a completely prespecified time. Moreover, a comprehensive theoretical discussion is provided to show that the Zeno behavior can be excluded during the whole time span except the prespecified settling time T . The simulation results demonstrate the feasibility of the provided methods.

Distributed finite-time bipartite consensus of multi-agent systems on directed graphs: Theory and experiment in nano-quadcopters formation

This work deals with the analysis and protocol design problems of finite-time consensus for multi-agent systems on signed and directed networks. A new distributed protocol with two reciprocal fractional power feedbacks of local consensus error has been proposed to remove the influence of initial states on the consensus time. By introducing a well-structured Lyapunov function, the technical difficulty arising from the asymmetrical Laplacian matrices of directed graphs is circumvented. Furthermore, it is shown that the feasibility of this proposed protocol can be extended to directed graphs with a spanning tree by mathematical induction method. The upper bounds of the finite-time periods are given under the circumstances of directed networks with a spanning tree apart from the strongly-connected ones. This new protocol is then extended to the application of finite-time bipartite formation control of multi-agent systems. Simulations and experiments of bipartite formation of multiple nano-quadcopters are implemented to prove the validity and practicability of this new protocol. In the experiment, a novel fuzzy logic is also introduced to realize the group collision avoidance of all nano-quadcopters.

Event-triggered bipartite consensus of multi-agent systems with switching partial couplings and topologies

Bipartite consensus of multi-agent systems with switching communication topologies is addressed in this paper. Neighboring agents are partially coupled with each other and possess cooperative and antagonistic relationships. Moreover, the couplings can vary according to the change of topology. In order to reduce the number of control updates, centralized and distributed event-triggered mechanisms are adopted in designing consensus protocols. Particularly, the given event-triggered conditions are piecewise functions depending on the variable couplings and topologies. Based on the signed graph theory, the error system for bipartite consensus is derived, meanwhile, errors are verified to converge to zero by constructing a suitable Lyapunov function. A union graph is put forward to represent transmission of singe-level state information within a time interval, then bipartite consensus of the multi-agent system is realized if each union graph has a spanning tree. In addition, Zeno behavior is excluded in the presented event-triggered conditions. Numerical examples further validate the obtained theoretical results.

Distributed Finite-time Bipartite Consensus of Multi-agent Systems via Event-triggered Control

This paper investigates a distributed finite-time event-triggered bipartite consensus control for multi-agent systems. Under scenarios of energy limitation, an event-triggered strategy coupled with a nonlinear distributed control protocol is proposed only relying on local information, where the controller only updates at triggered instants. We proved that when the antagonistic network contains a spanning tree, the event-triggered controller can drive all agents to reach consensus value with an identical magnitude but opposite signs. Moreover, both the convergence time depending on the initial state and the positive lower bound of inter-event times are achieved. Simulation results show that the proposed controller has better disturbance rejection properties and can achieve bipartite consensus faster compared to an asymptotic controller.

The Bipartite Consensus for Multi-Agent Systems With Matrix-Weight-Based Signed Network

This brief focuses on the consensus problem of multi-agent systems (MASs) consisting of friends and enemies in a matrix-weight-based signed topological network. To highlight the effects of matrix coupling, we analyze the integrator model in a competitive-cooperative coexistence network. Unlike scalar-weight-based topological networks, the phenomenon of clustering in matrix-weight-based networks naturally exists, which means the important role of matrix coupling in convergence. Hence, different form existing results, depending on matrix coupling, the research shows bipartite consensus can be achieved in an unbalanced situation. Algebraic conditions are proposed for achieving a bipartite consensus and our results on structural unbalanced graph are shown to be more universality. Finally, some simulation results are given to vindicate the analysis.

Event-triggered Bipartite Consensus for Multi-agent Systems with Antagonistic Interactions

This paper investigates event-triggered control for first-order multi-agent systems with structurally balanced signed graphs. A distributed continuous event-triggered consensus mechanism is firstly proposed for each agent, including the control law based on local sampled states, and the triggering condition constructed with its own state, the sampled states of itself and its neighbours, and an extra signal. No knowledge of the global network is needed. By applying Lyapunov stability theory and the algebraic graph theory, we prove that all agents can reach agreement with identical magnitude but opposite sign while Zeno behaviour is excluded. Moreover, the periodic implementation of the event-triggered consensus algorithm is proposed. The criteria of co-designing the triggering condition parameter and the verification period is established to guarantee the bipartite consensus of the systems. Finally, simulations, including a numerical example and a group of multiple mobile robots, are shown to illustrate the efficiency of the proposed theoretical results.

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.

Bipartite Consensus for Multi-Agent Systems With Time-Varying Delays Based on Method of Delay Partitioning

Bipartite consensus protocol is designed for multi-agent systems with time-varying delays. Then, the bipartite consensus problem is transformed into a corresponding stability problem by methods of gauge transformation and state transformation. The Lyapunov–Krasovskii functional is constructed, and the linear matrix inequality theory based on methods of delay partitioning and free matrix integral inequality is used to obtain sufficient conditions for a bipartite consensus of multi-agent systems. Both the first-order and second-order multi-agent systems are investigated. Finally, the effectiveness of the obtained results is illustrated by virtue of simulation results.

Bipartite Consensus of Discrete-Time Double-Integrator Multi-Agent Systems with Measurement Noise

The effects of measurement noise are investigated in the context of bipartite consensus of multi-agent systems. In the system setting, discrete-time double-integrator dynamics are assumed for the agent, and measurement noise is present for the agent receiving the state information from its neighbors. Time-varying stochastic bipartite consensus protocols are designed in order to lessen the harmful effects of the noise. Consequently, the state transition matrix of the closed-loop system is analyzed, and sufficient and necessary conditions for the proposed protocol to be a mean square bipartite consensus protocol are given with the help of linear transformation and algebraic graph theory. It is proven that the signed digraph to be structurally balanced and having a spanning tree are the weakest communication assumptions for ensuring bipartite consensus. In particular, the proposed protocol is a mean square bipartite average consensus one if the signed digraph is also weight balanced.

Finite-Time Bipartite Consensus for Multi-Agent Systems on Directed Signed Networks

This paper addresses the finite-time bipartite consensus problem for multi-agent systems (MASs) on a directed signed network. Some properties for signed digraphs are first investigated and two nonlinear control protocols are then designed for first- and second-order MASs, respectively, where agents may be influenced by bounded disturbances. Particularly, for MASs with second-order dynamics, a new estimation technique is developed to estimate the settling time. Simulation results are finally presented to verify the effectiveness of the proposed control protocols.