Consensus Problems for High-Order Multi-Agent Systems

Based on the algebraic graph theory, the networked multi-agent continuous systems are investigated. Firstly, the digraph (directed graph) represents the topology of a networked system, and then a consensus convergence criterion of system is proposed. Secondly, the issue of stability of multi-agent systems and the consensus convergence problem of information states are all analysed. Furthermore, the consensus equilibrium point of system is proved to be global and asymptotically reach the convex combination of initial states. Finally, two examples are taken to show the effectiveness of the results obtained in this paper.

With the development of swarm intelligence in last decades, consensus problem of multi-agent systems has been attracting much attention. To reveal the inherent mechanism of leader-following consensus in multi-agent systems with stochastic dynamics, PI control protocols are designed in this paper. Owing to the stochastic analysis techniques, algebraic graph theory, and constructing appropriate Lyapunov function, it is proved that the leader-following consensus of nonlinear stochastic dynamical multi-agent systems can be reached in mean square. Sufficient condition are deduced to select the PI control protocol parameters. Finally, the theoretical results are demonstrated through a simulation example.

In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis.

This paper studies the distributed H∞ control problem of identical linear time invariant multi-agent systems subject to external disturbances. A directed graph containing a spanning tree is used to model the communication topology. Based on the relative states of the neighbor agents and a subset of absolute states of the agents, distributed static H∞ controllers are proposed. The concept of an H∞ performance region is extended to the directed graph situation. Then the results are used to solve the leader–follower H∞ consensus problem. Sufficient conditions are proposed based on bounded real lemma and algebraic graph theory. The effectiveness of the theoretical results is illustrated via numerical simulations.

Sampled-data leader-following consensus of nonlinear multi-agent systems subject to impulsive perturbations

In this paper, a robust consensus tracking problem for a class of second-order multi-agent systems has been addressed in the presence of disturbances and unmodeled dynamics. The desired trajectory to be tracked is only provided to a small group of team members. An identifier is developed to estimate the unknown disturbances and unmodeled dynamics. A continuous consensus tracking controller is developed based on this identifier to achieve asymptotic consensus tracking using the local information obtained from neighboring agents. A sufficient condition is derived to ensure consensus tracking and asymptotic stability of the closed-loop system using algebraic graph theory, Lyapunov-based analysis, and an invariance-like theorem. Numerical simulations are provided to demonstrate the effectiveness of the developed robust consensus controller.

This paper investigates the problem of fixed-time event-triggered consensus control for a class of multi-agent systems with disturbed and non-linear dynamics. A fixed-time consensus protocol based on an event-triggered strategy is proposed, which can ensure a fixed-time event-triggered consensus, reduce energy consumption, and decrease the frequency of controller updates. The control protocol can also be applied to the case when the systems are free of disturbances; it solves the problem of high convergence time of the systems and reduces energy consumption of the systems. Sufficient conditions are proposed for the multi-agent systems with disturbed and non-linear dynamics to achieve the fixed-time event-triggered consensus by using algebraic graph theory, inequalities, fixed-time stability theory, and Lyapunov stability theory. Finally, simulation results show that the proposed control protocol has the advantages of both event-triggered and fixed-time convergence; compared to previous work, the convergence time of the new control protocol is greatly reduced (about 1.5 s) and the update times are also greatly reduced (less than 50 times), which is consistent with the theoretical results.

This paper investigates the periodic event-triggered asymmetric bipartite consensus problem of multi-agent systems (MASs) under structurally balanced undirected signed graphs. In order to reduce the consumption of communication resources and continuous detection in the control process of MASs, a novel periodic detection event-triggered asymmetric bipartite consensus control protocol is proposed. In particular, each agent samples only in a fixed period. For each agent, two event conditions are given, and only when state error satisfies this event condition can the event be triggered. A new type of Laplacian matrix is constructed to achieve asymmetric bipartite consensus. The control method can guarantee the performance of MASs and have less communication resources. Based on the Lyapunov stability theorem and algebraic graph theory, the proposed periodic event-triggered control strategy is able to implement the asymmetric bipartite consensus when the topology is structurally balanced undirected signed graphs. The proposed method in this paper can reduce the restriction on the sampling period and automatically exclude Zeno behavior. Finally, the validity of the conclusion is verified by numerical simulation.

This paper focuses on addressing consensus and flocking issues in second-order nonlinear multi-agent systems (MASs) under the false data injection attacks. Novel adaptive control protocols are proposed to effectively mitigate the impact of these attacks by updating adaptive parameters. Based on algebraic graph theory, matrix theory and the Lyapunov approach, various sufficient conditions are established, which show the fixed-time consensus and finite-time flocking can be achieved for the MASs. Moreover, some upper bounds for the settling time are derived in terms of the parameters of the model. Finally, three simulation examples are presented to validate the efficacy of our proposed theoretical results.

This paper is concerned with the joint effects of agent dynamic and network topology on leader-following consensus of continuous-time multi-agent systems. All the follower agents have identical MIMO linear dynamics which can be expressed in any order, while subject to different norm-bounded parameter uncertainties. The control input of each follower agent can only use local error states. By combining the tools of algebraic graph theory, Riccati inequality and Lyapunov inequality, sufficient conditions are derived for all agents to follow the leader under fixed topologies. Finally, an example with simulations is presented for illustration.

In this work, stochastic consensus of linear multi-agent systems with multiplicative measurement noises is investigated under undirected graphs. Based on the algebraic graph theory and the matrix theory, the consensus problem is converted into the stochastic stability problem of stochastic differential equations (SDEs) driven by multiplicative noises. Then by stochastic stability theorem for SDEs, the stochastic consensus conditions are given for the multi-agent systems. For the general linear multi-agent systems, the sufficient conditions for the mean square and the almost sure consensus are obtained based on the solution to an algebraic Riccati equation, where the consentability condition on the algebraic connectivity and the channel uncertainties is revealed. For the case of second-order integrator dynamics, by choosing some appropriate Lyapunov functions, the sufficient conditions for the mean square and the almost sure consensus, and the necessary conditions for the mean square consensus are derived. Moreover, it is shown that for any bounded noise intensities, the mean square and the almost sure consensus can be achieved by carefully choosing the control gain.

The consensus of fractional-order multi-agent nonlinear systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, a novel sufficient condition for achieving the consensus of a class of fractional-order multi-agent nonlinear systems are derived. Finally, one numerical simulation is given to illustrate the effectiveness of the proposed methods.

The consensus problem of multi-agent nonlinear systems with or without uncertain parameters is studied in this paper. Based on the theory of impulsive differential equations, Lyapunov stability theory and algebraic graph theory, some impulsive consensus conditions are given to realize the consensus of a class of multi-agent nonlinear systems. Compared with the existing investigations of impulsive consensus of multi-agent systems, the proposed impulsive control protocol with uncertain parameters is more rigorous and effective in practical systems. Two numerical simulations are verified to confirm the effectiveness of the proposed methods.

This paper investigates the leaderless and leader-following consensus problem for a second-order multi-agent systems with input saturation, i.e., the control input is required to be priori bounded. Moreover, the control coefficients are unknown and cannot be lower or upper bounded by known constants. By virtue of adaptive control technique, Lyapunov theory, algebraic graph theory and Barbalat's lemma, it is proved that the states of the multi-agent systems can achieve consensus under the assumption that the interconnection topology is undirected and connected. Finally, two simulation examples are provided to illustrate the effectiveness of the theoretical results.

In this paper, high order consensus problem of multi-agent systems with non-identical unknown nonlinear dynamics following an unknown and nonlinear leader is investigated in networks with fixed and switching topologies. By parameterizations of unknown nonlinear dynamics of agents in the system, neighbor-based adaptive consensus algorithms are proposed by incorporating consensus errors in addition to relative position feedback. Base on algebraic graph theory, Lyapunov theory, Riccati inequalities and PE condition, analysis of stability and parameter convergence of the proposed algorithm are conducted. Finally, a simulation in switching networks is worked out to illustrate the effectiveness of the theoretical results.