Leader-following Consensus Of Multi-agent Systems Research Articles

Leader-Following Consensus of Multiagent Systems via Asynchronous Sampled-Data Control: A Hybrid System Approach

In this article, we develop a hybrid system approach for sampled-data-based leader-following consensus of multiagent systems over a static/switching directed network. First, an asynchronous sampled-data hybrid consensus control protocol is proposed, which has an extra reset control part in contrast with the traditional linear control protocol and is beneficial for achieving better transient consensus performance. Then, with several properly defined internal variables, a hybrid model consisting of both flow and jump dynamics is constructed to describe the closed-loop dynamics. Based on this model and internal decreasing functions, Lyapunov-based stability conditions are derived, and larger upper bound of sampling period can be obtained compared to the existing related work. Finally, an example is given to show the superiority of the proposed approach.

Consensus of nonlinear multiagent systems with intermittent dynamic event-triggered protocols

This paper studies the consensus of leader-following multiagent systems with nonlinear dynamics. Consider that control protocols for the consensus work under an intermittent framework due to inevitable factors; meanwhile, the event-triggered mechanism is introduced, so as to reduce the update frequency of the control protocols. In particular, threshold parameters in the event-triggered conditions are supposed to be dynamically changed, and the minimum event-triggered intervals are set to be positive in advance. Furthermore, according to whether event-triggered conditions depend on combined measurements or a single measurement, two forms of event-triggered schemes are designed; then, the corresponding distributed control protocols are demonstrated. Based on the graph theory and Lyapunov function method, sufficient conditions and a concrete algorithm for the consensus of multiagent systems are presented. It is shown that the intermittent dynamic event-triggered protocols given in this paper can effectively reduce the update frequency of control and exclude Zeno behavior. Finally, detailed numerical examples are supplied to illustrate the proposed results.

Robust Formation Control Based on Leader-Following Consensus in Multi-Agent Systems With Faults in the Information Exchange: Application in a Fleet of Unmanned Aerial Vehicles

In this paper, a robust leader-following consensus protocol for multi-agent systems (MASs) subject to faults in the information exchange and disturbance is presented. The problem under consideration is to guarantee the convergence of the agent trajectories to a leader agent when all the agent followers are under faults in the information exchange as smooth time-varying delays and disturbances. The main contribution in this paper is the design of a robust leader-following control through the Lyapunov approach and an optimal \mathscr H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> criterion such that all agents follow a virtual leader agent despite faults in the information exchange and disturbances. Linear matrix inequalities (LMIs)-based conditions are obtained whose solution allows computing the robust controller gain. In order to show the effectiveness of the proposed approach, numerical examples are carried out comparing a state-of-the-art approach and the proposed strategy in a fleet of unmanned aerial vehicles (UAVs) subject to wind turbulence which are shown to achieve the formation control.

PDE-Based Leader-Following Consensus of Multi-Agent Systems with Input Delay under Spatial Boundary Communication

This paper studies the leader-following consensus problem for a class of multi-agent systems with input delay via spatial boundary communication. The multi-agent systems are modelled by a class of linear hyperbolic partial differential equations (PDEs). By considering the input delay and adopting some transformations, a novel PDE stability problem is formulated. Then, based on the spatial boundary communication scheme and Lyapunov stability theory, a boundary controller is developed to ensure the stability of the PDE system. Finally, the derived results are verified via a numerical simulation.

New Results on Consensus of Multi-Agent Systems With Time-Varying Delays: A Cyclic Switching Technique

This paper studies the leader-following consensus problem of discrete-time multi-agent systems with time-varying delays by developing a new cyclic switching scheme. First, two delay-dependent cycle dwell time switching laws are proposed for the first time. Second, by the proposed cyclic switching laws and constructed Lyapunov functionals, new leader-following consensus criteria for discrete-time multi-agent systems with time-varying delays are derived in the form of linear matrix inequalities. Compared with the existing literature, the developed cyclic switching method not only greatly improves the upper bound of time-varying delays in the multi-agent system, but also gives the estimation of upper and lower bounds for dwell time of the system. Finally, some simulations for the leader-following consensus of multi-agent systems with time-varying delays are presented to verify the feasibility of the proposed scheme.

Leader-following consensus of multi-agent systems via novel sampled-data event-triggered control

A novel sampled-data event-triggered control (SDETC) for multi-agent systems (MASs) is proposed in this study, which is a more general form with the advantages of more flexible triggering techniques such as LIoDT, EIoDT, LT described in Remark 2.1, 2.2 covering many existing cases [1, 2, 3, 4]. It eliminates the Zeno behavior based on itself structure without difficult proof in the triggering scheme and has the upper triggering interval easily, avoiding the problem that it is not easy to solve linear matrix inequalities (LMIs) if applying the existing method [5] due to the triggering instants in LMIs. The node-based triggering time instants {tsi} in SDETC and the non-node-based impulsive time instants {tk} are well integrated. Cyber attack is considered in the transmission of information in the controller with SDETC for MASs. Leader-following consensus conditions of MASs via the novel impulsive SDETC are constructed. Finally, numerical examples give verification of the proposed methods.

Leader-following consensus for multi-agent systems with actuator faults via adaptive event-triggered control

In this paper, the leader-following consensus problem is investigated by event-triggered control for multi-agent systems subject to time-varying actuator faults. Firstly, for a case of the leader without control input, a distributed event-triggered fault-tolerant protocol is proposed with the help of adaptive gains. Secondly, the proposed protocol is developed by an auxiliary nonlinear function to compensate the effect of the leader’s unknown bounded input. It is shown that under the both obtained protocols the tracking errors converge to an adjustable neighborhood around the origin, meanwhile the Zeno behavior is avoided. Moreover, the protocols are fully distributed in sense that any global information associated with the network is no longer utilized. Finally, numerical examples are presented to show the validity of the obtained protocols.

Leader-Following Consensus of Non-linear Multi-agent Systems with Interval Time-Varying Delay via Impulsive Control

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.

Adaptive controller design for fixed-time leader-following consensus of multi-agent systems with discontinuous dynamics

This paper investigates the adaptive fixed-time consensus of a class of multi-agent systems with discontinuous dynamics. First, under the framework of Filippov solutions, a new theorem is established to achieve fixed-time consensus of discontinuous multi-agent systems using the proposed control protocol. Furthermore, an adaptive control protocol is provided in the second theorem that highly improves the control signals of the system. Finally, numerical simulations are worked out to illustrate the effectiveness of our theoretical results.

H ∞ consensus of multi-agent systems with semi-Markovian switching topologies and mode-dependent delays

This paper addresses leader-following consensus of multi-agent systems with semi-Markovian switching topologies and time-varying delays. Unlike the classic Markovian switching topologies, the transition rates are time-varying in the semi-Markovian switching topologies, which can better model the switching of topologies due to inevitable stochastic changes. Moreover, compared with existing works on multi-agent systems with switching topologies and time delays, the delays in the paper are dependent on the switching modes. By designing the distributed mode-dependent consensus protocol and constructing Lyapunov functional, sufficient conditions in terms of LMIs are derived to ensure that leader-following consensus is asymptotically achieved in the mean square. Finally, a numerical example is provided to show the effectiveness of the main results.

Dynamic Event-Triggered Control for Leader-Following Consensus of Multiagent Systems

In this paper, the leader-following consensus problem of multiagent systems with general dynamics under event-triggered mechanisms is investigated. A centralized event-triggered mechanism (CEM) is first proposed. Then, a distributed dynamic event-triggered mechanism is developed by introducing an internal variable. In the CEM case, each agent uses global information of the multiagent system, while in the distributed case, each agent only uses local information of its own and its neighbors. The multiagent system can achieve asymptotic consensus as well as exclude the Zeno phenomenon under the designed event-triggered rules in both cases. A multiagent system consisting of interconnected pendulums is provided to demonstrate the merits and correctness of the proposed methods.

Observer-Based Dynamic Event-Triggered Strategies for Leader-Following Consensus of Multi-Agent Systems With Disturbances

This paper studies leader-following bounded consensus problem for linear multi-agent systems (MASs) with exogenous disturbances under an observer-based dynamic event-triggered scheme. To guarantee performance requirements, and avoid frequent updates of the sensors, and the controllers at the same time, two independent event-triggered schemes with dynamic threshold are proposed in sensor-to-observer (S-O), and controller-to-actuator (C-A) channels, respectively. And a fully distributed observer event-based controller is designed, which only requires the observer information from neighboring followers, and itself for each follower. With the help of the Riccati equation, and inequality techniques, some simple, and convenient sufficient conditions are derived to ensure that the closed loop system converges to a bounded region exponentially. Moreover, the proposed dynamic event-triggered mechanisms in S-O, and C-A channels do not only lessen the transmission load, and controller update, but also exclude the Zeno behavior. Finally, a numerical example is given to verify the correctness, and efficiency of our results.

Leader-following consensus for multi-agent systems with nonlinear dynamics subject to additive bounded disturbances and asynchronously sampled outputs

This paper is concerned with the leader-following consensus problem for a class of Lipschitz nonlinear multi-agent systems with uncertain dynamics, where each agent only transmits its noisy output, at discrete instants and independently from its neighbors. The proposed consensus protocol is based on a continuous-discrete time observer, which provides a continuous time estimation of the state of the neighbors from their discrete-time output measurements, together with a continuous control law. The stability of the multi-agent system is analyzed with a Lyapunov approach and the exponential practical convergence is ensured provided that the tuning parameters and the maximum allowable sampling period satisfy some inequalities. The proposed protocol is simulated on a multi-agent system whose dynamics are ruled by a Chua’s oscillator.

Leader-following Consensus of Multi-agent Systems via a Hybrid Protocol with Saturation Effects

In this paper, a hybrid protocol which can control multi-agent systems to achieve “leader-following consensus” is proposed, the control protocol is periodic and is composed of continuous control and impulse control. Considering the power limitation and the time error of the actual industrial production equipments, the impulse saturation effects and the impulse time window are introduced. In this paper, the multi-agent system is modeled, one of the agents is designated as the leader, and the rest of the agents are the followers. Then the error system equations of the multi-agent system is derived. The stability of the error system is analyzed by constructing the Lyapunov function. Theorem 1 and theorem 2 are obtained as the criteria of state consensus of the multi-agent system. Finally, a numerical experiment is carried out to verify the reliability and efficiency of the conclusions are given in this paper. Because it takes into account the impulse time window and impulse saturation effects, which is more in line with the actual industrial production.

Leader-following consensus of multi-agent systems under antagonistic networks

In this paper, we address the leader-following consensus of multi-agent systems (MASs) under a class of antagonistic networks. Different from the traditional literature, in our model, whether a follower can access the leader depends on a matrix instead of a scalar. For antagonistic and directed networks with structurally balanced properties, sufficient conditions are established under which the MASs will achieve bipartite consensus. Detailed algorithms are proposed to design the gain matrices and the coupling strength. What is more, we design adaptive laws to self-tune the value of the coupling strength. Simulation results are also given to verify the effectiveness of our methods.

On Leader-Following Consensus in Multi-Agent Systems with Discrete Updates at Random Times

This paper studies the leader-following consensus problem in continuous-time multi-agent networks with communications/updates occurring only at random times. The time between two consecutive controller updates is exponentially distributed. Some sufficient conditions are derived to design the control law that ensures the leader-following consensus is asymptotically reached (in the sense of the expected value of a stochastic process). The numerical examples are worked out to demonstrate the effectiveness of our theoretical results.

Distributed Fuzzy Adaptive Control for Heterogeneous Nonlinear Multiagent Systems with Similar Composite Structure

A distributed fuzzy adaptive control with similar parameters is constructed for a class of heterogeneous multiagent systems. Unlike many existing works, the dimensions of each multiagent dynamic system are considered to be nonidentical in this paper. Firstly, similar properties for different dimensions of multiagent systems are introduced, and some similar parameters among multiagent systems are also proposed. Secondly, a distributed fuzzy adaptive control on the basis of similar parameters is designed for the consensus of leader-follower multiagent systems. Following the graph theory and Lyapunov stability approach, it is concluded that UUB (uniformly ultimately bounded) of all signals in the closed-loop system can be guaranteed, and the consensus tacking error converges to a small compact zero set. Finally, a simulation example with different dimensions is provided to illustrate the effectiveness of the proposed method.

Necessary and sufficient conditions for leader-following consensus of multi-agent systems with random switching topologies

This paper is concerned with leader-following consensus of general linear multi-agent systems with random switching topologies, where the dwell time in each topology consists of a fixed part and random part, and the topology switching signal in random part is modeled by a semi-markov process. First, a semi-Markov switched system with state jumps is constructed, and the stochastic stability of the constructed system is shown to be equivalent to that of the original system. Then a necessary and sufficient condition is established by using a Lyapunov approach in terms of linear matrix inequalities. Finally, the effectiveness of our results is illustrated by a numerical example and a practical example.

Distributed input observer-based finite-time consensus for the leader-following multi-agent systems

This paper mainly studies the problem of robust finite-time consensus for leader-following multi-agent systems in detail-balanced graphs. It is evident that the knowledge of the leader’s input will provide significant assistance to a follower in tracking the leader. For this reason, an observer is constructed to estimate the input of the leader for each follower. Compared with many existing works of leader-following consensus, we do not assume that the input of the leader is bounded, but assume instead that its derivative is bounded. Based on input observer, two discontinuous protocols are proposed firstly that require only the sign information of the differences between a given agent’s state and that of its neighbors. Then, the finite-time consensus and the upper-bound of the settling time are obtained by using matrix theory, Lyapunov control approach, and the algebraic graph theory. Finally, the availability of the theoretical results is demonstrated through an example.

Finite-time Consensus of Leader-following Multi-agent Systems with Multiple Time Delays over Time-varying Topology

This paper studies the finite-time consensus of leader-following multi-agent systems with multiple time delays over time-varying topology. The finite-time consensus protocol based on the agents’ states and the communication topology is designed. By adopting the algebraic graph theory, Lyapunov stability theory and pinning control method, some sufficient conditions for the finite-time consensus are given. It is proved that the system can reach consensus in a finite time both over the connected and disconnected topology. Moreover, the upper bound of the convergence time is given. Several simulations are presented to verify the effectiveness of the adopted method.