Consensus Of Linear Multi-agent Systems Research Articles

Distributed Event-Triggered Control for Prescribed Finite-Time Consensus of Linear Multi-Agent Systems

In this paper, the prescribed finite-time consensus problem of linear multi-agent systems (MASs) is considered based on distributed event-triggered control strategies. It has been presented in the literatures that the prescribed finite time is independent of initial conditions or any other parameters, and can be pre-specified by the designer. Different from the existing prescribed finite-time consensus control rules that are based on continuous communication between agents and their neighbors, the proposed control laws in this paper are built on event-triggered mechanism. Furthermore, because the control schemes involve a time-varying scaling function, the Zeno behavior is hard to be excluded by the traditional approaches. To solve this problem, a dynamical event-triggered controller concerning time-varying variables to agents is proposed. Numerical simulations demonstrate the effectiveness of theoretical results.

Multipartite tracking consensus of linear MASs with arbitrarily projective parameters

This paper proposes distributed bipartite and multipartite tracking consensus for linear multiagent systems (MASs) with arbitrarily nonzero projective parameters in networks, which includes traditional consensus, bipartite consensus and group consensus as its special items. Based on the projective similarity transformation and Riccati inequality, novel types of protocols are designed to achieve bipartite and multipartite consensus exponentially without analysing signed graph as in most current literature on bipartite problem. For obtaining multipartite consensus involving less global information, the distributed protocols with adaptive tuning of the coupling strength are further designed. The theoretical results are illustrated through two numerical simulation examples when linear systems are equilibrium point and periodic states.

Distributed bipartite leader-following consensus of linear multi-agent systems with input time delay based on event-triggered transmission mechanism

This study focuses on the distributed bipartite consensus tracking for linear multi-agent systems with input time delay based upon event-triggered transmission mechanism. Both cooperative interaction and antagonistic interaction between neighbor agents are considered. A novel distributed bipartite control technique with event-triggered mechanism is raised to address this consensus issue. Different from the existing methods, our control technique does not need continuous communication among agents, is capable of addressing the case of input delay, and is applicable for the signed communication topology. Moreover, to avoid continuous monitoring of one’s own state, a self-triggered control strategy is further proposed. And when the system states cannot be measured, the observer-based bipartite control technique with event-triggered mechanism is thus put forward. Furthermore, the results in leader-following consensus are extended to containment control. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, simulation experiments are used to test the practicability of the theoretical analysis.

Consensus of Linear Multiagent Systems With Input-Based Triggering Condition

This paper considers the consensus problem of multiagent systems with the input-based triggering condition. A model-based approach is first given to estimate the relative interagent states between intermittent communications instead of absolute states. A novel consensus protocol consisting of the relative interagent states is proposed for the consensus problem. Besides, compared with some results on the triggering condition consisting of state measurement error, a new triggering condition is constructed based on the control input. Then, the consensus protocol is executed by every agent in a fully distributed way, which has the advantage that the controller design is related to the number of agents instead of using global information. Moreover, the bounds of parameters of the controller and the triggering condition can be obtained by the proposed algorithm simultaneously, which depends on the total number of agents in multiagent networks. The proposed control scheme can ensure that states of all agents can achieve consensus. It is shown that “Zeno behavior” does not appear under the proposed algorithm. Finally, an illustrative example is given to verify the proposed method.

Leader-Following Consensus for Linear Multiagent Systems via Asynchronous Sampled-Data Control

In this article, we consider the sampled-data leader-following consensus problem for a class of general linear multiagent systems over both static directed networks and switching directed networks. A distributed asynchronous sampled-data state feedback control law is proposed. We show by Lyapunov analysis that the problem can be solved by the proposed control law as long as the sampling periods of all agents are smaller than a given threshold, which can be explicitly calculated. An example is given to illustrate the effectiveness of our approach.

Observer-based consensus for linear multi-agent systems with intermittent communication

This paper considers an observer-based consensus problem of linear multi-agent systems with intermittent communication. An observer-based protocol with both continuous and sampled data is proposed. Consensus criteria and protocol design are obtained by matrix theory. Compared with the previous protocol, it is shown that our protocol can solve the consensus problem with lower communication time rate especially when the time interval without communication is sufficiently short. Finally, several examples are provided to show the effectiveness of the derived results.

Asynchronous consensus of linear multi-agent systems with impulses effect

This paper investigates the asynchronous consensus problem of linear multi-agent systems (MASs) with fixed and switching communication topologies. The proposed impulsive control approach does not need the impulse to occur simultaneously for all agents. Some sufficient conditions on asynchronous consensus are presented. The obtained results show that the consensus of MASs can be achieved exponentially by designing some control gain and impulsive sequence when the dynamic of each agent is unstable and the consensus of MASs is robust against certain impulsive permutation when the dynamic of each agent is stable. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

Distributed Model Predictive Control for Tracking Consensus of Linear Multiagent Systems With Additive Disturbances and Time-Varying Communication Delays.

In this article, we investigate a robust distributed model predictive control (DMPC) scheme for tracking the consensus of linear multiagent systems (MASs) subject to additive disturbances and time-varying communication delays. A terminal constraint set is constructed by the Lyapunov-Razumikhin functional, and a corresponding local controller is designed for each agent. Furthermore, the sufficient conditions ensure that the terminal constraint set is provided in the form of linear matrix inequalities (LMIs). The recursive feasibility of the proposed algorithm is guaranteed based on the designed terminal constraint set, terminal cost, and local controller. Moreover, the closed-loop system is shown to be input-to-state stable (ISS). An illustrative example is given to verify the effectiveness of the presented approach.

Event-Triggered Consensus of Linear Multiagent Systems With Time-Varying Communication Delays.

In this paper, the event-triggered consensus problem of linear multiagent systems with time-varying communication delays is addressed. Different from the existing event-triggered consensus results with communication delays, more general nonuniform time-varying communication delays are considered. To avoid the asynchronous phenomenon caused by nonuniform delays, a novel periodic switching controller is developed. Based on this controller, the resulting consensus error system can be modeled as a periodic switching system. Furthermore, the exponential stability of the consensus error system is derived by utilizing the Lyapunov approach and the dwell-time analysis method. Finally, an illustrative example is presented to demonstrate the effectiveness of the developed method.

Leader–Follower Bipartite Consensus of Linear Multiagent Systems Over a Signed Directed Graph

In this brief, leader–follower bipartite consensus of a group of linear multiagent systems is studied over a signed directed graph where all the followers are subjected to mismatched unknown bounded disturbances. To that end, a distributed extended state observer where the disturbances are the extended state and a distributed relative output feedback consensus control law are designed to achieve bipartite consensus. With the suitable design of scaler coupling gain parameters, and feedback gain and observer gain matrices obtained from linear matrix inequalities, it is shown that if the signed directed graph contains a directed spanning tree rooted at the leader node, then the designed consensus protocol simultaneously stabilizes both the bipartite consensus error and observer estimation error with the errors converging to a small bounded set. The simulation results verify the effectiveness of the proposed method.

Leader–Follower Bipartite Consensus of Uncertain Linear Multiagent Systems With External Bounded Disturbances Over Signed Directed Graph

In this letter, leader-follower bipartite consensus of linear multiagent systems (MASs) has been studied over a signed directed graph. The agents in the MAS are subjected to system parametric uncertainties and unknown external bounded disturbances. A distributed observer-based relative output feedback control law is designed for each follower to achieve bipartite consensus. It has been shown that if the underlying directed communication graph is structurally balanced and contains a directed spanning tree rooted at the leader, then the appropriate design of scalar coupling gains, and controller feedback gain and observer gain obtained from solving two suitable linear matrix inequalities (LMIs) stabilizes both the bipartite consensus error and observer estimation error to a bound. The simulation results verify the effectiveness of the proposed methods.

Consensus of Linear Multiagent Systems With Distributed Infinite Transmission Delays: A Low Gain Approach

This paper considers the consensus problem of linear multiagent systems with distributed infinite transmission delays. A novel low gain controller is proposed and it is shown that the proposed controller can solve the consensus problem if the open loop agent dynamics have no exponentially unstable eigenvalues and the communication topology is fixed and contains a spanning tree. One of the distinctive advantages of the proposed controller is that it does not require the knowledge of transmission delays. Our proofs are established based on a stability result on infinite delays, which can be seen as an extension of the commonly used frequency domain method. Our results include those results on distributed bounded delays and constant delays as their special cases. Simulation examples are provided to illustrate the effectiveness of the proposed controller.

Robust consensus for linear multi-agent systems with structured uncertainties

ABSTRACT This paper addresses a robust consensus problem for linear multi-agent systems subject to structured uncertainty and external disturbances under the leaderless framework. A distributed dynamic output-feedback protocol is proposed, which utilises not only relative output information of neighbouring agents but also relative state information of neighbouring controllers. Through model transformations, the robust consensus control problem of multi-agents network is reduced to a set of independent stabilisation problems for single linear subsystems. For robust consensus, it is shown that the analysis and full state-feedback synthesis conditions for such subsystems can be formulated as linear matrix inequality (LMI) optimisation problems. On the other hand, the synthesis condition for dynamic output-feedback protocol is formulated as non-convex bilinear matrix inequality (BMI) optimisation problem. An iterative LMI algorithm is then presented to solve the resulting BMI optimisation problem. An example of multiple mass-spring-damper systems has been used to demonstrate theoretical results.

Finite-Time Consensus for Linear Multiagent Systems via Event-Triggered Strategy Without Continuous Communication

Taking into account multiagent systems with general linear dynamics and directed topologies, the issue of achieving finite-time consensus in a distributed event-triggered fashion is discussed in this paper. A novel model-based triggering function, which depends only on local information, is adopted. To ensure the finite-time convergence of the disagreement vector and the triggering error, a dynamic threshold, which is guaranteed to converge to zero in finite time, is adopted in the proposed triggering function design. By employing a novel distributed event-triggered controller for each agent, finite-time consensus of multiagent systems can be achieved. In the proposed approach, no continuous communication is needed in either controller updates or triggering detection. Furthermore, the triggering number is significantly reduced and the high frequency triggering is restrained. In addition, the feasibility of the proposed approach is guaranteed by the comprehensive theoretical demonstration of the finite-time consensus stability and the analysis of the Zeno behavior. Finally, numerical simulations are carried out to illustrate the effectiveness of our results.

Consensus in Asynchronous Multiagent Systems. II. Method of Joint Spectral Radius

We describe mathematical methods for analyzing the stability, stabilizability and consensus of linear multiagent systems with discrete time. These methods are based on the idea of using the notion of joint/generalized spectral radius of matrix sets to analyze the rate of convergence of matrix products with factors from the sets of matrices with special properties. This is a continuation of the survey by the same authors named “Consensus in Asynchronous Multiagent Systems”; the first part was published in [1].

Lag‐bipartite consensus of linear multiagent systems under saturating input over signed graph

The objective of this study is to investigate lag-bipartite consensus of linear multiagent systems under saturating input with dead-zone constraint where two separate groups of follower agents reach the modulus of the leader state, but of opposite sign with a certain delay. The leader–follower bipartite consensus problem of saturating input with dead-zone is considered with the input signals of the followers being subjected to leader-influenced input additive uncertainties and disturbances. It is shown that if the agents interacting with each-other over the structurally balanced undirected graph having a directed spanning tree rooted at the leader are asymptotically null controllable with bounded controls, then the two proposed control laws – (i) a low-high gain based control law and (ii) a low-gain based variable-structure continuous tracking control law, can achieve lag-bipartite consensus as long as the initial conditions of all the agents remain within a priori bounded set. The numerical simulations establish the effectiveness of the theoretical results.

Observer-Based Bipartite Consensus of Linear Multi-Agent Systems With Measurement Noises

This paper considers the bipartite consensus of linear multi-agent systems with measurement noise, in which both the cooperation and competition relations exist among agents. To attenuate the influence of measurement noises, an important function $\alpha (t)$ is introduced. Then, the output-based controller with both the noisy part and noise-free part is proposed. It is proved that the proposed controller can guarantee the mean-square bipartite consensus with the assumption in which the signed graph is connected and structurally balanced. Meanwhile, the obtained result releases the limitation on time-varying function $\alpha (t)$ . Finally, an example with six agents is utilized to illustrate the effectiveness of the proposed controller.

基于事件触发策略的多智能体系统的最优主-从一致性分析

The leader-follower consensus of linear multi-agent systems was investigated. An event-triggered adaptive dynamic programming method was proposed based on the undirected graph formed by means of the communication topology among agents, and the approximate optimal control was designed with the approximate properties of neural networks. According to the Lyapunov stability theorem, the stability of multi-agent error systems was analyzed, and a sufficient condition for the ultimate boundedness of the error system was found. Finally, numerical simulation results further verify the effectiveness of the theoretical analysis.

$H_{\infty}$ Consensus of Linear Multi-Agent Systems With Semi-Markov Switching Network Topologies and Measurement Noises

This paper investigates the H∞ consensus of linear multi-agent systems with semi-Markov switching network topologies and measurement noises. The information that each agent measures its neighbors's has multiplicative noises. The switching of the network topologies are modeled by a semiMarkov process. Taking the external disturbance into account, H∞ consensus of multi-agent systems with multiplicative noises is achieved under semi-Markov switching network topologies by using semi-Markov jump theory, stochastic theory and algebraic graph theory. Finally, simulation example is provided to illustrate the effectiveness of the theoretical results.

Distributed Event-Triggered Adaptive Control for Consensus of Linear Multi-Agent Systems with External Disturbances.

This paper investigates the consensus problem of linear multi-agent systems subject to external disturbances via distributed event-triggered adaptive control. First, a distributed event-triggered adaptive output feedback control strategy is proposed for each agent. It is shown that under this control strategy, the consensus problem can be solved for any connected undirected communication graph in a fully distributed manner without using any global information. Then a distributed self-triggered adaptive output feedback control strategy is designed with which continuous monitoring of the measurement error is no longer needed. It is further shown that for the proposed event-triggered and self-triggered control strategies, no agent will exhibit Zeno behavior. Finally, the effectiveness of the proposed two control strategies is illustrated on a group of two-mass-spring systems.