Consensus Problem Of Multi-agent Systems Research Articles

Consensus of Multiagent Systems with Packet Losses and Communication Delays Using a Novel Control Protocol

This paper studies the consensus problem of multiagent system with packet losses and communication delays under directed communication channels. Different from previous research results, a novel control protocol is proposed depending only on periodic sampling and transmitting data in order to be convenient for practical implementation. Due to the randomicity of transmission delays and packet losses, each agent updates its input value asynchronously at discrete time instants with synchronized time stamped information and evolves in continuous time. Consensus conditions for multiagent system consists of three typical dynamics including single integrator, double integrator, and high-order integrator that are all discussed in this paper. It is proved that, for single integrator agents and double integrator systems with only communication delays, consensusability can be ensured through stochastic matrix theory if the designed communication topology contains a directed spanning tree. While, for double integrator agents and high-order integrator agents with packet losses and communication delays, the interval system theory is introduced to prove the consensus of multiagent system under the condition that the designed communication topology is a directed spanning tree. Finally, simulations are carried out to validate the effectiveness of the proposed solutions.

Leaderless and leader‐following consensus for heterogeneous multi‐agent systems with random link failures

This study investigates the heterogeneous consensus problem for multi-agent systems with random link failures between each agent. The discrete-time heterogeneous multi-agent systems are described by first-order and second-order dynamics, and the communication network is assumed to be directed with fixed topology. Since each link between the agents is subject to failure with a certain probability, the control protocol is designed considering the random link failures. The random link failures are presented by a Bernoulli probability sequence, that is, the control protocol for failure occurrence is designed using the one step previous data that is sent by adjacency neighbouring agents. The control protocol for heterogeneous multi-agent systems is designed for first-order dynamics and second-order dynamics using the Lyapunov method. The mean square stability is shown for leaderless and leader-following heterogeneous multi-agent systems in terms of a set of linear matrix inequalities, and some simulation results are provided to verify the effectiveness of the proposed methods.

Suboptimal Event-Triggered Consensus of Multiagent Systems

In this paper the suboptimal event-triggered consensus problem of Multiagent systems is investigated. Using the combinational measurement approach, each agent only updates its control input at its own event time instants. Thus the total number of events and the amount of controller updates can be significantly reduced in practice. Then, based on the observation of increasing the consensus rate and reducing the number of triggering events, we have proposed the time-average cost of the agent system and developed a suboptimal approach to determine the triggering condition. The effectiveness of the proposed strategy is illustrated by numerical examples.

Consensus Problems in Multiagent Systems with Event-Triggered Dynamic Quantizers

Considering the constrained communication data rate and compute capability that commonly exists in multiagent systems, this paper modifies a current consensus strategy by introducing a kind of dynamic quantizer in both state feedback and control input and updates dynamic quantizers by employing event-triggered strategies, thus forming a new quantitative consensus strategy. The numerical simulation example is built for state quantization and the results show the consistency with expectation.

Distributed Event-Triggered Control of Multiagent Systems with General Linear Dynamics

This paper discusses the event-triggered consensus problem of multiagent systems. To investigate distributed event-triggering strategies applied to general linear dynamics, we employ a dynamic controller to convert the general linear dynamic to the single-integrator model by a change of variable. The consensus value of these new states is a constant so that the distributed event-triggering scheme is obtained under periodic event detections, in which agents with general linear dynamics require knowledge only of the relative states with their neighbors. Further, an event-triggered observer is proposed to address the case that only relative output information is available. Hence, the consensus of both the state-based and observer-based cases is achieved by the distributed event-triggered dynamic controller. Finally, numerical simulations are provided to demonstrate the effectiveness of theoretical results.

Consensus of Multi-Agent Systems by Distributed Event-Triggered Control

In this paper, the consensus problem for multi-agent systems with general linear dynamics is studied. A novel event-triggered control scheme with some desirable features, including distributed, asynchronous and independent, is proposed. It is shown that consensus of the controlled multi-agent system can be reached asymptotically. The feasibility of the event-triggered strategy is further verified by the exclusion of both singular triggering and Zeno behaviors. The proposed control scheme is applied to solve a spacecraft formation flying problem. Simulations illustrate the effectiveness of the control scheme.

Consensus of Multiagent Systems with Directed Topology and Communication Time Delay Bases on the Laplace Transform

This paper investigates the consensus problem of multiagent systems with directed topologies. Different from the literatures, a new method, the Laplace transform, to study the consensus of multiagent systems with directed topology and communication time delay is proposed. The accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. It is proved that all the agents could aggregate and eventually form a cohesive cluster in finite time under certain conditions, and the consensus center is only determined by the initial states and the communication configuration among the agents. Finally, simulations are given to illustrate the theoretical results.

Robust Control, Optimization, and Applications to Markovian Jumping Systems

Robust Control, Optimization, and Applications to Markovian Jumping Systems

An Event-Triggered Consensus Control with Sampled-Data Mechanism for Multi-agent Systems

In this paper, an event-triggered control strategy with sampled-data mechanism is proposed to address the consensus problem for multi-agent system. The states of each agent are obtained periodically instead of continuous detection by using sampling technology. Rather than traditional Lyapunov technique, the system stability is analyzed by introducing a disagreement vector whose convergence is proved by contraction mapping, and a necessary condition about the upper bound of sampling period is derived under which systems could achieve consensus. Simulations results are presented to show the effectiveness of proposed event-triggered control strategy with sampled data mechanism compared to the basic one.

Output Feedback Control for Couple-Group Consensus of Multiagent Systems

This paper deals with the couple-group consensus problem for multiagent systems via output feedback control. Both continuous- and discrete-time cases are considered. The consensus problems are converted into the stability problem of the error systems by the system transformation. We obtain two necessary and sufficient conditions of couple-group consensus in different forms for each case. Two different algorithms are used to design the control gains for continuous- and discrete-time case, respectively. Finally, simulation examples are given to show the effectiveness of the proposed results.

Consensus for Multiagent Systems with Nonlinear Dynamics and Time Delays Using a Two-Hop Relay Adaptive Method

This paper investigates the consensus problem for multiagent systems with nonlinear dynamics and time delays. A distributed adaptive consensus protocol is proposed in which the time delays are explicitly included in the adaptive algorithm. It is shown that the resultant closed loop system involves doubly larger time delays, making the stability analysis nontrivial. Stability condition on maximum tolerable time delay is established and controlled by the proposed two-hop adaptive algorithm. The explicit expression of the delay margin is derived and analyzed in the frequency domain. Both the agent state errors and the estimation parameter errors converge to zero. A simulation example is illustrated to verify the theory results.

Consensus of high-order multi-agent systems with large input and communication delays

We study in this paper the consensus problem for multi-agent systems with agents characterized by high-order linear systems with time delays in both the communication network and inputs. Provided that the open-loop dynamics of the agents is not exponentially unstable, but may be polynomially unstable, and the communication topology contains a directed spanning tree, a truncated predictor feedback approach is established to solve the consensus problem. It is shown that, if the delays are constant and exactly known, the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays. If it is further assumed that the open-loop dynamics of the agents only contains zero eigenvalues, the delays are allowed to be time-varying and unknown. Numerical examples are worked out to illustrate the effectiveness of the proposed approaches.

Consensus for nonlinear multi-agent systems with sampled data

This paper deals with the consensus problems of multi-agent systems with nonlinear dynamics and sampled data information. The control input of each agent is based on the information of its neighbors at discrete sampling instants rather than the whole continuous process. An input delay approach is utilized to transform the sampling data into the time-varying delayed data. A novel time-dependent Lyapunov functional consisting of the continuous term and the discontinuous term is proposed. Tools like matrix theory, algebraic graph theory, relaxed matrix approach, and convex analysis technique are utilized to derive the sufficient conditions. The estimated upper bound of the sampling interval can be obtained by the proposed conditions. Then, the necessary and sufficient conditions for consensus in systems with linear dynamics are presented. It is shown that the consensus conditions depend on the parameters of the sampling interval, spectra of the Laplacian matrix, and coupling strength. The effectiveness of the proposed design method is demonstrated by the simulation examples.

$M$-Matrix Strategies for Pinning-Controlled Leader-Following Consensus in Multiagent Systems With Nonlinear Dynamics

This paper considers the leader-following consensus problem for multiagent systems with inherent nonlinear dynamics. Some M-matrix strategies are developed to address several challenging issues in the pinning control of multiagent systems by using algebraic graph theory and the properties of nonnegative matrices. It is shown that second-order leader-following consensus in a nonlinear multiagent system can be reached if the virtual leader has a directed path to every follower and a derived quantity is greater than a positive threshold. In particular, this paper analytically proves that leader-following consensus may be easier to be achieved by pinning more agents or increasing the pinning feedback gains. A selective pinning scheme is then proposed for nonlinear multiagent systems with directed network topologies. Numerical results are given to verify the theoretical analysis.

Consensus of linear multi-agent systems based on full-order observer

This paper considers distributed consensus problem of multi-agent systems consisting of general linear dynamics with a time-invariant communication topology. A distributed full-order observer type consensus protocol based on relative output measurements of neighbor agents is proposed. It is found that the consensus problem of linear multi-agent systems with a directed communication topology having a spanning tree can be solved if and only if all subsystems are asymptotically stable. Some necessary and sufficient conditions are obtained for ensuring consensus in multi-agent systems. The design technique is based on algebraic graph theory, Riccati inequality and linear control theory. Finally, simulation example is given to illustrate the effectiveness of the theoretical results.

Consensus of Discrete-Time Second-Order Multi-Agent Systems with Partial Information Transmission

This paper investigates the consensus problem of multi-agent systems with partial information transmission under an undirected topology. A distributed consensus protocol is proposed with local velocity feedback and the position information from neighbors. The consensus problem is converted to the stabilization problem by transforming the original systems into a reduced order state system. Then, by using graph theory and Jurys stability test, a sufficient and necessary condition for consensus of multi-agent systems is derived. An example is given to illustrate the effectiveness of the presented results.

Finite-time Consensus for Multi-agent Systems via Nonlinear Control Protocols

This paper investigates the finite-time consensus problem of multi-agent systems with single and double integrator dynamics, respectively. Some novel nonlinear protocols are constructed for first-order and second-order leader-follower multi-agent systems, respectively. Based on the finite-time control technique, the graph theory and Lyapunov direct method, some theoretical results are proposed to ensure that the states of all the follower agents can converge to its leader agent's state in finite time. Finally, some simulation results are presented to illustrate the effectiveness of our theoretical results.

Consensus control of multi-agent systems with missing data in actuators and Markovian communication failure

This article investigates the consensus problem of multi-agent systems (MASs) with imperfect communication both in channels and in actuators. The data transmission among agents may fail due to limited communication capacity, and the actuators may fail to receive information owing to noisy environment. We use a Markov chain approach to characterise the occurrence of the two types missing data in a unified framework. A sufficient consensus condition is first obtained in terms of linear matrix inequalities. Then, based on this condition, a novel controller design method is further developed such that the MAS with imperfect communication reaches mean-square consensus. It is shown that the consensus problem for MASs with switching topology can be regarded as a special case of the problem considered in this article, and the related theoretical results are presented as well. Numerical examples are provided to illustrate the effectiveness of the proposed approach.

H ∞ Dynamic Output Feedback Consensus Control for Discrete-Time Multi-Agent Systems with Switching Topology

In this paper, we consider distributed H∞ consensus problem for multi-agent systems with discrete-time high-dimensional linear coupling dynamics subjected to external disturbances. The interaction topology among the agents is assumed to be switching and undirected. To achieve consensus, a neighbor-based dynamic output feedback protocol is proposed for each agent. By using Schur orthogonal transformation, the considered multi-agent H∞ consensus control problem is converted into H∞ control problem of a discrete-time switching subsystem. Based on graph theory and common Lyapunov function method, a sufficient condition in terms of linear matrix inequalities is established to solve H∞ consensus problem of the considered multi-agent systems. Moreover, the feedback gain matrix can be obtained from the feasible solution to the linear matrix inequalities. Finally, a simulation example is given to illustrate our established theoretical result.

Continuous-time and sampled-data-based average consensus with logarithmic quantizers

This paper considers the average consensus problem for multi-agent systems with continuous-time first-order dynamics. Logarithmic quantization is considered in the communication channels, and continuous-time and sampled-data-based protocols are proposed. For the continuous-time protocol, we give an explicit upper bound of the consensus error in terms of the initial states, the quantization density and the parameters of the network graph. It is shown that in contrast with the case with uniform quantization, the consensus error in the logarithmic quantization case is always uniformly bounded, independent of the quantization density, and the β-asymptotic average consensus is ensured under the proposed protocol, i.e. the asymptotic consensus error converges to zero as the sector bound β of the logarithmic quantizer approaches zero. For the sampled-data-based protocol, we give sufficient conditions on the sampling interval to ensure the β-asymptotic average consensus. Numerical examples are given to demonstrate the effectiveness of the protocols.