Consensus Problem Of Multi-agent Systems Research Articles

A Hybrid Systems Approach to Event-Triggered Consensus of Multiagent Systems With Packet Losses

This article addresses the event-triggered consensus problem of multiagent systems (MASs) with packet losses. The packet losses are not restricted to be identical, and a hybrid systems framework is proposed to handle the considered problem with or without leader in a unified framework. Distributed control law is constructed based on an estimator, whose dynamics are related to whether packet losses occur. A novel hybrid event-triggering mechanism (ETM) is proposed, and a lower bound of the interevent times is enforced to guarantee Zeno-freeness. For stability analysis, a unified hybrid model is constructed to describe the dynamics of MAS with or without leader. In accordance to this model, how to design the hybrid ETM and consensus analysis are formally developed, and the maximum allowable successive packet losses can be explicitly computed. Moreover, even if there exist nonlinearities and disturbances in system dynamics, and the leader has nonzero input, the proposed method can still be applied. Finally, examples are provided to illustrate the superiority of the proposed method.

Regional Consensus Control for Multi-Agent Systems with Actuator Saturation

This paper considers the regional consensus problem for multi-agent systems with actuator saturation. By utilizing the theory of convex set, a novel multiple nonlinear feedback control protocol is presented, which can effectively reduce the conservatism in dealing with saturated nonlinear input. In order to obtain a larger estimate on the domain of consensus, the composite Laplacian quadratics function is constructed to derive sufficient conditions for the consensus of multi-agent systems. In addition, an alternative convex hull representation is employed to further enlarge the above-mentioned domain of consensus. Finally, a numerical simulation case study illustrates the validity as well as the superiority of the proposed approaches.

Fault-tolerant consensus of leader–following multi-agent systems with jointly connected topologies

The fault-tolerant leader–following consensus problem of multi-agent systems (MASs) with jointly connected topologies is considered in this paper. A control law, which is compensated by adaptive estimation of fault parameters using finite interval projection operator, is designed and enables the MAS with jointly connected topologies to achieve consensus in the presence of actuator faults. Furthermore, compared with the most existing works of fault-tolerant consensus with fixed and switching connected topologies, the results with jointly connected topologies are more general in practical systems. Moreover, the effectiveness of the controller for the considered problem is proved based on the Lyapunov stability theory. At the final part, by a numerical simulation, the validity of the results is verified.

Leader-following consensus of linear multi-agent systems via reset control: A time-varying systems approach

In this work, we address the leader-following consensus problem of multi-agent systems by developing a novel reset consensus protocol with a time-varying gain matrix. The reset consensus protocol is distinct from existing results in the sense that it integrates a high-dimensional element with the reset actions triggered by a prescribed reset band. After converting the original closed-loop system to an equivalent linear time-varying system, we develop the time-varying system approach for linear multi-agent system over fixed/switching networks. It further shows that the proposed reset consensus protocol helps to improve the transient performance. Finally, two numerical examples are presented to illustrate the theoretical results and effectiveness.

Secure Consensus of Multiagent Systems via Impulsive Control Subject to Deception Attacks

This brief studies the secure consensus problem of multiagent systems (MASs) via impulsive control under deception attacks. In most existing work, deception attackers are assumed to attack the agents rather than the communication channels, and the neighbors of the attacked agent receive the same tampered information from the attacked agent. The deception attacker is assumed to inject false data into the communication channels, and each neighbor of each agent may receive different tempered information from the same agent. Attacking the communication channels leads to an inconsistent dimension of the matrices in the controller, which brings difficulties in analyzing the convergence of MASs. To overcome the challenge, the extended diagonal matrix is proposed to analyze the effect of the deception attacks on the convergence of MASs, and sufficient conditions for the secure consensus are derived. The consensus error bound converges to a bounded area dependent on the total attack energy. Finally, a simulation example is given to verify the effectiveness of the results.

Consensus of double integrator multiagent systems under nonuniform sampling and changing topology

<abstract><p>This article considers a consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. In the considered problem, the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in an arbitrarily selected region. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are undirected and have a spanning tree. Also, explicit bounds for controller parameters are given. A sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of undirected topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.</p></abstract>

Scaled consensus problems of multi agent systems via impulsive protocols

This paper studies scaled consensus problems of multi-agent systems under fixed and switched topologies. Firstly, the scaled consensus protocols are designed for solving consensus problems of multi-agent systems under fixed topologies. Secondly, the scaled consensus problems of multi-agent systems under switching topologies are considered. Thirdly, scaled consensus of multi-agent systems with external perturbations is investigated via impulsive mechanism. Using matrix theory, graph theory and Lyapunov algorithm, we can show that under appropriate conditions the scaled consensus problems can be solved. Moreover, our results show that the boundedness of the sampling period depending on scalar scales and degree of networks has strong impact for achieving scaled consensus of the systems. Some numerical examples are provided to illustrate the effectiveness of the theoretical results.

Bipartite Consensus for Second-Order Multiagent Systems With Matrix-Weighted Signed Network

The second-order scalar-weighted consensus problem of multiagent systems has been well explored. However, in some practical antagonistic interaction networks, the interdependencies of multidimensional states of the agents must be described by matrix coupling. In order to highlight the influence of matrix coupling in the antagonistic interaction network, we investigate the second-order matrix-weighted bipartite consensus problem on undirected structurally balanced signed networks. Under the proposed bipartite consensus protocol, an algebraic condition is obtained for achieving second-order bipartite consensus via utilizing matrix-valued Gauge transformation and stability theory. Then, using the obtained criteria, a more direct algebraic graph condition is given for reaching bipartite consensus. Besides, because of the existence of negative (positive) semidefinite connections, the matrix-weighted network may have clustering phenomena, which means that matrix weights play a critical role in achieving consensus. An algebraic graph condition for admitting cluster bipartite consensus is provided. By designing matrix weights in practical scenarios, the required number of clusters can be obtained. Finally, the theoretical results are verified by five simulation examples.

Second-Order Consensus for Multi-Agent Systems With Various Intelligent Levels via Intermittent Sampled-Data Control

This brief is concerned with the second-order consensus problem of multi-agent systems (MASs) over directed communication topologies. Due to engineering applications, agents in the network may have nonidentical intelligent degrees in practical scenarios. A novel intermittent sampled-data control protocol with different intelligent levels is proposed. Necessary and sufficient conditions are derived to guarantee the desired consensus under the protocol. Nevertheless, since the velocity states of real agents may not be measured, a novel protocol only utilizing past sampled position data with distinct intelligent levels is presented, under which the conditions of realizing consensus can be attained via similar analysis. Finally, the asymptotic consensus of MASs can be verified by some numerical simulations. The states of agents with the same intelligent level can be validated to converge to the common value as well.

Finite-time fault-tolerant consensus for leader-following multi-agent systems with semi-Markov switching topologies

This paper investigates the finite-time leader-following consensus problem for multi-agent systems with switching topologies. First of all, consider the characteristic of failures, a failure distribution model which is more in line with the actual situation is established, and a semi-Markov chain is used to describe the topology switching of the multi-agent system, in which the transfer rate is time-varying. Secondly, based on the past state information, a topology-dependent consensus protocol is established, then the fault-tolerant consensus problem of leader-following multi-agent is transformed into the issue of system stability, according to the mode-dependent Lyapunov function and the finite time stochastic theorem, the sufficient conditions for the stability of the closed-loop system and the constraints of average residence time are obtained. In addition, an initial-state based H ∞ performance index is proposed to reduce the influence of zero initial conditions on the system. Finally, a numerical example is provided to show the effectiveness of the proposed method.

Consensus of multi-agent systems with heterogeneous unknown nonlinear switching dynamics: A dwelling time approach

This paper investigates the consensus problem of multi-agent systems with unknown heterogeneous nonlinear switching dynamics. First, an extended model-free adaptive controller is proposed to mitigate the effect of unknown switching dynamics. Then, an average dwelling time is provided to guarantee the stability of the multi-agent system and ensure consensus with both directed and undirected communication topologies. Finally, numerical examples are provided to show the impact of switching dynamics on the standard model-free adaptive controller. Then, the average dwelling time is calculated and added to ensure consensus in the presence of switching dynamics.

Event-triggered consensus control of multi-agent systems under denial-of-service jamming attacks

ABSTRACT This work focuses on a consensus problem of multi-agent systems (MASs) under an event-triggered control (ETC) subject to denial-of-service (DoS) jamming attacks. To reduce the communication cost, a novel event-triggering mechanism (ETM) is applied to determine whether the sampled signal should be transmitted or not. Unlike the periodic DoS jamming attacks strategy, the occurrence of DoS jamming attacks is irregular in this article, where attack attributes such as attack frequency and attack ratio are uncertain. Moreover, compared with some existing related results considering fixed undirected topologies, the communication topologies may change due to DoS jamming attacks in this work. In view of this, based on the piecewise Lyapunov function, sufficient conditions are derived to guarantee that the consensus problem of the MASs can be solved. Finally, the effectiveness and correctness of the theoretical results are verified by a numerical example.

Non-oscillating quantized average consensus over dynamic directed topologies

In this paper we study the distributed average consensus problem in multi-agent systems with dynamically-changing directed communication links that are subject to quantized information flow. We present and analyze a distributed averaging algorithm which operates exclusively with quantized values (i.e., the information stored, processed and exchanged between neighboring agents is subject to deterministic uniform quantization) and relies on event-driven updates (e.g., to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage). We characterize the properties of the proposed distributed algorithm over dynamic directed communication topologies subject to some connectivity conditions and we show that its execution allows each agent to reach, in finite time, a fixed state that is equal (within one quantization level) to the average of the initial states. The main idea of the proposed algorithm is that each agent (i) models its initial state as two quantized fractions which have numerators equal to the agent’s initial state and denominators equal to one, and (ii) transmits one fraction randomly while it keeps the other stored. Then, every time an agent receives one or more fractions, it averages their numerators with the numerator of the fraction it stored, and then transmits them to randomly selected out-neighbors. Finally, we provide examples to illustrate the operation, performance, and potential advantages of the proposed algorithm. We compare against various quantized average consensus algorithms and show that our algorithm’s convergence speed is among the fastest in the current literature.

High-order leader following consensus for multi-agent systems via intermittent sampled position data control

This paper considers the leader-following consensus problem of multi-agent systems, where agents are described by high-order dynamics under a directed graph. An algorithm depending on a distributed control protocol with time delay and intermittent sampled position information only is proposed. The protocol makes use of past position data. We show that such protocol cannot work if not enough past position information is taken into account. For nth-order system, we take n past position data. To achieve consensus, a necessary and sufficient condition depending on communication width, time delay, and sampling period is derived. Furthermore, the control protocol can be extended to leaderless consensus problem. Numerical simulations illustrate that appropriately chosen control gains can verify the theoretical analysis.

Sampled-Data Dynamic Output Feedback Consensus Control of Multi-Agent Systems

This paper investigates the consensus problem of multi-agent systems (MAS) with sampled-data dynamic output feedback (DOF) control. A distributed DOF control law is designed by utilizing sampled relative output information between neighboring agents, and the sampling period can be asynchronous. For the purpose of consensus analysis and appropriately choosing sampling period, a closed-loop system model with hybrid dynamics is constructed, which incorporates flow/jump dynamics and the sampling period. Based on this model, Lyapunov-based analysis is presented and stability conditions are formally developed. Compared with the existing works, observer design is not required and only sampled relative output information is used, and moreover, the maximum allowable sampling period (MASP) can be explicitly computed. Finally, illustrative examples are provided to demonstrate effectiveness of the proposed DOF control method.

Resilient Consensus for Multi-Agent Systems Under Adversarial Spreading Processes

This paper addresses novel consensus problems for multi-agent systems operating in an unreliable environment where adversaries are spreading. The dynamics of the adversarial spreading processes follows the susceptible-infected-recovered (SIR) model, where the infection induces faulty behaviors in the agents and affects their state values. Such a problem setting serves as a model of opinion dynamics in social networks where consensus is to be formed at the time of pandemic and infected individuals may deviate from their true opinions. To ensure resilient consensus among the noninfectious agents, the difficulty is that the number of infectious agents changes over time. We assume that a local policy maker announces the local level of infection in real-time, which can be adopted by the agent for its preventative measures. It is demonstrated that this problem can be formulated as resilient consensus in the presence of the socalled mobile malicious models, where the mean subsequence reduced (MSR) algorithms are known to be effective. We characterize sufficient conditions on the network structures for different policies regarding the announced infection levels and the strength of the epidemic. Numerical simulations are carried out for random graphs to verify the effectiveness of our approach.

Robust secure consensus of multiagent systems with DoS attacks

The secure consensus problem of multiagent systems with fixed topology and external disturbances is investigated in this paper. Along with external disturbances, the studied multiagent system is also subjected to denial-of-service (DoS) attacks. First, some graph-based Lyapunov functions are presented for the robust consensus analysis. Second, the duration and attack frequency are introduced to quantitatively analyze the DoS attacks’ effects on the consensus. Third, the gain of the controller is acquired by solving an algebraic Riccati equation (ARE), which can always be guaranteed compared with solving linear matrix inequalities (LMIs). Finally, a numerical simulation of a microgrid test system is provided to demonstrate the effectiveness of the proposed strategy.

Optimal Consensus via OCPI Regulation for Unknown Pure-Feedback Agents With Disturbances and State Delays

In this article, we present a novel methodology to address the optimal output consensus problem for multiagent systems. We propose a distributed variable transformation that recasts the aforementioned problem into a simpler regulation problem of the new variables. The transformation requires only relative output measurements and is independent of any underlying agent dynamics and therefore applicable to a general class of systems. Classical control techniques, which take into account the agent dynamics and only need the relative outputs to be shared between neighbors, can then be employed to regulate the new variables. We utilize the methodology to address, for the first time, the problem of optimal output consensus for unknown pure-feedback agents with disturbances and state delays. Simulation studies on a group of continuous stirred tank reactors illustrate the validity of the theoretical analysis.

Consensus of linear multi-agent systems by distributed event-triggered strategy with designable minimum inter-event time

This paper investigates the consensus problem of multi-agent systems under the event-triggered control with designable minimum inter-event time, in which each agent has an identical linear dynamic model. The goal is to devise a novel control method which can not only reduce actuator consumption but also guarantee the state consensus of the controlled systems. Two event-triggered mechanisms are considered, namely, the static event-triggered mechanism and the dynamic event-triggered mechanism. To this end, a novel distributed static event-triggered control algorithm is presented at first. Then the distributed dynamic event-triggered control algorithm is developed. The major superiority of the presented distributed static and dynamic event-triggered control algorithms is that the controller of each agent is only triggered at its own event time, which effectively reduces the update frequency of the controller in practice. Further, the minimum inter-event time is adjustable by the parameter of the parametric Lyapunov equation, which makes it easier to find a trade-off between the inter-event times and the control performance of the controlled system. Subsequently, it is proved that the consensus of the multi-agent systems is reached asymptotically and non-occurrence of the Zeno phenomenon is proved. The superiority of the designed algorithms is testified by the simulation.

Positive Consensus of Directed Multiagent Systems

This technical note investigates the positive consensus problem of multiagent systems with directed communication topologies, where all the agents have identical continuous-time positive linear dynamics. Existing works of such a problem mainly focus on the case, where networked communication topologies are of either undirected and incomplete graphs, or strongly connected directed graphs. In contrast to them, we study this problem in which the communication topologies of the multiagent system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Based on the existing results in spectral graph theory and positive linear systems theory, several necessary, and sufficient conditions on positive consensus of the directed multiagent system are derived through using linear matrix inequality techniques. A primal-dual iterative algorithm is developed for the computation of solutions. Finally, several numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results.