Consensus Problem Of Multi-agent Systems Research Articles

Consensus of MASs With Input and Communication Delays by Predictor-Based Protocol.

In this article, the consensus problem of multiagent systems (MASs) affected by input and communication delays is investigated. A predictor-based state feedback protocol is used to reach the consensus of linear MASs by delay compensation. In order to analyze the maximum delay under the predictor-based protocol, the overall MASs are equivalent to the feedback interconnection system, including a linear time-invariant system and a time-delay operator, in view of the characteristic of the Laplacian matrix. Then, the maximum delay corresponding to the predictor-based protocol is evaluated by using the small gain theorem (SGT). Finally, two numerical examples are given to verify the effectiveness of the obtained consensus condition.

Distributed optimal consensus of multi-agent systems: A randomized parallel approach

In this paper, a randomized parallel algorithm is proposed to solve the distributed optimal consensus problem of multi-agent systems. Involving both the transient response and the final consensus state, the problem is described as a constrained non-separable optimization problem. Inspired by the randomized Jacobi proximal alternating direction method of multipliers, the proposed algorithm makes it possible for only a fraction of agents to solve their private subproblems in parallel at each iteration, which greatly saves computational resources and enhances running efficiency. The convergence analysis of the algorithm gives fully distributed convergence conditions. A trade-off between the convergence speed and resource savings is then obtained, where the convergence rate is estimated to be at least O1t. Furthermore, the algorithm can be accelerated to enjoy a convergence rate of O1t2 by adaptively adjusting the auxiliary parameters properly. Numerical simulations demonstrate the effectiveness of the theoretical results.

Event-triggered impulsive control for multi-agent systems with actuation delay and continuous/periodic sampling

The paper explores the event-triggered impulsive control for consensus problems in multi-agent systems (MASs) with actuation delay. Two types of event-triggered delayed impulsive control (ETDIC) schemes, predicated on continuous and periodic sampling, are proposed respectively. Several exponential consensus criteria for MASs are derived by using Lyapunov method. A correlation function is established between event parameters, actuation delay, and control strength to promote the co-design of the event-triggering policy and impulsive controller. It is shown that under the proposed ETDIC schemes, the interaction between neighboring agents is executed discontinuously, the upper bound information on the interval of two consecutive event impulses is not directly required. This results in reduced resource consumption of communication and control actions, as well as enhancing flexibility of the generated sequences of event impulses. Moreover, two representative examples with simulation results are given to illustrate the theoretical results.

Adaptive Self-Triggered Control for Multi-Agent Systems with Actuator Failures and Time-Varying State Constraints

This work focuses on the consensus problem for multi-agent systems (MASs) with actuator failures and time-varying state constraints, and presents a fixed-time self-triggered consensus control protocol. The use of time-varying asymmetrical barrier Lyapunov functions (BLF) avoids the violation of time-varying state constraints in MASs, ensuring stability and safety. Meanwhile, the system’s performance is further enhanced by leveraging the proposed adaptive neural networks (NNs) control method to mitigate the effects of actuator failures and nonlinear disturbances. Moreover, a self-triggered mechanism based on a fixed-time strategy is proposed to reach rapid convergence and conserve bandwidth resources in MASs. The mechanism achieves consensus within a predefined fixed time, irrespective of the system’s initial states, while conserving communication resources. Finally, the proposed method’s effectiveness is confirmed through two simulation examples, encompassing diverse actuator failure scenarios.

Consensus of nonlinear multiagent systems with mode‐dependent delay via stochastic sampled data under Markovian switching topologies

AbstractIn this article, we investigate the mean‐square consensus problem of multiagent systems with one leader and multiple followers. In consideration of the uncertain disturbance from external environment or internal change of system, the interaction topology and time‐varying delay switch randomly which are regulated by a time‐homogeneous Markovian chain. The distributed control protocol is designed based on the stochastic sampling information from its neighbors and the leader. Using stochastic Lyapunov theory and linear matrix inequality (LMI) approach, the sufficient condition is concluded to guarantee the mean‐square consensus. For the undirected topology case, a low‐dimensional LMI‐based consensus criterion is further derived based on the matrix diagonalization method. Finally, a numerical simulation is provided to demonstrate the reasonability of the theoretical results.

Distributed Model-Predictive Control Using Exponentially Weighted Laguerre Functions and Periodic Time Triggering for Dynamic Consensus of Linear Multiagent Systems

Model Predictive control (MPC) is becoming increasingly popular in addressing the consensus problem of multi-agent systems (MAS) due to its ability to manage constraints in a multivariable control framework and to perform online optimization. However, in order to achieve the desired closed loop performance, longer prediction and control horizons are essential for conventional MPC. This increases the computational complexity and causes the numerical instability of the optimization problem. This concern is addressed in this article by introducing an exponential-data-weighted Laguerre-based control design that minimises computational burden, improves numerical conditioning, and provides a specified degree of closed loop stability of the MAS. The proposed design which incorporates an embedded integrator model, rejects constant disturbances, avoiding the need for a separate disturbance model. Furthermore, periodic time-triggered control (PTTC) is incorporated with the consensus algorithm, enabling a relaxation in the over-usage of resources. An explicit formula for computing the upper bound of triggering interval is also derived. The proposed algorithm outperforms current methods in terms of numerical conditioning, stability margins, and rejection of deterministic disturbances. Validation of the proposed strategy is performed through simulation of dynamic consensus on a cluster of grounded vehicles.

Application-Oriented Homogeneous Control Protocol Design for Multi-Agent Systems Under Input Constraints

An application-oriented homogeneous control protocol is proposed to solve the consensus problem of multi-agent system (MAS) modeled by higher-order integrator. This nonlinear control protocol is able to homogenize the linear system with a special degree called homogeneity degree. This homogeneous control protocol ensures asymptotically/finite-time stable multi-agent systems (MASs) (or fixed-time attractive to compact sets containing the origin) by selecting different homogeneity degrees. If the linear control protocol for each agent is provided, the proposed nonlinear homogeneous control protocol in this paper can be easily implemented without requiring any tuning of the control parameters. A bounded homogeneous control protocol, which is a special form of the controller proposed, is also introduced to address the same problem with input constraints. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed approach.

Transmission-Constrained Consensus of Multiagent Networks

This paper studies the consensus problem for multiagent systems with transmission constraints. A novel model of multiagent systems is proposed where the information transmissions between agents are disturbed by irregular distortions or interferences (named transmission constraint functions), and this model is universal which can be applied in many cases, such as interval consensus and discarded consensus. In the transmission-constrained consensus problem, we obtain the necessary and sufficient condition that agents can converge to state consensus. Furthermore, a more general case is studied in which the system reaches an equilibrium. Based on some techniques of stability theory, the existence, uniqueness and stability of the system equilibrium point can be proven, which means the system can reach an asymptotically stable equilibrium. Moreover, the state values of the equilibrium are only decided by the network structure and transmission constraint functions, but not the agents' initial states. Finally, numerical simulations are presented to illustrate the proposed theorems and corollaries.

Distributed fixed-time and prescribed-time average consensus for multi-agent systems with energy constraints

This paper is devoted to the investigation of the fixed-time and prescribed-time average consensus problem for multi-agent systems (MASs) with energy constraints. For the purpose of the fixed-time and prescribed-time average consensus of MASs, two control algorithms are firstly developed in this paper on the basis of the fixed-time technique and the prescribed-time technique. Then, the time integral of the quadratic function is constructed to calculate the energy consumption by the error between each agent and the reference state. And the sufficient conditions for the stability of the Lyapunov function are provided by designing the parameters and the gain matrix. Ultimately, the theoretical results are effectively and correctly verified by utilizing simulations.

Hybrid Event-Triggered Bipartite Consensus Control of Multiagent Systems and Application to Satellite Formation

This work studies event-triggered bipartite consensus problem of multi-agent systems (MAS) with structurally balanced signed graph. A hybrid system approach is proposed to deal with the leaderless and leader-following bipartite consensus problems in a unified framework, and a novel hybrid event-triggering mechanism (ETM) is proposed to reduce the usage of communication resources. By appropriately defining closed-loop states, a unified hybrid model is constructed for both leaderless and leader-following MAS. Then, stability analysis and ETM design results are given under hybrid systems framework. It is worth noting that the designed hybrid ETM is in decentralized form rather than distributed form. Moreover, the lower bound of triggering intervals can be pre-selected, i.e., Zeno-freeness is guaranteed, that is important for control implementation. The proposed method is applied to satellite formation system in simulation results to show the effectiveness. <i>Note to Practitioners</i>&#x2014;This paper considers bipartite consensus control problem of MAS, which can be applied to some practical systems, e.g., bidirectional formation of unmanned air vehicles, since the control objective in these applications can be transformed into bipartite consensus control problem of MAS. Compared with the existing results, a hybrid system approach is proposed for consensus analysis of MAS with or without leader, and a novel event-triggering mechanism is proposed, which is more easier to be implemented, so, the proposed approach is more friendly for control engineers. The obtained results are applied to satellite formation control problem and the effectiveness is verified, and it is expected that the proposed approach can be extended to MAS with more realistic network-induced constraints and applied to more practical engineering systems.

Lag Group Consensus of High-Order Multiagent Systems in Directed Network Settings

This article studies lag group consensus problems of multiagent systems with directed information transformations. Agents in the network are divided into finite groups, and modeled by high-order systems. Distributed consensus protocols with constant lags are presented to realize the lag group consensus: the states of the agents in a group approach to a consensus value asymptotically, while there exist given ratios between the final values of different groups. Necessary and sufficient criteria for the lag group consensus are obtained by the Laplace transformation. Finally, theoretical results are proved to be effective by several simulation results.

Average Consensus Problem in Multi-Agent System in an Environment with Obstacles

Multi-agent systems (MASs) are composed of multiple autonomous agents, and the overall behavior of an MAS is determined by the local interactions between its agents. In recent years, research on MASs aimed at their application in real-world environments has garnered considerable interest. In particular, consensus control in environments with constrained communication range of agents and obstacles is being extensively investigated. In this study, the consensus problem of MASs is examined by considering the effects of obstacles. In particular, an obstacle avoidance algorithm is developed as a control method for real-world autonomous machines such as autonomous mobile robots. In conventional control methods, obstacles are provided as coordinate points; however, in this study, they are introduced as variously shaped polygons. Furthermore, the graph topology is dynamic, which enables more realistic situations. Finally, a simulation study is performed, and the effectiveness of the developed algorithm for applying to the MAS consensus problem is demonstrated.

Formula omitted] Consensus of multi-agent systems under hybrid cyber attacks via a sampled-data-based dynamic event-triggered resilient consensus protocol

This paper studies the H∞ consensus problem of multi-agent systems (MASs) under external disturbances and hybrid cyber attacks. First, to save limited network resources, a sampled-data-based dynamic event-triggered mechanism is proposed for MASs under hybrid cyber attacks. Different from the existing dynamic event-triggered mechanisms, the negative influences of deception attacks and denial-of-service attacks are considered in the proposed dynamic triggering function. The communication frequencies between agents are reduced by the proposed event-triggered mechanism. Then, based on the proposed sampled-data-based dynamic event-triggered mechanism, a corresponding resilient consensus protocol is designed to ensure that MASs with external disturbances and hybrid cyber attacks can achieve consensus with a weighted H∞ performance. Finally, simulation examples are conducted to verify the effectiveness of the proposed methods.

Quasi-Sure Consensus of Multiagent Systems: G-Noise Communication Protocols Under DoS Attacks

This paper addresses the quasi sure consensus problem for multi-agent systems (MASs) in the context of Denial-of-Service (DoS) attacks. Instead of adopting the conventional noise-based protocols driven by Brownian motion, a novel G-noise communication protocol is first proposed to realize the consensus. Moreover, the consensus protocol not only contains time-varying and nonlinear characteristics, but also focuses on DoS attacks. The protocol driven by G-Brownian motion is characterized in the sublinear expectation framework, which leads to the infeasibility of the existing theory. To overcome the difficulty, a new theoretical framework is established to develop consensus criterion. More specifically, first, the non-zero property of MASs is introduced to ensure the rationality of the construction for the Lyapunov function. Then a sufficient criterion for guaranteeing the consensus of MASs is demonstrated by utilizing Lyapunov method, graph theory, stochastic analysis theory, which depends on DoS duration, noise intensity and G-Brownian motion parameters. Ultimately, theoretical results are associated with islanded microgrid systems with a numerical simulation being exploited.

Preassigned-Time Bipartite Flocking Consensus Problem in Multi-Agent Systems

This article is concerned with the bipartite flocking problem in multi-agent systems. Our contributions can be summarized as follows. Firstly, a class of preassigned-time consensus protocols is proposed to solve the issue of multi-agent systems. Secondly, with the aid of the symmetric properties of the graph theory and the Lyapunov stability theorem, we prove that agents can be divided into two disjointed clusters in a finite time, and they move to opposite directions at the same magnitude and speed. The protocol is novel among existing fixed/finite-time protocols in that the associated settling time is a preassigned constant and a parameter of the protocol. Moreover, it is proven that the diameters of the clusters are bounded and independent of other the protocol parameters. These results are demonstrated through both theoretical analysis and simulation examples.

Distributed consensus for nonlinear multi-agent systems with two-time-scales: A hybrid reinforcement learning consensus algorithm

The optimal consensus problem for nonlinear two-time-scales multi-agent systems with completely unknown system dynamics is investigated in this paper. First, the original system is linearly represented based on the Takagi-Sugeno fuzzy model. Then, the optimal consensus problem for multi-agent systems is transformed into solving the game algebraic Riccati equation associated with agents and their neighbors. And individual agent dynamics studied in this paper are replaced with local error dynamics. Moreover, an offline hybrid iteration algorithm with rapid convergence speed and no initial stable control policy is presented for multi-agent systems. Meanwhile, to avoid the utilization of the knowledge of system matrices, an online hybrid reinforcement learning algorithm that only uses the state and control input data of each agent and its neighbors is given to generate the distributed optimal control policy. The convergence of proposed algorithms is also discussed. Finally, the applicability of the presented method is illustrated by an example.

Privacy-Preserving Average Consensus in Multiagent Systems via Partial Information Transmission

This article investigates the privacy-preserving average consensus problem in multiagent systems. A new approach is proposed to achieve the accurate average consensus value while protecting the initial state information of agents. The key idea to achieve these goals is based on partial information transmission. Each agent decomposes its initial state information into several different subinformation. The values of these subinformation are chosen randomly but with their mean value fixed to the original initial value. Then, based on multiple communication channels, agents share all their subinformation, but ensure that each neighbor can only obtain partial subinformation. We prove that the privacy can be protected under our method if each agent has at least two neighbors, and one of the neighbors is neutral. The generalization on the directed graph about this method is also considered. Finally, two examples are provided to illustrate the design process and practical applications of the proposed approach.

Leaderless and Leader-Following Bipartite Consensus of Multiagent Systems With Sampled and Delayed Information.

This article proposes a hybrid systems approach to address the sampled-data leaderless and leader-following bipartite consensus problems of multiagent systems (MAS) with communication delays. First, distributed asynchronous sampled-data bipartite consensus protocols are proposed based on estimators. Then, by introducing appropriate intermediate variables and internal auxiliary variables, a unified hybrid model, consisting of flow dynamics and jump dynamics, is constructed to describe the closed-loop dynamics of both leaderless and leader-following MAS. Based on this model, the leaderless and leader-following bipartite consensus is equivalent to stability of a hybrid system, and Lyapunov-based stability results are then developed under hybrid systems framework. With the proposed method, explicit upper bounds of sampling periods and communication delays can be calculated. Finally, simulation examples are given to show the effectiveness.

Dynamic asynchronous edge-based event-triggered consensus of multi-agent systems

This paper studies the asynchronous edge-based dynamic event-triggered consensus problems for multi-agent systems (MASs) with general linear dynamics. First, the static-gain edge-based protocol is proposed to assure that the agents achieve consensus asymptotically and that a uniformly positive minimum inter-event time (MIET) exists under the corresponding dynamic triggering mechanism. Then, to remove the requirement for the global information associated with the graph, an asynchronous edge-based event-triggered consensus control law that involves a dynamic gain is developed. A novel triggering mechanism that includes two dynamic parameters and a class of positive L1 functions under no Zeno behavior is further proposed to determine triggering instants of each edge in the graph. In addition, the continuous communication link is avoided. Finally, the application in a group of fixed-wing aircraft illustrates the validity of the theoretical results.

The most exigent eigenvalue: Guaranteeing consensus under an unknown communication topology and time delays

In the analysis of consensus problems for multi-agent systems affected by time delays, the delay margin for a given protocol is heavily dependent on the communication topology being used. This document aims to answer the question of what is the largest delay value under which convergence to consensus is still possible even if the communication topology is not known. To answer this question we revisit the concept of most exigent eigenvalue, applying it to two different consensus protocols for agents driven by second order dynamics. We show how the delay margin depends on the structure of the consensus protocol and the communication topology, and arrive to a boundary that guarantees consensus for any connected communication topology. The switching topologies case is also studied and It is shown that for one protocol the stability of the individual topologies is sufficient to guarantee consensus in the switching case, whereas for the other one it is not.