Consensus Problem Of Multi-agent Systems Research Articles

Guaranteed-performance consensus for multi-agent systems with Lipschitz nonlinearity

This paper mainly addresses the guaranteed-performance consensus problem of multi-agent systems (MASs), under the energy constraints and Lipschitz nonlinear dynamics. First, to reach consensus under energy constraints, the consensus protocol and the quadratic performance function are proposed. Afterward, by using the properties of nonsingular transformation matrix and Lipschitz’s nonlinear representation, the consensus function conditions are expressed. Moreover, considering the guaranteed-performance cost, this paper designs the quadratic performance function derived from the Riccati inequality and Lyapunov–Krasovskii theorem. Eventually, numerical simulations are implemented to validate the theoretical results.

Event-triggered predictive control for cooperation-competition multi-agent systems under DoS attacks

This paper concerns the bipartite consensus problem of multi-agent systems(MASs) with competitive- cooperative network topology under denial-of-service (DoS) attacks. Firstly, this work extensively analyzes the competitive phenomena that may exist in the information interchange of agents in contrast to the single cooperative behavior between agents. Based on this, some necessary conditions are provided for the system to attain the bipartite consensus. In addition, the event-triggered mechanism (ETM) effectively lowers unnecessary information sharing between agents and eliminates Zeno behavior. Furthermore, the predictive method provides the system with exceptional resistance against common energy-limited DoS attacks and the ability to compensate for information loss caused by DoS attacks. Finally, a numerical simulation proves that the proposed approach is feasible.

Design and Analysis of a Novel Distributed Gradient Neural Network for Solving Consensus Problems in a Predefined Time.

In this article, a novel distributed gradient neural network (DGNN) with predefined-time convergence (PTC) is proposed to solve consensus problems widely existing in multiagent systems (MASs). Compared with previous gradient neural networks (GNNs) for optimization and computation, the proposed DGNN model works in a nonfully connected way, in which each neuron only needs the information of neighbor neurons to converge to the equilibrium point. The convergence and asymptotic stability of the DGNN model are proved according to the Lyapunov theory. In addition, based on a relatively loose condition, three novel nonlinear activation functions are designed to speedup the DGNN model to PTC, which is proved by rigorous theory. Computer numerical results further verify the effectiveness, especially the PTC, of the proposed nonlinearly activated DGNN model to solve various consensus problems of MASs. Finally, a practical case of the directional consensus is presented to show the feasibility of the DGNN model and a corresponding connectivity-testing example is given to verify the influence on the convergence speed.

Consensus of multi-agent systems with randomly occurring nonlinearities via uncertain pinning control under switching topologies

This paper is focused on the consensus problem of multi-agent systems via uncertain pinning control under switching topologies. The stochastic disturbances and randomly occurring nonlinearities are proposed to describe more realistic systems. The communication topology is modeled by a directed graph and it is divided into two cases, the consensus problem is discussed in these two cases. In addition, there exist some uncertain pinning connections between the followers and leader due to switching topologies, the distributed control protocol is designed to satisfy the follower asymptotically converge to the leader. By constructing suitable multiple Lyapunov functions and utilizing tools of M-matrix theory, some sufficient consensus criteria are deduced to reach this goal. Finally, two examples are given to verify the correctness of the proposed method.

Privacy-Preserving Adaptive Resilient Consensus for Multiagent Systems Under Cyberattacks

This article investigates the secure and privacy-preserving consensus problem of multi-agent systems (MASs) with directed interaction topologies under multiple cyber attacks, which contain deception attacks and DoS attacks. First, a unified attack model is introduced to characterize such a multiple attack phenomenon. Besides, considering the existence of eavesdroppers who can intercept the data transmitted on the links, a fully distributed agent value reconstruction method based on the idea of state decomposition is designed to prevent the leakage of the agent's initial information. Then, a novel privacy-preserving adaptive resilient consensus algorithm (PPARCA) with certain graph robustness condition for MASs under the multiple cyber attacks is proposed. The algorithm adaptively takes different countermeasures in the face of different cyber attacks. PPARCA uses the reconstructed agents' states and combines with the modified Secure Acceptance and Broadcast Algorithm (SABA). Theoretical analysis shows that the proposed algorithm can effectively protect the privacy of the initial state of the agents, and reach resilient consensus in the face of cyber attacks. Finally, numerical simulations and Raspberry Pi MASs practical application experiments demonstrate the effectiveness of the proposed results.

Distributed Fixed-Time Leader-Following Consensus for Multi-Agent Systems: An Event-Triggered Mechanism

In this work, a fixed-time leader-following event-triggered (ET) consensus problem for multi-agent systems (MASs) with external disturbances is investigated. A distributed observer is developed to achieve the estimated state of the leader. By means of the observation information, the consensus error system for multi-agents is reformulated into a tracking error system, wherein individual follower agent aims to track the leader agent. Building upon Lyapunov technology and fixed-time stability theory, a new ET protocol is introduced to mitigate communication wastes. Notably, the proposed controller incorporates a strong robust fixed-time control form with lower complexity, and a reliable dynamic triggering condition also ensures the excellent performance of the system. Rigorous demonstrations underscore the stability and robustness of the ET method, while guaranteeing the avoidance of Zeno behavior. Finally, several numerical simulations are provided to underscore the efficacy of the proposed protocols.

Guaranteed-performance consensus control for multi-agent systems with external disturbances via event-triggered strategy

In this paper, we investigate the leader-following guaranteed performance consensus problem for multi-agent systems(MASs) controlled by event-triggered under external disturbances. First, a disturbance observer is designed for each follower, which can be used to efficiently estimate external disturbances. Second, to reduce the waste of communication resources, a new distributed event-triggered strategy based on the state estimation of neighboring agents is presented, which does not need continuous communication among agents. And the growing estimation error is reset by communication updates. The analysis illustrates that Zeno behavior can be effectively averted by formulating a lower bound on the number of normals for the minimum inter-event interval. Also, based on the above proposed state feedback consensus protocol with guaranteed performance, sufficient conditions are derived to guarantee that a MASs can achieve leader-following consensus. In addition, the consensus criterion with guaranteed performance is put forward in the form of a linear matrix inequality. The cost of guaranteed performance with leader-following structural properties is also established. At last, an example of numerical simulation is presented to confirm the derived analytical solution.

Hybrid protocols for leader–follower consensus of multi-agent systems with distributed delays

The primary focus of this paper is to investigate the leader–follower consensus problem of multi-agent systems (MASs) with discrete and distributed delays in complex domains. We propose a new hybrid consensus protocol that incorporates a continuous-time protocol based on the communication topology of follower agents, along with an event-triggered pinning impulsive control (ETPIC) protocol. Using the Lyapunov functional method in complex domains, we establish delay-dependent sufficient conditions for leader–follower consensus of delayed complex-valued MASs. Our results demonstrate that the proposed hybrid protocol can ensure leader–follower consensus even when the size of discrete and distributed delays exceeds the length of intervals between two consecutive triggering instants. Furthermore, we prove that the Zeno phenomenon can be excluded under the proposed control protocol. In particular, as a special case, we derive the leader–follower consensus result for delay-free complex-valued MASs based on a reduced hybrid control protocol. Two numerical examples are presented to validate the effectiveness of the proposed control scheme.

Consensus of Multiagent Systems With Time-Varying Delays and Switching Topologies Based on Delay-Product-Type Functionals.

This article investigates the consensus problem of multiagent systems (MASs) with time-varying delays subject to switching topologies. For the purpose of obtaining less conservative consensus conditions, first, a delay-product-type Lyapunov-Krasovskii functional (LKF) based on the auxiliary function-based integral inequality (AFBII) is constructed. Then, the generalized reciprocally convex matrix inequality (GRCMI) and a relaxed quadratic function negative-determination lemma are introduced to obtain the maximal-allowable upper bound of time-varying delays. Moreover, a proportional and derivative-like (PD-like) protocol is designed and the result is extended to the leader-following consensus of agents under Lipschitz nonlinear dynamics. Finally, two illustrative examples, including Chua's circuit, are given to demonstrate the advantages of the new consensus criteria.

Adaptive Dynamic Event-Triggered Distributed Output Observer for Leader-Follower Multiagent Systems Under Directed Graphs.

Leader-follower consensus problem for multiagent systems (MASs) is an important research hotspot. However, the existing methods take the leader system matrix as a priori knowledge for each agent to design the controller and use the leader's state information. In fact, only the output information may be available in some practical applications. On this basis, this article first designs a novel adaptive distributed dynamic event-triggered observer for each follower to learn the minimum polynomial coefficients of the leader system matrix instead of the leader system matrix. The proposed method is scalable and suitable for large-scale MASs and can reduce the information transmission dimension in observer design. Then, an adaptive dynamic event-triggered compensator based on the observer and leader output information is designed for each follower, thereby solving the leader-follower consensus problem. Finally, several simulation examples are given to verify the effectiveness of the proposed scheme.

Distributed Dynamic Event-Triggered Consensus Control for Multiagent Systems With Guaranteed Performance and Positive Inter-Event Times

This paper addresses the distributed consensus issue of linear multiagent systems (MASs) subject to disturbances. First, a fully distributed adaptive control law is established for each agent, removing the assumption that global information should be known prior. Additionally, unlike existing consensus studies, the restrictions on continual communication among agents and constant controller updates are eliminated through the designed state observers and event-triggered conditions (ETCs). Moreover, an innovative event-triggered condition (ETC) is created that, via the inclusion of a dynamic parameter, captures mixed triggering and time-varying thresholds as special cases. Particularly, distinct from some dwell time methods that enforce inter-event time (IET) greater than zero at the expense of asymptotic stability, positive inter-event times (IETs) and asymptotic stability can be guaranteed simultaneously by the suggested event-triggered conditions (ETCs) in the absence of disturbances. Furthermore, positive minimum inter-event times (MIETs) can be maintained even in the presence of disturbances, which indicates the robustness of the proposed event-triggered mechanism (ETM). It is shown that the suggested technique performs disturbances suppression for all agents in a completely distributed manner while omitting Zeno behavior. Finally, a simulation example demonstrates the suggested scheme’s efficacy. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The multiagent consensus problem is considered in this paper, which can be applied to some practical systems, e.g., the unmanned aerial vehicles formation problems, as the control objective in these applications can be converted into the consensus problem of MASs. Different from existing results, a novel ETM is proposed, reducing agents’ communication and preventing continuous controller updates. In addition, disturbances widely exist in engineering. The proposed method ensures that the interval between two consecutive event triggers is greater than a small positive constant. Therefore, it is helpful for applying the proposed method in practical engineering. Finally, the established method is applied to a two-mass-spring control problem, and the effectiveness is illustrated. It is anticipated that the proposed approach can be extended to MASs with more realistic network-induced constraints and applied to more practical engineering systems.

Observer-Based Adaptive Consensus Protocol Design for Multi-Agent Systems with One-Sided Lipschitz Nonlinearity

This paper considers the observer-based leader–follower consensus problem of multi-agent systems with one-sided Lipschitz conditions and quadratic inner-boundedness nonlinearity. Based on the relative outputs of neighboring agents, an adaptive protocol over a directed graph is designed via assigning a time-varying coupling weight to each node. Compared with the existing protocols, the proposed protocol can not only be utilized in the unidirectional flow of information, but it does not require any global graph information for its design. It has been shown that the established criteria can not only make the observer error tendency zero, but one can also achieve the leader–follower consensus of such nonlinear multi-agent systems. Furthermore, the gains of observer and protocol parameters can be constructed by solving the linear matrix inequalities (LMIs), which are conveniently checked. The results are illustrated by numerical simulations.

Improved Adaptive Dynamic Event-Triggered Consensus of Multi-Agent Systems

This brief exploits the adaptive dynamic event-triggered (ADET) consensus problem for multi-agent systems (MASs). Firstly, we propose a novel ADET protocol which improves the existing dynamic event triggered (DET) protocol and adaptive event-triggered (AET) protocol based on sampling control. The possibility that linear matrix inequalities (LMIs) has no feasible solution is reduced by presetting an adaptive maximum threshold. The asymptotic stability criterion is obtained. Subsequently, the controller gain and ADET parameters are obtained. Finally, the validity of the theoretical results in this brif is verified by a numerical simulation.

Consensus Control of Multiagent Systems Under Switching Topology and Denial-of-Service Attacks

This article studies the consensus problem of multiagent systems (MASs) under denial-of-service (DoS) attacks and switching topology. Compared with the previous papers, under the switching topology, the impact of DoS attacks on the MAS is considered, and thus, the difficulty of consensus protocol design is further increased. First, a piecewise resilient consensus protocol is proposed to ensure that the MAS can achieve consensus under switching topology and DoS attacks. Then, by considering the different convergence rates caused by the switching topology in each sleep period of DoS attacks, a piecewise Lyapunov–Krasovskii function is established. The sufficient conditions on the global convergence of the system are obtained under switching topology and DoS attacks. In the meantime, the lower bound of average dwell time of the switching topology is determined under DoS attacks. The relationship between average dwell time and the parameters of DoS attacks is discussed. Finally, the simulation example is conducted to verify the effectiveness of the proposed method.

Asymptotical Neuro-Adaptive Consensus of Multi-Agent Systems With a High Dimensional Leader and Directed Switching Topology.

We study the asymptotical consensus problem for multi-agent systems (MASs) consisting of a high-dimensional leader and multiple followers with unknown nonlinear dynamics under directed switching topology by using a neural network (NN) adaptive control approach. First, we design an observer for each follower to reconstruct the states of the leader. Second, by using the idea of discontinuous control, we design a discontinuous consensus controller together with an NN adaptive law. Finally, by using the average dwell time (ADT) method and the Barbǎlat's lemma, we show that asymptotical neuroadaptive consensus can be achieved in the considered MAS if the ADT is larger than a positive threshold. Moreover, we study the asymptotical neuroadaptive consensus problem for MASs with intermittent topology. Finally, we perform two simulation examples to validate the obtained theoretical results. In contrast to the existing works, the asymptotical neuroadaptive consensus problem for MASs is firstly solved under directed switching topology.

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.