A Fully Distributed Protocol with an Event-Triggered Communication Strategy for Second-Order Multi-Agent Systems Consensus with Nonlinear Dynamics.

This paper presents the communication strategy for second-order multi-agent systems with nonlinear dynamics. To address the problem of the scarcity of communication channel resources and get rid of using continuous signals among the followers in lead-follower multi-agent systems, a novel event-triggered communication mechanism is proposed in this paper. To avoid employing the centralized information that depends on the Laplacian matrix spectrum, a network protocol with updated coupling gains is proposed, as well as an event-triggered strategy with updated thresholds. To eliminate the ill effects of inter-node communicating noise, relative positions are employed by the protocol instead of absolute positions. By a Lyapunov-Krasovskii functional, it is rigorously proven that the leader-following consensus of MASs is achieved without Zeno behavior, under the control of the proposed protocol with an event-triggered mechanism communication. The effectiveness of the proposed protocol is verified through numerical examples.

Event-Triggered Fixed-Time Integral Sliding Mode Control for Nonlinear Multi-Agent Systems with Disturbances.

In this paper, the leader-following consensus problem of first-order nonlinear multi-agent systems (FONMASs) with external disturbances is studied. Firstly, a novel distributed fixed-time sliding mode manifold is designed and a new static event-triggered protocol over general directed graph is proposed which can well suppress the external disturbances and make the FONMASs achieve leader-following consensus in fixed-time. Based on fixed-time stability theory and inequality technique, the conditions to be satisfied by the control parameters are obtained and the Zeno behavior can be avoided. In addition, we improve the proposed protocol and propose a new event-triggering strategy for the FONMASs with multiple leaders. The systems can reach the sliding mode surface and achieve containment control in fixed-time if the control parameters are designed carefully. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.

On Leader-Following Consensus in Multi-Agent Systems with Discrete Updates at Random Times.

This paper studies the leader-following consensus problem in continuous-time multi-agent networks with communications/updates occurring only at random times. The time between two consecutive controller updates is exponentially distributed. Some sufficient conditions are derived to design the control law that ensures the leader-following consensus is asymptotically reached (in the sense of the expected value of a stochastic process). The numerical examples are worked out to demonstrate the effectiveness of our theoretical results.

Scaled consensus for second-order multi-agent systems subject to communication noise with stochastic approximation-type protocols.

This work is dedicated to the leaderless/leader-following stochastic scaled consensus issue of second-order stochastic multi-agent systems (SMASs) in a noisy environment. Scaled consensus represents that the ratios among agents asymptotically tend to designated constants rather than the common convergence value. To lessen the influence of communication noise, some stochastic approximation protocols with time-varying gain are designed for our underlying system, where the time-varying gain remove the restriction of nonnegative value. Compared with the existing consensus results with communication noise, the major challenge is that the introduction of time-varying gain results in the inapplicability of Lyapunov-based technique. To cope with it, a state decomposition method is utilized, and a series of sufficient necessary conditions are set up for interacting agents with constant velocity and zero velocity if the topology includes a spanning tree. Furthermore, it is conducted that the consensus and bipartite consensus can be seen as two special cases of our work. Finally, the validity of our results is demonstrated by a simulation example.

Matrix measure-based distributed impulsive consensus on nonlinear multi-agent systems with mixed time-varying delays.

This paper concentrates on researching the global and exponential leader-following consensus issue for an array of nonlinear multi-agent systems with the system time-varying delay and the distributed time-varying delay. An innovative distributed impulsive controller is proposed to force the states of all agents to track the trajectories of leader agent. By jointly introducing the matrix measure protocol, the comparison principle for impulsive systems, and the average impulsive interval, sufficient criteria for the realization of leader-following consensus are derived. In addition, considering different functions of impulsive signal, two different convergence rates are precisely estimated by utilizing the parameter variation formula, respectively. Finally, two numerical examples are given to demonstrate the effectiveness of proposed control strategy and the rightness of theoretical analysis.

Fully distributed consensus of discrete-time linear multi-agent systems with large input and communication delays.

This paper investigates the consensus problem for discrete-time leader-following multi-agent systems subject to large time delays. Building upon two assumptions, a novel fully distributed protocol is devised by utilizing a normalized weighting matrix, depending solely on the relative output measurement. It is shown that, for arbitrarily large yet bounded input and communication delays that are constant and exactly known, the consensus problem can be effectively addressed by both the proposed protocol and its truncated version. Assuming further that followers incorporate solely input delays, then the permitted delays can be time-varying and different. The proposed protocols do not rely on global information of the directed communication topology, thus ensuring robustness against alterations in the communication topology. A numerical example is employed to validate the effectiveness of the suggested approach.

A leader-following consensus of multi-agent systems with actuator saturation and semi-Markov switching topologies.

The leader-following consensus (LFC) issue is investigated in this paper for multi-agent systems (MASs) subject to actuator saturation with semi-Markov switching topologies (SMST). A new consensus protocol is proposed by using a semi-Markov process to model the switching of network topologies. Compared to the traditional Markov switching topologies, the SMST is more general and practical because the transition rates are time-varying. By using the local sector conditions and a suitable Lyapunov-Krasovskii functional, some sufficient conditions are proposed such that the leaderfollowing mean-square consensus is locally achieved. Based on the derived sufficient conditions, an optimization problem is analyzed to determine the consensus feedback gains and to find a maximal estimate of the domain of consensus attraction (DOCA) of a closed-loop model. At the end, a numerical case is presented to verify the performance of the design method.

An adaptive neurodynamic approach for solving nonsmooth N-cluster games.

In this paper, N-cluster games with coupling and private constraints are studied, where each player's cost function is nonsmooth and depends on the actions of all players. In order to seek the generalized Nash equilibrium (GNE) of the nonsmooth N-cluster games, a distributed seeking neurodynamic approach with two-time-scale structure is proposed. An adaptive leader-following consensus technique is adapted to dynamically adjust parameters according to the degree of consensus violation, so as to quickly obtain accurate estimation information of other players' actions which facilitates the evaluation of its own cost. Benefitting from the unique structure of the approach based on primal dual and adaptive penalty methods, the players' actions enter the constraints while completing the seeking for GNE. As a result, the neurodynamic approach is completely distributed, and prior estimation of penalty parameters is avoided. Finally, two engineering examples of power system game and company capacity allocation verify the effectiveness and feasibility of the neurodynamic approach.

Observer-based event-triggered leader-following consensus of multi-agents with generalized Lipschitz nonlinear dynamics.

This paper discusses a leader-following consensus problem for nonlinear multi-agent systems (MASs) subjected to generalized Lipschitz-type nonlinearity using output feedback. An event-triggered (ET) leader-following control scheme, based upon estimated states using observers, is proposed for efficient bandwidth utilization by application of invariant sets. Distributed observers are designed to estimate the states of the followers because actual states are not always readily available. Besides, in order to reduce unnecessary data communication among the followers, an ET strategy has been formulated which excludes Zeno behavior as well. Under this proposed scheme, sufficient conditions are formulated using Lyapunov theory. These conditions not only guarantee the asymptotic stability of estimation error, but also ensure the tracking consensus of nonlinear MASs. Further, a simple and less conservative design approach using a decoupling scheme for assuring necessity and sufficiency for the main design approach has also been explored. The decoupling scheme is similar to separation principle for linear systems. Contrary to the existing works, the nonlinear systems considered in this study cover a wide family of Lipschitz nonlinearities, including both globally and locally Lipschitz systems. Moreover, the proposed approach is more efficient in handling ET consensus. Finally, the obtained results are verified with single link robots and modified Chua's circuits.

Leader-following output-feedback consensus for second order multiagent systems with arbitrary convergence time and prescribed performance.

This paper investigates the prescribed-time leader-following output-feedback consensus problem for second order multiagent systems without velocity measurement. Firstly, by introducing a time-scaling function, novel prescribed-time state observers are designed to estimate the second-order states of the agents. Then, a distributed output-feedback scheme is proposed to achieve leader-following consensus, where the transient performance, including the convergence rate and the overshoot, can be offline pre-assigned. It should be noted that the singularity-like problem is solved for the system under measurement errors by adopting a form of piecewise functions. Moreover, the control strategy is modified by introducing an auxiliary system when taking the common saturation problem into account. Finally, the efficiency of the proposed schemes is illustrated by numerical simulation examples.

Dynamic event-triggered adaptive finite-time consensus control for multi-agent systems with time-varying actuator faults.

In this study, the adaptive finite-time leader-following consensus control for multi-agent systems (MASs) subjected to unknown time-varying actuator faults is reported based on dynamic event-triggering mechanism (DETM). Neural networks (NNs) are used to approximate unknown nonlinear functions. Command filter and compensating signal mechanism are introduced to alleviate the computational burden. Unlike the existing methods, by combining adaptive backstepping method with DETM, a novel finite time control strategy is presented, which can compensate the actuator efficiency successfully, reduce the update frequency of the controller and save resources. At the same time, under the proposed strategy, it is guaranteed that all followers can track the trajectory of the leader in the sense that consensus errors converge to a neighborhood of the origin in finite time, and all signals in the closed-loop system are bounded. Finally, the availability of the designed strategy is validated by two simulation results.

Leader-following consensus for multi-agent systems subject to cyber attacks: Dynamic event-triggered control.

This paper addresses the event-triggered consensus problem for multi-agent systems (MASs) under cyber attacks in the leader-following framework. Via introducing a recoverable cyber attack and dynamic event-triggered mechanism (DEM), the centralized and distributed event-triggered controllers are co-designed. Meanwhile, some dynamic triggering criteria are given to ensure the MASs can achieve consensus. The DEM contains time-varying dynamic parameters, which can extend the interevent time interval to avoid Zeno phenomenon. The simulation results verify the effectiveness of the proposed scheme.

Reset control for leader-following consensus of multi-agent systems.

This paper studies the leader-following consensus problem of linear multi-agent systems over directed communication graphs. This paper proposes a novel distributed reset proportional-integral consensus controller with guaranteed Zeno-freeness property. With the proposed reset consensus controller, the closed-loop system becomes a hybrid system consisting of the flow dynamics and jump dynamics. By adopting a novel Lyapunov function and the hybrid system analysis approach, it obtains the conditions under which consensus is achieved. It further shows that the proposed reset consensus controller helps to improve the transient performance. Finally, a numerical example is presented to illustrate the theoretical results and effectiveness.

Robust leader-following consensus of cyber-physical systems with cyber attack via sampled-data control.

The leader-following consensus problem is investigated for complex cyber-physical systems under cyber attacks. The communication channels of the agents in the cyber-physical systems may be destroyed by attacks, and the damage is assumed to be repaired after a period of time by a restoration mechanism. Considering the parameter disturbance in the wireless communication, a robust sampled-data control law is designed so that the leader-following consensus can be achieved. The sampling period, attack length rate and attack frequency are analyzed on the basis of Lipschitz condition or QUAD condition, respectively. By using proper Lyapunov functional and inequality techniques, it is shown that robust leader-following consensus of cyber-physical systems with sampled-data control can be guaranteed under cyber attack. Finally, two examples are provided to confirm the theoretical results.

A novel event-triggered communication strategy for second-order multiagent systems.

This paper concentrates on the design of an event-triggered communication strategy for secondary multi-agent systems. Many existing results in this field usually require centralized information depending on the Laplacian matrices. In a real application, however, such the constraint is conservative. To address it, this paper proposes an event-triggered sampling mechanism for interagent communication with updated thresholds. Accordingly, consensus protocols with adaptive coupling control gains are proposed for both a fixed topology and switching topologies. It is proven that the proposed method guarantees the leader-following consensus for second-order multiagent systems with an arbitrarily connected topology and even with jointly connected switching topologies. The effectiveness of the proposed scheme is verified by simulation examples.

Leader-following consensus of nonlinear discrete-time multi-agent systems with limited bandwidth and switching topologies.

This paper considers the leader-following consensus problem of discrete-time nonlinear multi-agent systems over switching topologies with limited bandwidth. Through the encoding-decoding data, we design a distributed feedback control protocol which is closely associated with the connectivity of relevant channel at each time step. An adaptive communication mechanism is presented to ensure fewer bits of information transmission at each time step under the premise that the quantizer for encoding and decoding is not saturated. Although the nonlinear model over switching topologies introduces a cumulative error with respect to consensus error at previous time steps, the convergence rate of the system can be characterized. Through a rigorous convergence analysis, we illustrate that if the jointly connected condition of communication networks is satisfied, consensus issues will be resolved. A numerical simulation example shows that based on the designed distributed control law, all states of the follower agents are ultimately the same as the leader's state.

Adaptive fault-tolerant consensus for a class of leader-following systems using neural network learning strategy.

In this paper, the leader-following consensus problem of a class of nonlinearly multi-dimensional multi-agent systems with actuator faults is addressed by developing a novel neural network learning strategy. In order to achieve the desirable consensus results, a neural network learning algorithm composed of adaptive technique is proposed to on-line approximate the unknown nonlinear functions and estimate the unknown bounds of actuator faults. Then, on the basis of the approximations and estimations, a robust adaptive distributed fault-tolerant consensus control scheme is investigated so that the bounded results of all signals of the resulting closed-loop leader-following system can be achieved by using Lyapunov stability theorem. Finally, efficiency of the proposed adaptive neural network learning strategy-based consensus control strategies is demonstrated by a coupled nonlinear forced pendulums system.

Leader-following consensus of the second-order multi-agent systems under directed topology.

This paper investigates the consensus problem for second-order multi-agent systems with a dynamical leader. A simple and novel protocol based on the relative state of the neighboring agents is proposed. Using the linear matrix inequality method, sufficient conditions are derived to ensure the consensus for both the cases without and with communication delay in the multi-agent systems. Some numerical simulations are also given to show the effectiveness of the proposed results.