Sampled-data-based consensus of multi-agent systems under asynchronous denial-of-service attacks

This paper investigates the sampled-data-based consensus problem of multi-agent systems (MASs) under asynchronous denial-of-service (DoS) attacks. In order to describe asynchronous DoS attacks, a new definition of complete DoS attack and novel double-layer switched systems are proposed. A complete DoS attack refers to a DoS attack that consists of several consecutive successful DoS attacks. While a successful DoS attack denotes an attack that can break the connected communication topology into several isolated subgraphs. Based on this, the original system is transformed into a double-layer switched systems with a stable mode and several unstable modes. It should be pointed out that each unstable subsystem is also composed of finite second-level unstable subsystems that represent consecutive successful DoS attacks. Moreover, a new double-mode-dependent Lyapunov function (DMDLF) method is employed to obtain the lower and upper bounds of the corresponding average dwell time (ADT) of subsystems. It is proved that the consensus of MASs under asynchronous DoS attacks can be achieved by using the feedback consensus controllers which can be designed simultaneously. Finally, an illustrative example is provided to illustrate the effectiveness of the results proposed in this paper.     

Consensus seeking in multi-agent systems via hybrid protocols with impulse delays

This paper studies the consensus problem of multi-agent systems with both fixed and switching topologies. A hybrid consensus protocol is proposed to take into consideration of continuous-time communications among agents and delayed instant information exchanges on a sequence of discrete times. Based on the proposed algorithms, the multi-agent systems with the hybrid consensus protocols are described in the form of impulsive systems or impulsive switching systems. By employing results from matrix theory and algebraic graph theory, some sufficient conditions for the consensus of multi-agent systems with fixed and switching topologies are established, respectively. Our results show that, for small impulse delays, the hybrid consensus protocols can solve the consensus problem if the union of continuous-time and impulsive-time interaction digraphs contains a spanning tree frequently enough. Simulations are provided to demonstrate the effectiveness of the proposed consensus protocols.     

Randomly changing leader-following consensus control for Markovian switching multi-agent systems with interval time-varying delays

This paper considers the problem of leader-following consensus stability and also stabilization for multi-agent systems with interval time-varying delays. The randomly occurring interconnection information of the leader and the Markovian switching interconnection information of the agent are matters of concern in the systems. Through construction of a suitable Lyapunov–Krasovskii functional and utilization of the reciprocally convex approach, new delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by using various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Variable impulsive consensus of nonlinear multi-agent systems

In this paper, the consensus problem for nonlinear multi-agent systems with variable impulsive control method is studied. In order to decrease the communication wastage, a novel distributed impulsive protocol is designed to achieve consensus. Compared with the common impulsive consensus method with fixed impulsive instants, the variable impulsive consensus method proposed in this paper is more flexible and reliable in practical application. Based on Lyapunov stability theory and some inequality techniques, several novel impulsive consensus conditions are obtained to realize the consensus of multi-agent systems. Finally, some necessary simulations are performed to validate the effectiveness of theoretical results.     

Tracking consensus of nonlinear MASs with asymmetric communication delays in noisy environments

This paper investigates the tracking consensus problem of nonlinear multi-agent systems (MASs) with asymmetric time-varying communication delays in noisy environments under the conditions of fixed and switching directed topologies. A novel stochastic analysis approach is proposed, which guarantees that the designed two distributed tracking protocols can guide the controlled systems to achieve tracking consensus in the sense of mean square. In order to further reveal the influence of asymmetric communication delays on the tracking consensus ability for MASs, some new delay-dependent sufficient conditions for mean-square consensus are also developed. A simple example is finally given to illustrate the effectiveness of the proposed theoretical results.     

Formation control for second-order multi-agent systems with time-varying delays under directed topology

In this paper, we investigate a formation control problem for second-order multi-agent systems with directed graph interconnection topologies that contain time-varying coupling delays. By using a special multiple leaders’ framework, sufficient conditions are obtained for both time-invariant and time-varying formations as well as for time-varying formations for trajectory tracking, which guarantees the attainment of the formations is at exponentially converging speeds. Some numerical simulations are also conducted to validate the theoretical results.     

Integral representation of solutions of fractional system with distributed delays

The aim of the present paper is to obtain an integral representation of the solution of the Cauchy problem with discontinuous and continuous initial conditions for linear fractional differential system with Caputo-type derivatives and distributed delay. The obtained results are new even in the particular case of fractional system with constant delays.     

Distributed impulsive control consensus for a class of unknown nonlinear multi-agent systems based on event-triggered scheme

In this study, we are concerned with the impulsive consensus control problem for a class of nonlinear multi-agent systems (MASs) which have unknown dynamics and directed communication topology. The neural networks (NNs) method is the first utilized to construct distributed event-triggered impulsive consensus protocol. In contrast to the existing impulsive consensus protocol, the consensus protocol proposed in this paper does not need the dynamics of agents, which enhances the system robustness, and realizes distributed event-triggered communication between agents, which can reduce unnecessary consumption of communication resources. Sufficient conditions are derived to ensure the consensus of the controlled MASs and the exclusion of Zeno-behavior. Finally, simulation examples are presented to illustrate the effectiveness of the proposed control protocol.     

Consensus of the second-order multi-agent systems with an active leader and coupling time delay

This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.     

Asymptotic pinning synchronization of nonlinear multi-agent systems: Its application to tunnel diode circuit

This work proposes a pinning state-feedback control technique for synchronizing non-linear multi-agent systems (MASs) with time delays. A collection of switching-directed graphs describes the communication exchanges between all of the agents. The challenge of asymptotic stability analysis for some error systems is translated into the construction of a leader-following synchronization of the relevant MASs. The closed-loop system could be acquired by building a convenient Lyapunov–Krasovskii functional (LKF) that has two integral terms, and by using Kronecker product qualities combined with matrix inequality techniques. When these conditions are met, a state-feedback pinning controller can be built with linear matrix inequalities (LMIs), which can be derived easily from a number of efficient optimization algorithms. Further, the performance of the proposed control design system is verified based on a tunnel diode circuit (TDC) by numerical simulations.     

Robustness with respect to small delays for exponential stability of non-autonomous systems

Robustness of stability with respect to small delays, e.g., motivated by feedback systems in control theory, is of great theoretical and practical important, but this property does not hold for many systems. In this paper, we introduce the conception of robustness with respect to small time-varying delays for exponential stability of the non-autonomous linear systems. Sufficient conditions are given for the non-autonomous systems to be robust, and examples are provided to illustrate that the conditions are satisfied for a large class of the non-autonomous parabolic systems.     

Distributed containment control of second‐order multiagent systems with input delays under general protocols

This article addresses the distributed containment control problem in a group of agents governed by second‐order dynamics with directed network topologies. Considering there are multiple leaders, we study a general second‐order containment controller which can realize several different consensus modes by adjusting control gains. A necessary and sufficient condition on the control gains of the general containment controller is provided. Moreover, the delay sensitivity of the closed‐loop multiagent system under the general containment controller is studied; the maximal upper bound of the constant delays is obtained. Finally, several numerical examples are used to illustrate the theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 112–120, 2016     

Design of a robust tracker and disturbance attenuator for uncertain systems with time delays

This article considers the composite nonlinear feedback control method for robust tracker and disturbance attenuator design of uncertain systems with time delays. The proposed robust tracker improves the transient performance and steady state accuracy simultaneously. The asymptotic robust tracking conditions are provided in the form of linear matrix inequalities and the resultant conditions yield the controller gains. Moreover, to improve the reference tracking performance, a new nonlinear function for the composite feedback control law is offered. Simulation results are presented to verify the theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 340–348, 2015     

Asymptotic behavior of solutions for a class of predator-prey reaction-diffusion systems with time delays

The aim of this paper is to investigate the asymptotic behavior of solutions for a class of three-species predator-prey reaction-diffusion systems with time delays under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time-dependent solution to a constant steady-state solution. The conditions for the convergence are independent of diffusion coefficients and time delays, and the conclusions are directly applicable to the corresponding parabolic-ordinary differential system and to the corresponding system without time delays.