Leader-following consensus of semi-Markov jump nonlinear multi-agent systems under hybrid cyber-attacks

In this paper, the leader-following consensus issue is investigated for a class of nonlinear multi-agent systems with semi-Markov parameters subject to hybrid cyber-attacks. A semi-Markov chain is adopted to describe the variation of switching topologies caused by the complexity of the environment and makes the studied problem more general. Hybrid cyber-attacks consisting of denial-of-service attacks and deception attacks are described with the help of two groups of Bernoulli sequences which are assumed to be independent of each other. On this basis, a sufficient condition for the stability of the consensus error system is established by using linear matrix inequality techniques. Finally, the validity of the results obtained is verified by two numerical examples.     

Event-triggered leader-following consensus of multi-agent systems under semi-Markov switching topology with partially unknown rates

An event-triggered leader-following consensus problem for multi-agent systems with nonlinear dynamics was investigated in this study. The interaction topologies among the agents that we considered are randomly switched ones, governed by a semi-Markov process with partially unknown rates. By building the state error model between the leader and followers, the consensus problem is first converted into a stability problem. Moreover, an event-triggered transmission scheme based on sampling data was proposed to reduce communication redundancy. The consensus controller and event-triggered parameters can be designed effectively. By constructing a Lyapunov–Krasovskii functional (LKF) with a triple integral, the sufficient conditions required to guarantee the event-triggered consensus can be reached with respect to the linear matrix inequalities (LMIs). Ultimately, the validity of the theoretical results is demonstrated by a numerical example.     

Scaled consensus of second-order multi-agent systems based on edge-event driven control

In this paper, the scaled consensus of resource-limited multi-agent systems with second-order integrator dynamics and undirected topologies is investigated. In order to reduce bandwidth and computation requirements, a scaled consensus protocol based on periodic edge-event driven control is proposed. It is proven that all the agents could converge to a scaled consensus state while the interaction topology is connected. Moreover, a self-triggered scheme is proposed so as to further reduce communication times between agents. Notably, the event-detecting period is introduced so that Zeno behavior could be excluded in our model. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.     

Leader-following consensus control for semi-Markov jump multi-agent systems: An adaptive event-triggered scheme

The problem of event-triggered leader-following consensus control for semi-Markov multi-agent systems is investigated in this paper. A semi-Markov process is used to describe the sudden parameter changes between every agent. An adaptive event-triggered control strategy is proposed to make a balance between reducing unnecessary communication and meeting the required performance. A control protocol which can resist actuator faults is used to ensure the reliable leader-following consensus. By employing the Lyapunov–Krasovskii functional method, some sufficient conditions are provided to guarantee that the leader-following consensus can be achieved in mean-square sense. The consensus controller and the event-triggered parameter can be co-designed. Finally, the effectiveness of the proposed method is verified by a F-404 aircraft engine system.     

Fixed-time scaled consensus of multi-agent systems with input delay

The design of fixed-time scaled consensus protocol for multi-agent systems with input delay is developed in this article. First, by virtue of Artstein model reduction method, the time-delay system is converted into a delay-free one. Then, two novel controllers are designed such that the fixed-time scaled consensus of multi-agent systems can be realized for the undirected and directed topology, respectively. Sufficient conditions are derived to guarantee that all agents converge to the assigned ratios instead of the same value under any bounded input delay. Besides, an explicit estimate can be given for the uniform convergence time independent of the initial conditions. Moreover, it is proved that the convergence value of the system is not affected by the initial states of agents any more, but only related to initial states of the virtual agents set in advance. Finally, numerical simulations are given to demonstrate the feasibility of the proposed algorithms.     

A fully distributed approach for consensus of multi-agent systems under multiple state-variables-dependent interaction topologies

In this paper, the consensus problem of multi-agent systems with general linear dynamics is studied. Motivated by the MIMO communication technique, a general framework is considered in which different state variables are exchanged in different independent interaction topologies. This novel framework could improve the control system design flexibility and potentially improve the system performance. Fully distributed consensus control laws are proposed and analyzed for the settings of fixed and switching multiple topologies. The control law can be applied using only local information. And the control gain can be designed depending on the dynamics of the individual agent. By transforming the overall multi-agent systems into cascade systems, necessary and sufficient conditions are provided to guarantee the consensus of the overall systems under fixed and switching state variable dependent topologies, respectively. Two simulation examples are provided to illustrate the effectiveness of the proposed theoretical results.     

Finite-time group consensus via pinning control for heterogeneous multi-agent systems with disturbances by integral sliding mode

In this paper, the finite-time group consensus for a class of heterogeneous multi-agent systems (HMASs) with bounded disturbances is studied by designing a pinning control scheme with an integral sliding mode. For an HMAS without disturbance, a continuous finite-time consensus protocol with a pinning and grouping strategy is proposed. Under the designed control protocol, the HMAS achieves consensus according to the given grouping requirement in a finite time and the final states converge to the desired consistency values. The detailed theoretical proof is given on the strength of Lyapunov theory, LaSalle’s invariance principle and homogeneity with dilation principle. On this basis, this paper further introduces an integral sliding mode into finite-time group consensus protocol designed above such that the HMAS with one or more pinning agents can achieve accurate finite-time group consensus even if there exist uncertain bounded disturbances. It is noted that the control input is chattering-free. Two simulation examples are presented to illustrate the effectiveness of the proposed control schemes.     

Leader-following consensus considering effects of agents on each other via impulsive control: A topology dependent average dwell time approach

This paper intends to investigate the consensus problem of a nonlinear multi-agent system with new nonlinear terms added to the dynamics of each agent in the leader-following framework with impulsive control. The main contribution of this paper is introducing these new terms expressing the effect of each agent on neighbor agents. The new terms called effect terms (ETs) are considered with time-varying delay. Moreover, the communication interactions among all agents are addressed by a set of consensusable and unconsensusable switching topologies. In particular, the topology-dependent average dwell time (TDADT), one of the significant practical analysis methods for switched systems, has been calculated for each topology. The globally uniformly exponentially stability (GUES) for the consensus error dynamics is analyzed by employing algebraic graph theory and a multiple discontinuous Lyapunov function approach (MDLF) regarding separate Lyapunov functions for impulse instants. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that consensus can be achieved. Finally, the effectiveness of the theoretical analysis is corroborated by a numerical example.     

Synchronization of multiplex networks with stochastic perturbations via pinning adaptive control

This paper investigates the synchronization problems for the multiplex networks with both inter-layer and intra-layer couplings subject to the stochastic perturbations. In particular, the topologies of all layers are not the same, so the model can represent a class of multiplex networks. To synchronize the multiplex networks onto the trajectory of a virtual leader, a pinning adaptive protocol is proposed and some pinning criteria are derived for guaranteeing complete synchronization. Furthermore, when the results are extended to the systems with time delays, the pinning adaptive strategy is still proved to be effective. Finally, a two-layer network and a three-layer network are selected for numerical simulations to illustrate the theoretical results.     

Exponential stability of switched linear impulsive time-varying system and its application

This paper aims at the problem of exponential stability for switched linear impulsive time-varying system. By constructing two different switched discretized Lyapunov functions, some new sufficient conditions ensuring the global exponential stability of switched linear impulsive time-varying system are provided, which can be employed to the case when all subsystems are unstable. Furthermore, we apply theoretical results to the consensus of multi-agent system with switching topologies. Finally, numerical examples demonstrate the effectiveness of given results.     

Stabilization of discrete-time semi-Markov jump singularly perturbed systems subject to actuator saturation and partially known semi-Markov kernel information

In this paper, the stabilization issue is investigated for a family of discrete-time semi-Markov jump singularly perturbed systems (S-MJSPSs) subject to actuator saturation. The information of the semi-Markov kernel (SMK) is considered as partly known on account of that it is laborious to obtain the complete one in practice. With the consideration of the actuator saturation existing in virtually all practical applications, the convex hull approach is adopted to tackle this obstacle. Meanwhile, a unified controller design technique is presented to stabilize the underlying system irrespective of whether the fast state can be detected. Based on Lyapunov stability theory and SMK approach, some sufficient conditions guaranteeing the S-MJSPSs is mean-square (MS) stable are derived. Finally, the correctness and the validity of the presented control strategy are validated by a numerical example.     

Scaled consensus design for multiagent systems under DoS attacks and communication-delays

This paper aims to solve scaled consensus problem for general linear multiagent systems under denial-of-service (DoS) attacks. Firstly, we propose a new scaled disagreement vector and investigate its properties under switching and undirected graphs. Secondly, we establish sufficient conditions in terms of linear matrix inequalities in order to guarantee that the multiagent system achieves scaled consensus under DoS attacks. Contrary to most existing studies where DoS attacks on all the channels are same, in this note, we formulate the problem such that the adversary compromises each agent independently. Moreover, the distributed consensus protocol is investigated for networks with time-varying delay. Finally, two simulation examples are given to demonstrate effectiveness of the proposed design methodologies.     

Scaled group consensus in agent networks with finite sub-networks under continuous/discrete-time settings

We study scaled group consensus problems of the first/second-order multi-agent dynamics under continuous/discrete-time settings. For a directed multi-agent network with finite sub-networks, the scaled group consensus is concerned with this case that all the sub-networks reach consensus, separately, while maintain the given ratios among the multiple consensus. First/second-order distributed protocols with continuous/discrete data are designed to solve the scaled group consensus problems, and then necessary and sufficient criteria are established to guarantee the agents’ states reaching the scaled group consensus asymptotically applying both algebraic and analytical tools. Finally, the effectiveness of the theoretical results are verified by several simulation examples.     

Consensus of fractional-order multiagent system via sampled-data event-triggered control

This paper investigates the consensus of fractional-order multiagent systems via sampled-data event-triggered control. Firstly, an event-triggered algorithm is defined using sampled states. Thus, Zeno behaviors can be naturally avoided. Then, a distributed control protocol is proposed to ensure the consensus of fractional-order multiagent systems, where each agent updates its current state based on its neighbors’ states at event-triggered instants. Furthermore, the pinning control technology is taken into account to ensure all agents in multiagent systems reach the specified reference state. With the aid of linear matrix inequalities (LMI), some sufficient conditions are obtained to guarantee the consensus of fractional-order multiagent system. Finally, numerical simulations are presented to demonstrate the theoretical analysis.     

Finite-time scaled consensus tracking of a class of high-order nonlinear multi-agent systems with unstable linearization

In this paper, we consider the finite-time scaled consensus tracking of a class of high-order nonlinear multiagent systems(MASs)who owns unstable modes in its Jacobian linearized system. The presence of unstable linearization makes the high-order MASs in question essentially different from those in the existing works. Under a directed interaction topology, to overcome the difficulties caused by the asymmetry property of Laplacian matrix, the finite-time scaled consensus control scheme is developed by the modified addition of a power integrator method. Based on finite-time Lyapunov stability theorem and algebra graph theory, for high-order MASs with unstable linearization even in the presence of non-lipschitz nonlinear dynamic, all system states are bounded and the output tracking errors are finite-time uniformly ultimately bounded(FUUB). Finally, a numerical example is given to demonstrate the effectiveness of the theoretical results.     

Reliable consensus control for semi-Markov jump multi-agent systems: A leader-following strategy

This paper is devoted to the reliable leader-following consensus realization for a class of nonlinear multi-agent systems. The parameters of every agent are assumed to encounter sudden changes, which are governed by a semi-Markov process. A control protocol which possesses the performance of resisting actuator faults is employed for ensuring the reliable leader-following consensus and an analysis result is established by using the Lyapunov–Krasovskii functional method. Then an easy-to-implement condition is proposed for the issue of leader-following reliable consensus realization. If the condition is satisfied, the desired controller gain can be obtained via the numerical solutions of a set of linear matrix inequalities. At last, the feasibility of the proposed scheme is well explained by an illustrated example.     

A survey on global pinning synchronization of complex networks

In practice, it is almost impossible to directly add a controller on each node in a complex dynamical network due to the high control cost and the difficulty of practical implementation, especially for large-scale networks. In order to address this issue, a pinning control strategy is introduced as a feasible alternative. The objective of this paper is first to recall some recent advancements in global pinning synchronization of complex networks with general communication topologies. A systematic review is presented thoroughly from the following aspects, including modeling, network topologies, control methodologies, theoretical analysis methods, and pinned node selection and localization schemes (pinning strategies). Fully distributed adaptive laws are proposed subsequently for the coupling strength as well as pinning control gains, and sufficient conditions are obtained to synchronize and pin a general complex network to a preassigned trajectory. Moreover, some open problems and future works in the field are also discussed.     

Adaptive fuzzy finite-time control for spacecraft formation with communication delays and changing topologies

This paper aims to solve the finite time consensus control problem for spacecraft formation flying (SFF) while accounting for multiple time varying communication delays and changing topologies among SFF members. First, in the presence of model uncertainties and external disturbances, the coupled dynamics of relative position and attitude are derived based on the Lie group SE(3), in which the position and attitude tracking errors with respect to the virtual leader whose trajectory is computed offline are described by exponential coordinates. Then, a nonsingular fast terminal sliding mode (NFTSM) constructed by the exponential coordinates and velocity tracking errors is developed, based on which adaptive fuzzy NFTSM control schemes are proposed to guarantee that the ideal configurations of the SFF members with respect to the virtual leader can be achieved in finite time with high accuracy and all the aforementioned drawbacks can be overcome. The convergence and stability of the closed-loop system are proved theoretically by Lyapunov methods. Finally, numerical simulations are presented to validate the effectiveness and feasibility of the proposed controllers.     

A new approach to average consensus problems with multiple time-delays and jointly-connected topologies

This paper investigates average consensus problem in networks of continuous-time agents with delayed information and jointly-connected topologies. A lemma is derived by extending the Barbalat's Lemma to piecewise continuous functions, which provides a new analysis approach for switched systems. Then based on this lemma, a sufficient condition in terms of linear matrix inequalities (LMIs) is given for average consensus of the system by employing a Lyapunov approach, where the communication structures vary over time and the corresponding graphs may not be connected. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results.     

Formation consensus for discrete-time heterogeneous multi-agent systems with link failures and actuator/sensor faults

In this paper, a distributed control protocol is presented for discrete-time heterogeneous multi-agent systems in order to achieve formation consensus against link failures and actuator/sensor faults under fixed and switching topologies. A model equivalent method is proposed to deal with the heterogeneous system consists of arbitrary order systems with different parameters. Based on graph theory and Lyapunov theory, stability conditions to solve formation consensus problem are developed for the underlying heterogeneous systems with communication link failures. In order to tolerate actuator/sensor faults, a distributed adaptive controller is proposed based on fault compensation. The desired control is designed by linear matrix inequality approach together with cone complementarity linearisation algorithm. After applying the new control scheme to heterogeneous systems under the directed topologies with link failures and faults, the resulting closed-loop heterogeneous system is validated to be stable. The effectiveness of the new formation consensus control strategy and its robustness are verified by simulations.