Probability-guaranteed secure consensus control for time-varying stochastic multi-agent systems under mixed attacks

In this paper, the secure consensus control issue is investigated for a class of discrete time-varying stochastic multi-agent systems (MASs) subject to cyber-attacks. In order to give a comprehensive characterization of malicious threats against communication networks, a generic model is presented to take into account both random false data injection attacks (FDIAs) and replay attacks. The main objective of the problem under study is to design a control protocol via output feedback such that, despite the existence of mixed attacks, all the individual agents can be driven to reside within a desired ellipsoidal region in a pre-specified probability. Sufficient conditions are provided for the existence of the requested controller and the feedback gains are formulated in terms of the solution to certain matrix inequalities. Within the established framework, two optimization problems are considered with the aim to ensure the sub-optimal consensus performances from different perspectives. Finally, a simulation example is employed to illustrate the validity of the proposed control scheme.     

Distributed secure consensus control of nonlinear multi-agent systems under sensor and actuator attacks

In this paper, we focus on an output secure consensus control issue for nonlinear multi-agent systems (MASs) under sensor and actuator attacks. Followers in an MAS are in strict-feedback form with unknown control directions and unknown dead-zone input, where both sensors and nonlinear characteristics of dead-zone in actuators are paralyzed by malicious attacks. To deal with sensor attacks, uncertain dynamics in individual follower are separated by a separation theorem, and estimation parameters are introduced for compensating and mitigating the influence from adversaries. The influence from actuator attacks are treated as a total displacement in a dead-zone nonlinearity, and an upper bound, as well as its estimation, is introduced for this displacement. The dead-zone nonlinearity, sensor attacks and unknown control gains are gathered together regarded as composite unknown control directions, and Nussbaum functions are utilized to address the issue of unknown control directions. A distributed secure consensus control strategy is thus developed recursively for each follower in the framework of surface control method. Theoretically, the stability of the closed-loop MAS is analyzed, and it is proved that the MAS achieves output consensus in spite of nonlinear dynamics and malicious attacks. Finally, theoretical results are verified via a numerical example and a group of electromechanical systems.     

Distributed dynamic event-triggered consensus control for multi-agent systems under fixed and switching topologies

This paper is devoted to the dynamic event-triggered consensus problem of general linear multi-agent systems under fixed and switching directed topologies. Two distributed dynamic event-triggered strategies, where internal dynamic variables are involved, are introduced for each agent to achieve consensus asymptotically. Compared with the existing static triggering strategies, the purposed dynamic triggering strategies result in larger inter-execution times and less communication energy among agents. In addition, neither controller updates nor triggering threshold detections require continuous communication in the purposed control strategies. It is also proven that the Zeno behavior is strictly ruled out under fixed and switching directed topologies. Finally, the effectiveness of the theoretical analysis is demonstrated by numerical simulations.     

Distributed event-triggered adaptive finite-time consensus control for second-order multi-agent systems with connectivity preservation

In this paper, we consider the robust finite-time consensus problem for second-order multi-agent systems (MASs) with limited sensing range and weak communication ability. As a stepping stone, a novel distributed finite-time sliding mode manifold is developed for MASs. Then, by combining artificial potential function technique with the presented sliding mode manifold, a robust distributed control scheme is proposed to enable the finite-time consensus of MASs while preserving the prescribed communication connectivity. Furthermore, the sampling frequency and implementation burden of the proposed controller can be reduced with resort to the event-triggered methodology. Finally, numerical examples are given to show the effectiveness of the proposed method.     

Fixed-time bipartite consensus of nonlinear multi-agent systems using event-triggered control design

This paper focuses on designing a leader-following event-triggered control scheme for a category of multi-agent systems with nonlinear dynamics and signed graph topology. First, an event-triggered controller is proposed for each agent to achieve fixed-time bipartite consensus. Then, it is shown that the Zeno-behavior is rejected in the proposed algorithm. To avoid intensive chattering due to the discontinuous controller, the control protocol is improved by estimating the sign function. Moreover, a triggering function is proposed which avoids continuous communication in the event-based strategy. Finally, numerical simulations are given to show the accuracy of the theoretical results.     

Distributed disturbance observer based consensus control for linear multi-agent systems with mismatched disturbances

This paper proposes two kinds of distributed disturbance observer (DO) based consensus control laws for linear multi-agent systems (MAS) with mismatched disturbances. For a linear MAS with mismatched disturbances generated by exosystems, we design relative information based distributed DOs for each agent to obtain information of disturbances. The first method is to utilise the information of disturbances obtained by the distributed DO as a feedforward term to reject influence of exogenous disturbances for consensus results, where the gain matrix of the feedforward term is obtained via solving a matrix equation. The second method is to design an internal model based dynamic compensator to reject influence of exogenous disturbances, where the dynamic compensator is also updated by the distributed DO. The leaderless and leader-follower consensus are both considered in this paper, and rigorous proof of consensus results is also given. Finally, some numerical simulations verify effectiveness of the proposed consensus control laws.     

Distributed optimal consensus protocol for high-order integrator-type multi-agent systems

Optimal consensus control of high-order multi-agent systems (MASs) modeled by multiple integrator-type dynamics is studied. A fully distributed optimal control protocol that achieves the specific consensus behavior is designed for MASs with linear dynamics, where topology-dependent conditions are removed. Further, a distributed consensus protocol for high-order nonlinear MASs with one-sided Lipschitz continuity is presented using the optimization approach, and the optimal solution can be obtained by solving a standard algebraic Riccati equation. Some numerical examples are finally provided to illustrate the effectiveness of the presented approaches.     

Distributed control of cluster lag consensus for first-order multi-agent systems on QUAD vector fields

This paper addresses the problem of cluster lag consensus for first-order multi-agent systems which can be formulated as moving agents in a capacity-limited network. A distributed control protocol is developed based on local information, and the robustness of the protocol is analyzed by using tools of Frobenius norm, Lyapunov functional and matrix theory. It is shown that when the root agents of the clusters are influenced by the active leader and the intra-coupling among agents is stronger enough, the multi-agent system will reach cluster lag consensus. Moreover, cluster lag consensus for multi-agent systems with a time-varying communication topology and heterogeneous multi-agent systems with a directed topology are studied. Finally, the effectiveness of the proposed protocol is demonstrated by some numerical simulations.     

Distributed consensus of a class of networked heterogeneous multi-agent systems

In this paper, we consider the consensus problem of a class of heterogeneous multi-agent systems composed of the linear first-order and second-order integrator agents together with the nonlinear Euler–Lagrange (EL) agents. First, we propose a distributed consensus protocol under the assumption that the parameters of heterogeneous system are exactly known. Sufficient conditions for consensus are presented and the consensus protocol accounting for actuator saturation is developed. Then, by combining adaptive controller and PD controller together, we design a protocol for the heterogeneous system with unknown parameters (in the nonlinear EL dynamics). Based on graph theory, Lyapunov theory and Barbalat's Lemma, the stability of the controllers is proved. Simulation results are also provided to illustrate the effectiveness of the obtained results.     

Distributed consensus tracking control based on state and disturbance observations for mixed-order multi-agent mechanical systems

In this paper, we study the cooperative consensus control problem of mixed-order (also called hybrid-order) multi-agent mechanical systems (MMSs) under the condition of unmeasurable state, unknown disturbance and constrained control input. Here, the controlled mixed-order MMSs are consisted of the mechanical agents having heterogeneous nonlinear dynamics and even non-identical orders, which means that the agents can be of different types and their states to be synchronized can be not exactly the same. In order to achieve the ultimate synchronization of all mixed-order followers, we present a novel distributed adaptive tracking control protocol based on the state and disturbance observations. Wherein, a distributed state observer is used to estimate the followers’ and their neighbors’ unmeasurable states. And, a novel estimated-state-based disturbance observer (DOB) is proposed to reduce the effect of unknown lumped disturbance for the mixed-order MMSs. The proposed control protocol and observers are fully distributed and can be calculated for each follower locally. Lyapunov theory is used for proving the stability of the proposed control algorithm and the convergence of the cooperative tracking errors. A practical cooperative longitudinal landing control example of unmanned aerial vehicles (UAVs) is given to illustrate the effectiveness of the presented control protocol.     

Distributed bipartite consensus for multi-agent systems with dynamic event-triggered mechanism

This paper address the distributed bipartite consensus problem of multi-agent systems (MASs) under undirected and directed topologies with dynamic event-triggered (DET) mechanism. The relationship among agents not only collaborative interaction but also competitive interaction are taken into account. A novel DET control protocol is raised with internal dynamic variables to guarantee that each agent can reach the bipartite consensus. Compared with the existing static triggering laws, the introduced DET strategy can significantly enlarge the interval time between two triggering instants. In addition, continuous information transmission in either controller updating or between agent and its neighbors is not demanded, which implies that the communication frequency can be extremely decreased. It is also proven that Zeno behavior does not occur. Finally, two numerical examples verify the validity of the presented theoretical results.     

Containment control of fractional-order multi-agent systems with time-varying delays

In this paper, containment control problems of networked fractional-order multi-agent systems with time-varying delays are studied. The normalized directed graphs are employed to characterize the communication topologies. Two sampled-data based containment control protocols are proposed, which can overcome the time-varying delays and switching topologies. It is interestingly found that the decays of the closed-loop systems correspond to the Mittag-Leffler function and its approximation, which are the extensions of the exponential function and its approximation, respectively. Based on the algebraic graph theory, the properties of row-stochastic matrix, and the relation between the topologies and the matrices, some conditions for containment control are established. For the fixed topology, a necessary and sufficient condition is obtained; and for the switching topology, a sufficient condition is provided. Finally, the theoretical results are illustrated by several numerical simulations.     

Event-triggered time-varying formation control for general linear multi-agent systems

This paper investigates event-triggered formation control problems for general linear multi-agent systems. The time-varying formation this paper studied can be described by a bounded piecewise differentiable vector-valued function. Firstly, a time-varying formation control protocol based on event-triggered scheme is constructed by the states of the neighboring agents. Each agent broadcasts its state information to neighbor nodes if the triggering condition is satisfied, and the communication load is decreased significantly. Then, an algorithm consisting of three steps is proposed to design the event-triggered formation control protocol. Moreover, it is proven that under the designed event-triggered formation protocol, the multi-agent systems can achieve the desired time-varying formation which belongs to the feasible formation set with the bounded formation error and the closed systems do not exhibit Zeno behavior. Finally, simulation results are given to demonstrate the effectiveness of the theoretical analysis.     

Distributed state estimator-based consensus tracking of multi-agent systems with exogenous disturbance

The consensus tacking problem for multi-agent systems with a leader of none control input and unknown control input is studied in this paper. By virtue of the relative state information of neighboring agents, state estimator and disturbance estimator are designed for each follower to estimate the system states and exogenous disturbance, respectively. Meanwhile, a novel control protocol based on two estimators is designed to make tracking error eventually converge to zero. Furthermore, the obtained results are further extended to the leader with unknown control input. A novel state estimator with adaptive time-varying gain is proposed such that consensus tracking condition is independent of the Laplacian matrix with regard to the communication topology. Finally, two examples are presented to verify the feasibility of the proposed control protocol.     

Data-driven control of consensus tracking for discrete-time multi-agent systems

This paper investigates the consensus tracking problem of leader-follower multi-agent systems. Different from most existing works, dynamics of all the agents are assumed completely unknown, whereas some input-output data about the agents are available. It is well known from the Willems et al. Fundamental Lemma that when inputs of a linear time-invariant (LTI) system are persistently exciting, all possible trajectories of the system can be represented in terms of a finite set of measured input-output data. Building on this idea, the present paper proposes a purely data-driven distributed consensus control policy which allows all the follower agents to track the leader agent’s trajectory. It is shown that for a linear discrete-time multi-agent system, the corresponding controller can be designed to ensure the global synchronization with local data. Even if the data are corrupted by noises, the proposed approach is still applicable under certain conditions. Numerical examples corroborate the practical merits of the theoretical results.     

Distributed data driven control for multi-agent consensus with unknown system dynamics

This study investigates the consensus tracking problem for unknown multi-agent systems (MASs) with time-varying communication topology by using the methods of data-driven control and model predictive control. Under the proposed distributed iterative protocol, sufficient conditions for reducing tracking error are analyzed for both time invariable and time varying desired trajectories. The main feature of the proposed protocol is that the dynamics of the multi-agent systems are not required to be known and only local input-output data are utilized for each agent. Numerical simulations are presented to illustrate the effectiveness of the derived consensus conditions.     

Dissipative consensus problems for multi-agent networks via sliding mode control

In this paper, dissipative consensus problems are discussed for multi-agent networks. Firstly, sufficient conditions are proposed to ensure $(Q,S,R)?$dissipative consensus for multi-agent networks with external disturbances. Then, by designing an integral-type sliding surface function, a controller is obtained and the corresponding sufficient conditions are given to guarantee $(Q,S,R)?$dissipative consensus for multi-agent networks with external disturbances. Moreover, the sliding mode control law is formulated such that multi-agent networks drive onto the predefined surface in finite time. Finally, an example is given to illustrate the effectiveness of the obtained results.     

Predefined-time practical consensus for multi-agent systems via event-triggered control

This paper studies the predefined-time practical consensus problem for multiple single-integrator systems through event-triggered control. A new kind of time-varying functions is firstly proposed. Then, new event-triggered control inputs as well as triggering conditions are designed on the basis of the time-varying function and the local broadcasted states. In particular, the control scheme is fully-distributed because no global information of the system and the communication topology is needed. Furthermore, the consensus analysis is presented based on a sufficient condition for predefined-time practical stability. It illustrates that practical consensus can be ensured with a completely pre-specified time. Besides, the exclusion of Zeno behavior at all the time instants is addressed. Numerical results verify the validity of the obtained control method.     

Leader-following fixed-time quantized consensus of multi-agent systems via impulsive control

In this paper, we mainly tend to consider distributed leader-following fixed-time quantized consensus problem of nonlinear multi-agent systems via impulsive control. An appropriate quantized criterion and some novel control protocols are proposed in order to solve the problem. The protocols proposed integrates the two control strategies from the point of view of reducing communication costs and constraints, which are quantized control and impulsive control. The fixed-time quantized consensus of multi-agent is analyzed in terms of algebraic graph theory, Lyapunov theory and comparison system theory, average impulsive interval. The results show that if some sufficient conditions are met, the fixed-time consensus of multi-agent systems can be guaranteed under impulsive control with quantized relative state measurements. In addition, compared with finite-time consensus, the settling-time of fixed-time quantized consensus does not depend on the initial conditions of each agent but on the parameters of the protocol. Finally, numerical simulations are exploited to illustrate the effectiveness and performance to support our theoretical analysis.