A novel reset control approach to leader-following consensus of second-order nonlinear multi-agent systems

This paper investigates the leader-following consensus problem of second-order nonlinear multi-agent systems with directed graph. A novel reset control approach is proposed for the aim of improving transient consensus performance, e.g., settling time. By introducing consensus error into reset conditions, the output of reset integrator will keep the same sign with the consensus error, thus, the desired states can be compensated preferentially and the system transient performance is improved accordingly. To appropriately describe the closed-loop system with reset-induced jump dynamics, a hybrid system model consisting of both flow dynamics and jump dynamics is constructed. Based on this model, and combined with backstepping method, Lyapunov-based consensus analysis is presented under hybrid system framework. Finally, a numerical example is provided to show the effectiveness of the obtained results.     

Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data

This paper deals with the leader-following consensus problem of multi-agent systems with the consideration that each agent can only transmit its position state to the neighbors at irregular discrete sampling times. In the proposed algorithm, a continuous-discrete time observer is designed for the continuous estimation of both position and velocity from the discrete position information of the neighbors. These estimated states are then used for designing a continuous control law which solves the leader-following consensus problem. Moreover, the dynamics of the leader is not fixed and can be controlled through an external input. The stability analysis has been carried out by employing the Lyapunov approach which provides sufficient conditions to tune the parameters according to the maximum allowable sampling period. The developed algorithm has been simulated and then tested on an actual multi-robot system consisting of three differential drive wheeled robots. Both simulation and hardware results validate the effectiveness of the control algorithm.     

Event-triggered bipartite leader-following consensus of second-order nonlinear multi-agent systems under signed digraph

This paper investigates the bipartite leader-following consensus of second-order multi-agent systems with signed digraph topology. To significantly reduce the communication burden, an event-triggered control algorithm is proposed to solve the bipartite leader-following consensus problem, where a novel event-triggered function is designed. Under some mild assumptions on the network topology and node dynamics, a sufficient condition is derived using Lyapunov stability method and matrix theory to guarantee the bipartite consensus. In particular, it is shown that the continuous communication can be avoided and the Zeno-behavior can be excluded for the designed event-triggered algorithm. Numerical simulations are presented to illustrate the correctness of the theoretical analysis.     

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.     

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.     

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 rotating formation control of second-order leader-following multi-agent systems with nonuniform delays

In this paper, the leader-following rotating formation control problem is investigated for second-order multi-agent systems with nonuniform time-delays. We propose a distributed algorithm to drive all agents to achieve a desired formation and orbit around a common point. By a frequency domain analysis method, the upper bound of the maximum time-delay is obtained. Finally, a numerical simulation is given to illustrate the obtained results.     

Finite-time consensus for the second-order leader-following nonlinear multi-agent system with event-triggered communication

This study discusses the finite-time consensus for the second-order leader-following nonlinear multi-agent system with event-triggered communication. An event-triggered control protocol is established to achieve finite-time consensus, which can effectively avoid the Zeno behavior. Due to the unevenness of an event-triggered controller and the occurrence of the event-triggered condition, it is more challenging to analyze the event-triggered finite-time consensus. Based on the knowledge of graph theory, all agents can achieve finite-time consensus via the proposed event-triggered control protocol. Different from homogeneity, a Lyapunov function is constructed to obtain the settling time. Finally, a simulation example illustrates the validity of the main results.     

Fractional-order follower observer design for tracking consensus in second-order leader multi-agent systems: Periodic sampled-based event-triggered control

This paper investigates the tracking consensus problem for the second-order leader systems by designing fractional-order observer, where a periodic sampled-based data event-triggered control is employed. In order to track the position information of leader, observers for followers are designed by fractional-order system, where only the relative position information is available. Furthermore, in the process of observers design, a sampled-based event-triggered strategy is proposed so that observers use the event-triggered sampled-data, to reduce the overall load of the network. In our proposed event-triggered strategy, the event detection only works at every sampling time instant which determines whether the sampled-data should be discarded or used. Under this control strategy, the Zeno-behavior is absolutely excluded since the minimum of inter-event times is inherently lower bounded by one sampling period. It is found that the followers can track state of the leader if fractional-order observers are appropriately designed and relevant parameters are properly selected. By using the generalized Nyquist stability criterion, a necessary and sufficient condition for the observer tracking consensus of the second-order leader systems is derived. The results show that the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix, and fractional-order α of observer play a vital role in reaching consensus.     

Dynamic event-triggered leader-following consensus control of a class of linear multi-agent systems

We address the leader-following tracking consensus issue for a class of linear multi-agent systems (MASs) via dynamic event-triggered (DET) approaches in this paper. The DET communication mechanism is introduced by an additional internal dynamic variable, and is developed to schedule agents’ data transmission. State observers are also employed to tackle the scenario wherein inner information of follower agents are not available for measurement. And then, state-based and observer-based distributed control proposals are proposed on the basis of dynamic event-triggered mechanism (DETM), respectively. To avoid continuous measurement information monitor, we present a technical approach for generation of the combinational information from their own neighboring agents only at event instants. The stabilities of the resulting closed-loop systems, both state-feedback one and output-feedback one, are rigorously analyzed in theory, and it is proven that all signals in the closed-loop system are bounded and Zeno behavior is also excluded. Simulation examples are presented to illustrate the theoretical claims.     

Second-order group consensus for multi-agent systems via pinning leader-following approach

This paper addresses the group consensus problem of second-order nonlinear multi-agent systems through leader-following approach and pinning control. The network topology is assumed to be directed and weakly connected. The pinning consensus protocol is designed according to the agent property, that is, the inter-act agent and the intra-act agent. Some consensus criteria are proposed to guarantee that the agents asymptotically follow the virtual leader in each group, while agents in different groups behave independently. Numerical example is also provided to demonstrate the effectiveness of the theoretical analysis.     

Interval observer based event-triggered consensus control of networked multi-agent systems under DoS attacks

This paper presents an interval observer (IO) based event-triggered control strategy for networked multi-agent systems (MASs) under denial of service (DoS) attacks. The most significant contribution is the proposal of a new event-triggered controller based on distributed IO. Toward this, first, a new distributed IO based on output information is first constructed to estimate the state interval of each agent in the networked MASs. Then a novel distributed IO based event-triggered control (ETC) protocol is constructed using only the information observed by IO. Moreover, it turns out that based on the designed IO based ETC protocol, all agents can reach secure consensus exponentially and Zeno behavior is excluded. Finally, simulation example is used to verify the feasibility of the constructed IO based ETC protocol.     

Sliding-mode consensus algorithms for disturbed second-order multi-agent systems

In this paper, both leaderless and leader-follower consensus problems for a class of disturbed second-order multi-agent systems are studied. Based on integral sliding-mode control, sliding-mode consensus protocols are proposed for leaderless and leader-follower multi-agent systems with disturbances, respectively. Firstly, for leaderless second-order multi-agent systems, a sliding-mode consensus protocol is proposed to make the agents achieve asymptotic consensus. Secondly, for leader-follower second-order multi-agent systems, a finite-time sliding-mode consensus protocol is designed to make the agents achieve consensus in finite time. Both kinds of consensus protocols inherit the anti-disturbance performance and robustness of sliding-mode control and require less communication information. Finally, two numerical simulations are given for leaderless and leader-follower second-order multi-agent systems to validate the efficiency of the proposed consensus protocols.     

Containment control for second-order nonlinear multi-agent systems with aperiodically intermittent position measurements

In some real systems, the intermittent communications and the inaccurate velocity measurements are usually inevitable. To overcome these two communication limitations, this article aims at investigating the containment control problem for a class of second-order multi-agent systems with inherent nonlinear dynamics and aperiodically intermittent position measurements. Under the case that the velocity information is unavailable, a distributed filter is introduced for each second-order follower. Based on the distributed filter, a novel intermittent containment control protocol without velocity measurements is designed. Some sufficient conditions are derived under the common assumption that only relative position measurements between the neighbouring agents are utilized intermittently, and these conditions ensure that the second-order nonlinear multi-agent systems can achieve containment control. Furthermore, some simpler containment conditions are obtained for multi-agent systems with double-integrator dynamics under aperiodically intermittent communications. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.     

Reset output feedback control of cluster linear multi-agent systems

In this study, the distributed output consensus control issue is investigated for a class of linear cluster multi-agent systems (CMASs) under the control strategy of the reset observer. We consider a communication network consisting of several clusters, each of which is directed and contains a leader. The interactions among agents include continuous-discrete hybrid communication. Specifically, an instantaneous connectivity only exists between the clusters at discrete moments, called the reset time sequence. At the reset time, an instantaneous fixed directed network is formed such that only the leaders will consider the available information of neighboring leaders to reset their own states. During non-reset intervals, only the intra-clusters are connected while the inter-clusters are equivalent to a disconnected network topology. Considering that in practice, the state information may be partially unavailable, only the relative output information is utilized to estimate the unavailable state and thus control protocols are developed with the help of the reset full-order and reduced-order observers, respectively. The stability of the closed-loop CMAS at both the reset time and non-reset intervals is studied based on Lyapunov analysis. The consensus value depends only on the initial conditions and the network topology involved, and not on the reset time sequence. Finally, numerical simulations are provided to illustrate the theoretical results.     

Stochastic leader-following consensus of discrete-time nonlinear multi-agent systems with multiplicative noises

This paper studies the stochastic leader-following consensus problem of discrete-time nonlinear multi-agent systems (MASs) with multiplicative noises. The measurement information obtained from agents’ neighbors is inevitably affected by communication uncertainties, where the multiplicative noise is one of the important communication uncertainties. Multiplicative noises together with the intrinsic nonlinear dynamics bring more difficulties in the consensus control design under the leader-following topology. To solve the problem, the parameter-dependent Lyapunov functions are constructed to analyze the consensus control of first-order and second-order MASs, respectively. Some sufficient conditions, explicitly related to control gains, intensity of multiplicative noises and the Lipschitz constant regarding nonlinear functions, are established for reaching the mean square (m.s.) and almost sure (a.s.) leader-following consensus. Specifically, the obtained conditions are some scalar inequalities, which are more convenient in engineering application. Numerical simulations are conducted to validate the theoretical results.     

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.     

Event-triggered consensus for second-order multi-agent systems with sampled position data via impulsive control

In this paper, the sampled-data-based event-triggered (SDBET) consensus problem of second-order multi-agent systems (MASs) with sampled position data is studied via impulsive control. Firstly, two kinds of SDBET impulsive control protocols are proposed, both of which employ sampled position data only. Secondly, a novel SDBET transmission scheme is designed to ensure the maximum length of triggering intervals exists, which can be regulated by the parameters in the triggering function. Also, the Zeno behavior is naturally excluded under the SDBET transmission scheme. And by using the designed SDBET impulsive control scheme, consensus of second-order MASs can be achieved with lower transmission and control updating frequency than using the periodical impulsive control scheme. Thirdly, sufficient conditions on the communication topology, the length of triggering intervals and control gains are derived to achieve SDBET consensus. It is also shown that to achieve consensus, both the maximum and minimum lengths of triggering intervals should be restricted. Also, a practical method for calculating the sampling period and other triggering parameters is given to ensure that the length of the triggering interval does not exceed the given range, and the SDBET transmission scheme is truly realized. Finally, some numerical examples are given to demonstrate the effectiveness of the theoretical results.     

Quantized consensus in second-order multi-agent systems via event-trigger control with sampled data

This paper addresses the quantized consensus problem of second-order multi-agent systems (MASs) where the topology has a directed spanning tree. An event-trigger control protocol (ETCP) is proposed by designing a combined threshold. The combined threshold not only reduces more event triggers than the state-dependent threshold, but also is more practical than the time-dependent threshold. For further reducing computation resources and transmission cost, the sampled data, self-trigger scheme and data quantization are employed together. Under the proposed ETCP, the sufficient condition is derived to guarantee the quantized consensus of second-order MASs. Finally, the comparison experiments are conducted to demonstrate the superiority of ETCP based on the combined threshold.     

Memory-based event-triggered leader-following consensus for T-S fuzzy multi-agent systems subject to deception attacks

In this paper, the problem of fuzzy model-based leader-following consensus control for multi-agent systems (MASs) under deception attacks is investigated. For the sake of alleviating the communication burden, a novel memory-based event-triggered scheme (METS) is first proposed for the considered MASs to reduce redundant data transmission, and the leader-following consensus can be achieved faster with a smaller adjustment error by applying the historical released packets. Considering the designed METS and upper-bounded attacks synthetically, the closed-loop fuzzy system model is well established. Furthermore, with the help of Lyapunov-Krasovskii technique, some sufficient conditions are derived to ensure the consensus of MASs subject to deception attacks. Finally, a simulation example is introduced to manifest the effectiveness of the proposed method.