Global Mittag-Leffler consensus for fractional singularly perturbed multi-agent systems with discontinuous inherent dynamics via event-triggered control strategy

In this paper, the global Mittag-Leffler consensus tracking issue is considered for fractional singularly perturbed multi-agent systems (FSPMASs) based on event-triggered control strategy, where the inherent dynamic is modeled to be a discontinuous function with nondecreasing property. Firstly, a differential inequality with respect to fractional-order derivative of convex function is developed. As the special cases, the inequalities about fractional-order derivative of three known functions are also addressed. Secondly, a distributed event-triggered control scheme is designed to guarantee that the considered FSPMASs can achieve the global Mittag-Leffler consensus. Moreover, the Mittag-Leffer convergence speed of tracking the leader for followers can be adjusted to any desired values in advance. In addition, under fractional Filippov differential inclusion framework, by applying Lur’e Postnikov-type Lyapunov functional with variable upper limit integral item and Clarke’s non-smooth analysis technique, the global Mittag-Leffler consensus conditions are addressed in terms of matrix inequalities (MIs). Finally, two numerical simulations are provided to illustrate the validity of the proposed design method and theoretical results.     

Distributed tracking control of second-order multi-agent systems with sampled data

This paper studies the leader–follower consensus problem of second-order multi-agent dynamical systems with fixed and stochastic switching topologies in a sampled-data setting. A distributed linear consensus protocol is designed to track an active leader, where the current position information of neighbor agents and self-velocity data are utilized. A necessary and sufficient condition is established under fixed and directed topology for reaching consensus, which depends on the sampling period and control gain parameters. A sufficient condition is obtained under the Markov switching topology case. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results.     

Sampled-data-based event-triggered secure bipartite tracking consensus of linear multi-agent systems under DoS attacks

This paper investigates secure bipartite consensus tracking of linear multi-agent systems under denial-of-service(DoS) attacks by using event-triggered control mechanism with data sampling. Both bipartite leader-following and containment tracking consensus are considered in this paper. The event-triggered control protocol using sampled-data information is designed to save limited resources. The communication channels are interrupted by intermittent DoS attacks. Sufficient conditions on the sampling periods, attack frequency and attack duration are obtained to ensure secure bipartite tracking consensus of the multi-agent systems. Finally, simulation example is provided to illustrate the effectiveness of the theoretical results.     

Adaptive observer-based event-triggered finite time formation tracking for multi-agent systems with a non-cooperative leader

The event-triggered time-varying formation tracking for a class of second-order multi-agent systems (MASs) subject to a non-cooperative leader is investigated in this paper. First, in the presence of the unknown input of the leader and external disturbances, a distributed observer with adaptive parameters is put forward for followers to estimate the velocity tracking error. Then, based on the estimated tracking error and an auxiliary variable, a finite time formation controller is further constructed, which is updated depending on a pre-designed event-triggered mechanism. As a result, the desired time-varying formation configuration can be realized in finite time with less communication resource consumption. It’s noted that the constructed formation strategy doesn’t rely on any global information and thus is fully distributed. The stability of the controlled multi-agent system is proved rigorously and it’s verified that event-triggered intervals are with a positive lower bound. At last, simulations are carried out to illustrate the effectiveness of the presented algorithm.     

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.     

Switched observer-based dynamic event-triggered consensus of multi-agent systems under DoS attacks

This paper investigates the observer-based consensus control for high-order nonlinear multi-agent systems (MASs) under denial-of-service (DoS) attacks. When the DoS attacks appear, the communication channels are destroyed, and the blocked information may ruin the consensus of MASs. A switched state observer is designed for the followers to observe the leader’s state whether the DoS attacks occur or not. Then, a dynamic event-triggered condition is proposed to reduce the consumption of communication resources. Moreover, an observer-based and dynamic event-triggered controller is formulated to achieve leader-following consensus through the back-stepping method. Additionally, the boundedness of all closed-loop signals is obtained based on the Lyapunov stability theory. Finally, the simulation results demonstrate the effectiveness of the presented control strategy under DoS attacks.     

Practical time-varying output formation tracking for high-order multi-agent systems with collision avoidance,obstacle dodging and connectivity maintenance

Practical time-varying output formation tracking problems with collision avoidance, obstacle dodging and connectivity maintenance for high-order multi-agent systems are investigated, and the practical time-varying output formation tracking error is controlled within an arbitrarily small bound. The outputs of followers are designed to track the output of the leader with unknown control input while retaining the predefined time-varying formation. Uncertainties are considered in the dynamics of the followers and the leader. Firstly, distributed extended state observers are developed to estimate the uncertainties and the leader’s unknown control input. A strategy of obstacle dodging is given by designing an ideal secure position for the followers which are in the threatened area of the obstacles. By constructing collision avoidance, obstacle dodging and connectivity maintenance artificial potential functions, corresponding negative gradient terms are calculated to achieve the safety guarantee. Secondly, a practical time-varying output formation tracking protocol is proposed by using distributed extended state observers and the negative gradient terms. Additionally, an approach is presented to determine the gain parameters in the protocol. The stability of the closed-loop multi-agent system with the protocol is analyzed by using Lyapunov stability theory. Finally, a simulation experiment is provided to illustrate the effectiveness of the obtained methods.     

Disturbance observer-based fixed-time leader-following consensus control for multiple Euler–Lagrange systems: A non-singular terminal sliding mode scheme

This paper focuses on the fixed-time leader-following consensus problem for multiple Euler–Lagrange (EL) systems via non-singular terminal sliding mode control under a directed graph. Firstly, for each EL system, a local fixed-time disturbance observer is introduced to estimate the compound disturbance (including uncertain parameters and external disturbances) within a fixed time under the assumption that the disturbance is bounded. Next, a distributed fixed-time observer is designed to estimate the leader’s position and velocity, and the consensus problem is transformed into a local tracking problem by introducing such an observer. On the basis of the two types of observers designed, a novel non-singular terminal sliding surface is proposed to guarantee that the tracking errors on the sliding surface converge to zero within a fixed time. Furthermore, the presented control algorithm also ensures the fixed-time reachability of the sliding surface, while avoiding the singularity problem. Finally, the effectiveness of the proposed observers and control protocol is further verified by a numerical simulation.     

Leader-following successive lag consensus of nonlinear multi-agent systems via observer-based event-triggered control

This article investigates the leader-following successive lag consensus (SLC) for nonlinear multi-agent systems (NMASs) via the observer-based event-triggered control (OBETC), in which two scenarios including constant consensus delay and time-varying consensus delay are considered. Since the system states might not be directly available in actual scenes, the state estimation method is utilized for followers to track their full information. Based on the relative state, a class of distributed event-triggered control protocols is constructed, where the event-triggered strategy is introduced such that each follower can determine the broadcasting time to its neighbors. Obviously, these designed control protocols considerably lessen the expense over communication networks and the frequency of protocol updates. Furthermore, with the aid of the Lyapunov function method, a series of sufficient conditions for guaranteeing the leader-following SLC of NMASs is obtained. Meanwhile, it is proved that no Zeno behavior is exhibited. Finally, several numerical examples are given to illustrate the validity of our theoretical results.     

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.     

A new on-line observer-based controller for leader-follower formation of multiple nonholonomic mobile robots

In this paper, a novel on-line observer-based trajectory tracking strategy for leader-follower formation of multiple nonholonomic mobile robots is developed. In the proposed strategy, a leader robot follows a certain trajectory whereas a number of followers track the leader as specified by a formation protocol. Unlike other techniques in the literature, a predefined trajectory is not required, and it can be changed on-line. Moreover, this strategy aims to have a fast transient response without showing undesired overshoots. To achieve this feature, a new observer is introduced. Based on the output of that observer, a control strategy with two components is derived. The first control component is responsible for tracking the desired trajectory, whereas the second control component is used to regulate the robot to its desired steady state position. The stability of the closed loop control system is investigated. Applications of the proposed observer-based controller to different case studies are presented to illustrate the effectiveness, robustness and applicability of the developed technique. To show the superiority of proposed controller, its performance in a trajectory tracking application is compared to that of a Lyapunov-based controller.     

Observer-based event-triggered tracking consensus of non-ideal general linear multi-agent systems

In this paper, the leader-following consensus problem of general linear multi-agent systems without direct access to real-time state is investigated. A novel observer-based event-triggered tracking consensus control scheme is proposed. In the control scheme, a distributed observer is designed to estimate the relative full states, which are used in tracking consensus protocol to achieve overall consensus. And an event-triggered mechanism with estimated state-dependent event condition is adopted to update the control signals so as to reduce unnecessary data communication. Based on the Lyapunov theorem and graph theory, the proposed event-triggered control scheme is proved to implement the tracking consensus when real-time state cannot direct obtain. Moreover, such scheme can exclude Zeno-behavior. Finally, numerical simulations illustrate the effectiveness of the theoretical results.     

Aperiodically intermittent output feedback consensus control for second-order leader-following multi-agent systems based on observer

This study examines the leader-following consensus problem of a class of second-order nonlinear multi-agent systems, where the velocity information is supposed to be unmeasurable. Under the setting, this paper presents a novel aperiodically intermittent output feedback control protocol such that all followers reach consensus with the leader, in which a distributed state observer is built for each follower to observe the velocity state. Based on the Lyapunov stability theory and some matrix analysis techniques, a couple of sufficient conditions for the leader-following consensus of the nonlinear multi-agent system under study are obtained even though the velocity state is unavailable. Finally, the effectiveness of the theoretical results is verified by numerical simulation.     

Event-triggered bipartite consensus for nonlinear multi-agent systems under switching topologies: A time-varying gain method

In this paper, the event-triggered bipartite consensus problem is investigated for nonlinear multi-agent systems under switching topologies, only part of topologies contain directed spanning tree rooted at the leader. First, a dynamic bipartite compensator is constructed based on relative output information to provide control signal. Then, the time-varying gain method is adopted to propose a compensator-based event-triggered control protocol without Zeno behavior. Notably, the control protocol proposed achieves the bipartite consensus while reducing update frequency effectively. Moreover, a low conservative switching law is designed by the topology-dependent average dwell time strategy, which fully considers the differences among topologies and provides an independent average dwell time for each topology. As an extension, the nonlinear multi-agent systems with non-zero input of leader are further studied. Finally, a practical example is presented to demonstrate the feasibility of proposed control protocol.     

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.     

Decentralized event-triggered finite-time attitude consensus control of multiple spacecraft under directed graph

This article investigates the finite-time consensus problem for the attitude system of multiple spacecraft under directed graph, where the communication bandwidth constraint, inertia matrix uncertainties and external disturbances are considered. An event-triggered communication mechanism is developed to address the problem of communication bandwidth constraint. In this event-triggered mechanism, spacecraft sends their attitude information to their neighbors only when the given event is triggered. Furthermore, an adaptive law is designed to counteract the effect of inertia matrix uncertainties and external disturbances. Then, a finite-time attitude consensus tracking control scheme is proposed based on the event-triggered communication mechanism and adaptive law. The proposed control scheme can guarantee the finite-time stability and convergence of the multiple spacecraft systems and exclude the Zeno phenomenon. Finally, simulation results validate the effectiveness of the proposed control scheme.     

Time-varying output formation tracking of heterogeneous linear multi-agent systems with multiple leaders and switching topologies

This paper studies the time-varying output formation tracking problems for heterogeneous linear multi-agent systems with multiple leaders in the presence of switching directed topologies, where the agents can have different system dynamics and state dimensions. The outputs of followers are required to accomplish a given time-varying formation configuration and track the convex combination of leaders’ outputs simultaneously. Firstly, using the neighboring relative information, a distributed observer is constructed for each follower to estimate the convex combination of multiple leaders’ states under the influences of switching directed topologies. The convergence of the observer is proved based on the piecewise Lyapunov theory and the threshold for the average dwell time of the switching topologies is derived. Then, an output formation tracking protocol based on the distributed observer and an algorithm to determine the control parameters of the protocol are presented. Considering the features of heterogeneous dynamics, the time-varying formation tracking feasible constraints are provided, and a compensation input is applied to expand the feasible formation set. Sufficient conditions for the heterogeneous multi-agent systems with multiple leaders and switching directed topologies to achieve the desired time-varying output formation tracking under the designed protocol are proposed. Finally, simulation examples are given to validate the theoretical results.     

Event-triggered consensus control for second-order multi-agent system subject to saturation and time delay

The event-triggered consensus control for second-order multi-agent systems subject to actuator saturation and input time delay, is investigated in this paper. Based on the designed triggering function, a distributed event-triggered control strategy is presented to drive the system to achieve consensus. Communication energy can be saved as the agents send their state information only at infrequent event instants, the continuous communication among agents is not necessary. Lyapunov-Krasovskii functional is used together with linear matrix inequality technique to analyze the stability of the closed-loop error system. The results show that agents achieve exponentially consensus under the proposed controller. Furthermore, the bounds of solution are obtained by establishing the differential equation associated with the first delay interval. The initial domain is estimated by optimizing the linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed controller.     

Disturbance-observer-based formation-containment control for UAVs via distributed adaptive event -triggered mechanisms

In this paper, the adaptive event-triggered formation-containment control for unmanned aerial vehicles (UAVs) is investigated in the presence of multiple leaders and external disturbances. By utilizing the leader-following model, the reference leader provides the desired flight trajectory for multiple formation leaders while the followers are driven into the convex hull spanned by the formation leaders. Initially, some effective disturbance observers are designed to obtain the estimations for eliminating the negative effects of external disturbances. Secondly, in order to alleviate the network burden, a dynamic triggering law is designed for the adaptive event-triggered mechanism (AETM) and the triggering frequency is heavily related to the triggering errors. Then, by exploiting Kronecker product technique and Lyapunov stability theory, two sufficient conditions on the stability of closed-loop system are established, which can help achieve the desired formation control target. Furthermore, the controller gains and observer ones can be determined by calculating the derived linear matrix inequalities (LMIs). Finally, a simulation example is given to illustrate the feasibility of the designed control protocol.     

Observer-based distributed fault detection and isolation for second-order multi-agent systems using relative information

This paper considers fault detection and isolation problem for second-order leader-follower multi-agent systems in a distributed setting. With the existing tracking protocol, an observer is constructed at each agent based on the concept of unknown input observer using relative information between the agent and its neighbors. Fault in position, velocity, both position and velocity dynamics are considered separately. Based on the residual signal generated from the designed observer, two algorithms are proposed so that the faulty agent in network can be detected and isolated simply. Effectiveness of the presented strategy is validated by some application examples.