Distributed event‐triggered containment control for dynamical multiagent networks

This paper studies the event‐triggered containment control problem for dynamical multiagent networks of general MIMO linear agents. An event‐triggered containment control strategy is provided, which consists of a control law based on a relative‐state feedback and a distributed triggering rule based on both the relative‐state information and a time‐dependent threshold function. Compared to the previous related works, our main contribution is that the triggering rule depends only on local information of communication networks. It is proved that under the proposed event‐based controller, the containment errors are uniformly ultimately bounded and the Zeno behavior can be excluded. Moreover, when the derivation constant in the threshold function is equal to zero, the containment control problem can be solved. Then, the results are extended to the event‐triggered observer‐based containment controller design.     

Robust event‐triggered control of second‐order disturbed leader‐follower MASs: A nonsingular finite‐time consensus approach

This paper addresses the finite‐time and the prescribed finite‐time event‐triggered consensus tracking problems for second‐order multi‐agent systems (MASs) with uncertain disturbances. The prescribed finite‐time event‐triggered consensus of the second‐order disturbed MASs was obtained for the first time and the controller is nonsingular. Furthermore, a new self‐triggered control scheme is presented for the finite‐time consensus tracking, and the continuous communication can be avoided in the triggering condition monitoring. Hence, the finite‐time consensus tracking can be achieved with intermittent communication. Moreover, Zeno behavior is excluded for each follower. The efficiency of the proposed algorithms is verified by numerical simulations.     

Distributed event‐triggered fixed‐time consensus for leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances

This paper focuses on the distributed event‐triggered fixed‐time consensus control problem of leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances. Two distributed fixed‐time consensus protocols are proposed based on distributed event‐triggered strategies, which can substantially reduce energy consumption and the frequency of the controller updates. It is proved that under the proposed distributed event‐triggered consensus tracking control strategies, the Zeno behavior is avoided. Compared with the finite‐time consensus tracking, the fixed‐time consensus tracking can be achieved within a settling time regardless of the initial conditions. Finally, 2 examples are performed to validate the effectiveness of the distributed event‐triggered fixed‐time consensus tracking controllers.     

Decentralized event‐triggered circle formation control for multiagent systems via synchronous periodic event detection

This paper investigates circle formation problem of multiagent systems over a kind of strongly connected and weight‐unbalanced directed graphs. To solve the concerned problem, decentralized periodic event‐triggered algorithms subject to or not to time delays are proposed, which have the advantages of decreasing the overall burden of the network in terms of finite communication and control input updates. In such algorithms, each agent independently evaluates whether the locally sampled information of itself should be broadcasted to or not to its neighbors. Furthermore, another advantage of our proposed algorithms is to automatically exclude Zeno behavior, which should be seriously considered in a variety of event‐based network systems. Sufficient conditions on circle formation control are derived under which the states of all agents can be ensured to converge to some desired equilibrium point. Simulation results are given to validate the effectiveness of the proposed methods.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Data‐driven optimal event‐triggered consensus control for unknown nonlinear multiagent systems with control constraints

This paper considers optimal consensus control problem for unknown nonlinear multiagent systems (MASs) subjected to control constraints by utilizing event‐triggered adaptive dynamic programming (ETADP) technique. To deal with the control constraints, we introduce nonquadratic energy consumption functions into performance indices and formulate the Hamilton‐Jacobi‐Bellman (HJB) equations. Then, based on the Bellman's optimality principle, constrained optimal consensus control policies are designed from the HJB equations. In order to implement the ETADP algorithm, the critic networks and action networks are developed to approximate the value functions and consensus control policies respectively based on the measurable system data. Under the event‐triggered control framework, the weights of the critic networks and action networks are only updated at the triggering instants which are decided by the designed adaptive triggered conditions. The Lyapunov method is used to prove that the local neighbor consensus errors and the weight estimation errors of the critic networks and action networks are ultimately bounded. Finally, a numerical example is provided to show the effectiveness of the proposed ETADP method.     

Leaderless and leader‐following fixed‐time consensus for multiagent systems via impulsive control

This article addresses the leaderless fixed‐time consensus (LLFTC) and leader‐following fixed‐time consensus (LFFTC) problems for multiagent systems (MASs) via impulsive control. First, a novel fixed‐time stability for impulsive dynamical system is developed. Then the novel fixed‐time impulsive control protocols are designed to achieve leaderless and leader‐following consensus for MASs. Based on the impulsive control theory, fixed‐time stability theory and algebraic graph theory, some sufficient conditions are derived for each agent to achieve LLFTC and LFFTC under the proposed control protocols. Finally, numerical simulations are put forward to validate the theoretical results.     

Bounded consensus for multiagent systems by event‐triggered data transmission,time delay,and predictor‐based control

This paper investigates the consensus issue of multiagent systems with data transmission time delay. The state measurement of each local agent is directly sent to a private event‐trigger and further authorized to be broadcasted to its neighbors via communication network only when the threshold of the event‐trigger is violated. Since the controller always receives discrete‐time neighbor information with data transmission time delay, a predictor is employed to estimate the continuous‐time neighbor state. Based on the estimated state, a novel consensus protocol is mainly proposed for achieving the bounded consensus of the multiagent systems. By the proposed method, the asynchronous neighbor information is allowed and the margin of data transmission time delay is also given. Furthermore, it has been proved that the unwanted Zeno phenomena can be naturally excluded. Numerical example is provided to demonstrate the effectiveness of the proposed method.     

Distributed integral‐type event‐triggered synchronization of multiagent systems

This paper investigates the synchronization problem of generic linear multiagent systems via integral‐type event‐triggered control. Each agent can only utilize the intermittent information of its neighboring agents in the control scheme. Based on the integral‐type event conditions, an event‐triggered control protocol is designed to guarantee the synchronization of multiagent systems, and Zeno behavior is excluded by showing the existence of a positive lower bound on the inter‐event intervals. Then, we propose the integral‐type event‐triggered control algorithms to study the leader‐following synchronization. It is shown that under the control algorithms all the followers track the leader and no Zeno behavior occurs. The effectiveness of the proposed control schemes is demonstrated by simulation examples.     

Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

An adaptive fixed‐time trajectory tracking controller is proposed for uncertain mechanical systems in this study. The polynomial reference trajectory is planned for trajectory tracking error. Fractional power of linear sliding mode is applied to design the nonlinear controller, adaptive laws are used to adjust controller parameters. Trajectory planning and fractional power are combined to ensure the tracking‐error convergence in a fixed time. The boundary layer technique is used to suppress the model uncertainties and decrease the chattering phenomenon. The closed‐loop system stability is proved strictly in the Lyapunov framework to show that the trajectory tracking errors and adaptive parameters tend to zero in a fixed time set in advance. Numerical simulation results of robotic manipulators illustrate the effectiveness of the proposed controller.     

Fully distributed bipartite output consensus of heterogeneous linear multiagent systems based on event‐triggered transmission mechanism

This study investigates the fully distributed bipartite output consensus issue of heterogeneous linear multiagent systems (HLMASs) based on event‐triggered transmission mechanism. Both the cooperative interaction and the antagonistic interaction between neighbor agents are considered. A fully distributed bipartite compensator consisting of time‐varying coupling gain and dynamic event‐triggered mechanism is first proposed to estimate the leader's states. Different from the existing schemes, the proposed compensator is independent of any global information of the network topology, is capable of achieving intermittent communication between neighbors, and is applicable for the signed communication topology. Then the distributed output feedback control protocol is developed such that the fully distributed bipartite event‐triggered output consensus problem can be achieved. Moreover, we extend the results in HLMASs without external disturbances to HLMASs with disturbances, which is more challenging in three cases (a) the disturbances are not available for measurement, (b) the disturbances suffered by each agent are heterogeneous, and (c) the disturbances are not required to be stable or bounded. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, two examples are provided to illustrate the feasibility of the theoretical results.     

Node‐to‐node consensus of multi‐agent networks with event‐triggered control and packet losses

This paper studies the node‐to‐node consensus problem for multi‐agent networks possessing a leaders' layer and a followers' layer via the pinning control. In order to realize the consensus and reduce the update frequency of the controller, a suitable event‐triggered mechanism is introduced into the control strategy. Furthermore, the phenomenon of packet loss is considered in the designed controller. Based on the M‐matrix theory and Lyapunov stability theory, this paper presents the sufficient conditions for the node‐to‐node consensus of networks. Meanwhile, it is proved that the Zeno behaviour is excluded. Finally, two numerical simulations are provided to demonstrate the effectiveness of the theoretical results.     

Distributed adaptive integral‐type event‐triggered cooperative output regulation of switched multiagent systems by agent‐dependent switching with dwell time

This article presents a distributed adaptive integral‐type event‐triggered scheme (ETS) and an agent‐dependent switching strategy with dwell time to solve the cooperative output regulation problem for switched multiagent systems. First, by constructing an adaptive law to dynamically update the time‐varying coupling weights for all the communication links, a fully distributed ETS is designed, where only the local information of the topology is adopted. Based on the integral‐type triggering condition, the interevent interval is substantially enlarged and Zeno behavior is explicitly ruled out. Second, each agent permits all the subsystems to be unstabilizable. The switching signal for each agent is different, and any adjacent switches of each agent satisfy the preset dwell time. Under the designed switching strategy, the solvability of the regulation problem is guaranteed. Finally, the effectiveness of the designed ETS and switching strategy is substantiated by an example.     

Cooperative output regulation of heterogeneous multiagent systems based on event‐triggered control with fixed and switching topologies

This paper addresses the cooperative output regulation problem of multiagent systems with fixed and switching topologies. Each agent is a heterogeneous linear system, and the output of the exosystem can be available to only a subset of agents. For the agents that can directly access the exosystem, a common observer based on an event‐triggered strategy is constructed to estimate the exogenous signal for feedback control design. For the rest of the agents, estimators based on an event‐triggered mechanism to acquire the estimation value of the exogenous signal are designed under some essential assumptions. A decentralized event‐triggered formulation is considered first by applying a Lyapunov function for a fixed topology. Furthermore, a topology‐dependent triggering condition and the average dwell‐time switching law are deduced simultaneously by using multiple Lyapunov functions for switching topologies. Under communication constraints, we propose observer‐based and estimator‐based feedback controllers to solve the cooperative output regulation problem using available local information among agents. Two examples are finally provided to verify the effectiveness of the proposed theoretical results.     

Global adaptive finite‐time stabilization for a class of p‐normal nonlinear systems via an event‐triggered strategy

This article addresses the problem of global adaptive finite‐time control for a class of p‐normal nonlinear systems via an event‐triggered strategy. A state feedback controller is first designed for the nominal system by adding a power integrator method. Then, by the skillful design of adaptive dynamic gain mechanism, a novel event‐triggered controller is constructed for uncertain nonlinear system without homogeneous growth condition. It is proved that the global finite‐time stabilization of p‐normal nonlinear systems is guaranteed and the Zeno phenomenon is excluded. Finally, two examples are presented to indicate the effectiveness of the proposed control scheme.     

Distributed event‐triggered tracking control with a dynamic leader for multiple Euler‐Lagrange systems under directed networks

The distributed tracking control for multiple Euler‐Lagrange systems with a dynamic leader is investigated in this article via the event‐triggered approach. Only a portion of followers have access to the leader, and the communication topology among all agents is directed that contains a directed spanning tree rooted at the leader. The case that the leader's generalized velocity is constant is first considered, and a distributed event‐based control law is developed by using a velocity estimator. When the leader's generalized velocity is time‐varying, novel distributed continuous estimators are proposed to avoid the undesirable chattering effect while guaranteeing that the estimate errors converge to zeros. With the designed distributed estimators, another distributed event‐based control protocol is provided. Controller update frequency and resource consumption in our work can be reduced by applying the aforementioned two distributed control laws, and the tracking errors can converge to zeros. In addition, it is rigorously proved that no agent exhibits Zeno behavior. Finally, the effectiveness of the proposed distributed event‐based control laws is elucidated by a number of simulation examples.     

Cooperative path following of constrained autonomous vehicles with model predictive control and event‐triggered communications

We present a solution to the problem of multiple vehicle cooperative path following (CPF) that takes explicitly into account vehicle input constraints, the topology of the intervehicle communication network, and time‐varying communication delays. The objective is to steer a group of vehicles along given spatial paths, at speeds that may be path dependent, while holding a feasible geometric formation. The solution involves decoupling the original CPF problem into two subproblems: (i) single path following of input‐constrained vehicles and (ii) coordination of an input‐constrained multiagent system. The first is solved by adopting a sampled‐data model predictive control scheme, whereas the latter is tackled using a novel distributed control law with an event‐triggered communication (ETC) mechanism. The proposed strategy yields a closed‐loop CPF system that is input‐to‐state‐stable with respect to the system's state (consisting of the path following error of all vehicles and their coordination errors) and the system's input, which includes triggering thresholds for ETC communications and communication delays. Furthermore, with the proposed ETC mechanism, the number of communications among the vehicles are significantly reduced. Simulation examples of multiple autonomous vehicles executing CPF maneuvers in 2D under different communication scenarios illustrate the efficacy of the CPF strategy proposed.     

Adaptive event‐triggered global fast finite‐time control for a class of uncertain nonlinear systems

This article designs an adaptive event‐triggered controller to solve the problem of global finite‐time stabilization for a class of uncertain nonlinear systems. By using the symbol function technique, the event‐triggered error is completely compensated, the adaptive technique and the back‐stepping method are simultaneously applied to the controller design, and the new way of designing controller is completed on the basis of fast finite‐time stability theory. Subsequently, taking Lyapunov stability theorem into account, the system stability is proved, and the system is demonstrated by contradiction to be non‐zeno. Finally, giving a simulation example to display the feasibility of this method.     

Event‐triggered control via impulses for exponential stabilization of discrete‐time delayed systems and networks

This paper investigates the stabilization issue via event‐triggered controls (ETCs) for discrete‐time delayed systems (DDSs) and networks. Based on the recently proposed ETC scheme for discrete‐time systems without time delays, improved ETC (I‐ETC) and event‐triggered impulsive control (ETIC) are proposed for DDS. The algorithms for ETC, I‐ETC, and ETIC are given respectively to derive criteria of exponential stabilization of DDS. Moreover, the exponential stabilization and stabilization to ISS for discrete‐time delayed networks is achieved by employing the algorithms of ETC and ETIC. The issue of stabilization via ETCs for dynamical networks where different subsystems have different sequences of event instants is solved by introducing the check‐period into ETCs and establishing general ISS estimate of discrete‐time delayed inequality. In order to assess the performances of the control schemes, discussions on nontriviality are given by proposing the concept of rate of control and the function of control cost. Finally, two examples with numerical simulations are presented to demonstrate the effectiveness of theoretical results. From the obtained results on stabilization and the simulations, the ETIC is shown to have clear advantages and well performances than the classical state feedback control, the ETC recently proposed, I‐ETC, and the time‐based impulsive control on aspects of nontriviality, lower rate of control, lower cost of control, and robustness w.r.t. external disturbances.