Adaptive Consensus Control of Linear Multiagent Systems With Dynamic Event-Triggered Strategies

Distributed Edge-Based Nash Equilibrium Seeking With Event-Triggered Quantized Communication

This article investigates a noncooperative game of multiagent systems in incomplete information scenarios. To cooperatively seek the Nash equilibrium (NE), each agent aims to minimize its own cost function by interacting with its neighbors over undirected communication networks. While existing distributed NE seeking methods alleviate the computational burden, they also entail higher communication costs. To reduce communication frequency and bandwidth, we propose a class of distributed edge-based NE seeking methods by leveraging the advantages of event-triggered mechanisms and quantization techniques. In the proposed framework, a buffer is equipped on every communication channel, thereby reducing the workload of both agents at either end. It is shown that the convergence error can be made arbitrarily small by tuning a constant threshold, and it can asymptotically converge to zero by setting an exponentially decaying threshold or a dynamic threshold. Moreover, in the case of unawareness of any global information, we further provide a fully distributed event-triggered quantized algorithm, by which the convergence error is ultimately uniformly bounded. Finally, two numerical examples are utilized to illustrate the effectiveness of the proposed algorithms.

Integral Reinforcement Learning-Based Dynamic Event-Triggered Nonzero-Sum Games of USVs

In this article, an integral reinforcement learning (IRL) method is developed for dynamic event-triggered nonzero-sum (NZS) games to achieve the Nash equilibrium of unmanned surface vehicles (USVs) with state and input constraints. Initially, a mapping function is designed to map the state and control of the USV into a safe environment. Subsequently, IRL-based coupled Hamilton-Jacobi equations, which avoid dependence on system dynamics, are derived to solve the Nash equilibrium. To conserve computational resources and reduce network transmission burdens, a static event-triggered control is initially designed, followed by the development of a more flexible dynamic form. Finally, a critic neural network is designed for each player to approximate its value function and control policy. Rigorous proofs are provided for the uniform ultimate boundedness of the state and the weight estimation errors. The effectiveness of the present method is demonstrated through simulation experiments.

Uniform-performance-constrained fixed-time neuro-control for stochastic nonlinear systems under dynamic event triggering

This article studies the implementation of practical fixed-time control in stochastic nonlinear systems, implementing event-triggered communication between the controller and the actuator. Firstly, to accomplish the problem of uniform tracking error performance constraints, the improved performance function is investigated, which is combined with the asymmetric barrier Lyapunov function to achieve fast convergence speed and steady state accuracy. Secondly, the practical fixed-time stability is applied in the stochastic nonlinear closed-loop system, which fuses fixed-time command filtering and improved filtering error compensation mechanisms to avoid computational explosion issue. Furthermore, in order to relieve the communication load on the controller and actuator, adjustable trigger thresholds are designed, based on which dynamic event triggering mechanisms are presented for stochastic nonlinear systems. Additionally, the uncertain system behavior is estimated using RBF neuro-networks and the designed controller avoids the singularity problem. Finally, the proposed controller verifies that the system error converges to zero in a fixed time under the Lyapunov stability theory, and that the system output is within the preset boundaries, realizing boundedness of all signals. The superiority of the control method is further demonstrated by three simulation studies including two practical examples.

Convergence-Rate-Based Event-Triggered Mechanisms for Quasi-Synchronization of Delayed Nonlinear Systems on Time Scales

Most of the existing event-triggered mechanisms (ETMs) were designed according to the difference between the quadratic form of measurement errors and the quadratic form of sampling states (or real-time states). In order to reduce the amount of data transmission and develop ETMs for continuous-time and discrete-time delayed nonlinear systems (NSs) simultaneously, this article investigates quasi-synchronization (QS) of NSs on time scales based on a novel ETM, which is designed according to the convergence rate instead of measurement errors of the addressed systems. First, a novel ETM is designed under known nonlinear dynamics, and it is demonstrated that QS with given convergence rate and error level can be achieved under matrix inequality criteria. Second, if the nonlinear functions are unknown, we adapt our ETM to handle this special case. Not only QS but also complete synchronization with given convergence rate can be achieved under the ETMs. If the constructed Lyapunov functions passes through 0, the designed ETM will keep it at the origin. In this case, finite-time synchronization is achieved. Third, under the designed ETMs, it is proved that Zeno behavior can be excluded. At last, four numerical simulations are presented to demonstrate the feasibility and the advantage of the designed ETMs in this article.

Adaptive Descriptor Sliding-Mode Observer-Based Dynamic Event-Triggered Consensus of Multiagent Systems Against Actuator and Sensor Faults

Actuator and sensor faults are among the most common factors affecting the stability of multiagent systems (MASs). This article proposes a dynamic event-triggered fault-tolerant control (FTC) algorithm based on descriptor sliding-mode observers to address actuator and sensor faults in MASs. First, the MAS dynamics are reformulated into a descriptor form, enabling an observer to simultaneously achieve state estimation and fault diagnosis. Using the estimation results, an adaptive FTC algorithm is developed to maintain the stability of MASs in the presence of concurrent faults, with control gains updated based on the observer consensus error. A dynamic event-triggered mechanism is incorporated to manage data transmission and update neighboring agents' information for the controller, thereby reducing communication overhead. Finally, a numerical simulation involving multiple quadrotors is conducted to validate the effectiveness of the proposed method.

Fully Distributed Observer-Based Leader-Following Consensus of Linear Multiagent Systems by Adaptive Dynamic Event-Triggered Schemes

The leader-following consensus issue for general linear multiagent systems (MASs) is investigated under event-triggered communication (ETC). Based on the output measurement of agent, two novel adaptive dynamic event-triggered (ADET) strategies for synchronous and asynchronous ETC are proposed, in which adaptive triggering parameters and time-varying threshold are introduced. Simultaneously, the corresponding control protocols are developed under the ADET strategies. Different from most existing relevant results, triggering mechanisms and control protocols do not require global information and network size, ensuring a fully distributed implementation. The asynchronous ETC, in particular, gives a flexible for transmitting information. The effectiveness of ADET strategies is further analyzed and discussed, and a comparative analysis between observer-based and state-based ADET algorithms is provided, highlighting their efficiencies and applications. Theoretical claims are substantiated with a simulative example that demonstrates the practical effectiveness of the proposed strategies.

Resilient Output Control of Multiagent Systems With DoS Attacks and Actuator Faults: Fully Distributed Event-Triggered Approach

This article investigates the fully distributed resilient practical leader-follower bipartite output consensus (LFBOC) problem for heterogeneous linear multiagent systems (MASs) with denial-of-service (DoS) attacks and actuator faults. To estimate the leader matrix and state in the presence of DoS attacks, two novel adaptive event-triggered observers are proposed based on newly developed lemmas, and then the adaptive event-triggered fault-tolerant controller without chattering behavior is developed to solve the LFBOC problem. Different from most existing resilient practical LFBOC working with DoS attacks and actuator faults, our method does not rely on any global information, event-triggered communication between neighbors and discrete update controllers are implemented simultaneously. Finally, an example is presented to well illustrate the effectiveness of developed method.

Adaptive Dynamic Event-Triggered Distributed Output Observer for Leader-Follower Multiagent Systems Under Directed Graphs

Leader-follower consensus problem for multiagent systems (MASs) is an important research hotspot. However, the existing methods take the leader system matrix as a priori knowledge for each agent to design the controller and use the leader's state information. In fact, only the output information may be available in some practical applications. On this basis, this article first designs a novel adaptive distributed dynamic event-triggered observer for each follower to learn the minimum polynomial coefficients of the leader system matrix instead of the leader system matrix. The proposed method is scalable and suitable for large-scale MASs and can reduce the information transmission dimension in observer design. Then, an adaptive dynamic event-triggered compensator based on the observer and leader output information is designed for each follower, thereby solving the leader-follower consensus problem. Finally, several simulation examples are given to verify the effectiveness of the proposed scheme.

Dynamic event-triggered quantized secure output consensus of heterogeneous multi-agent systems under DoS attacks

This paper investigates secure output consensus problem of heterogeneous multi-agent systems (HMASs) under denial-of-service (DoS) attacks. First, an adaptive dynamic compensator depending on local measurement information is designed for tracking the signal of the virtual exosystem. Second, for mitigating network communication load, a novel adaptive control protocol is developed by introducing dynamic event-triggered control and quantized control strategies. Moreover, Zeno behavior can be eliminated under the proposed scheme. Third, the secure output consensus of HMASs under DoS attacks can be guaranteed by satisfying the designed sufficient conditions. Finally, simulation is shown to verify reliability of the proposed control protocol and theory.

Distributed Estimator-Based Event-Triggered Neuro-Adaptive Control for Leader-Follower Consensus of Strict-Feedback Nonlinear Multiagent Systems

This article investigates the leader-follower consensus problem for strict-feedback nonlinear multiagent systems under a dual-terminal event-triggered mechanism. Compared with the existing event-triggered recursive consensus control design, the primary contribution of this article is the development of a distributed estimator-based event-triggered neuro-adaptive consensus control methodology. In particular, by introducing a dynamic event-triggered communication mechanism without continuous monitoring neighbors' information, a novel distributed event-triggered estimator in chain form is constructed to provide the leader's information to the followers. Subsequently, the distributed estimator is utilized to consensus control via backstepping design. To further decrease information transmission, a neuro-adaptive control and an event-triggered mechanism setting on the control channel are codesigned via the function approximate approach. A theoretical analysis shows that all the closed-loop signals are bounded under the developed control methodology, and the estimation of the tracking error asymptotically converges to zero, i.e., the leader-follower consensus is guaranteed. Finally, simulation studies and comparisons are conducted to verify the effectiveness of the proposed control method.

Controllability on impulsive systems with delays in both input and impulse and its applications to multi-agent networks

This paper investigates the controllability of impulsive systems with input delay and impulse delay and its applications in multi-agent networks. We adopt the geometric and algebraic analytical tools to establish some easily verified controllability conditions for the considered system model. First, the analytic solution of the considered system is established on every impulsive interval by using ordinary differential equation theory. Then, according to the solution derived, some sufficient complete controllability criteria are developed to reveal the role of the Gramian matrices in different subintervals. By introducing a row matrix of different kinds of Gramian matrices, a complete controllability condition that is proved to be necessary and sufficient is further obtained. By using the relevant geometric matrix theory, the derived algebraic controllability condition is then converted to a geometric one. On other hand, we introduce a multi-agent network with delayed input and impulse and investigate its controllability. By resorting to graph theory and matrix theory, several factors affecting the controllability of the considered multi-agent networks are investigated, such as the topology structure, the inner coupling matrix, and the dynamics of each agent. Finally, two numerical examples are worked out to verify the derived controllability criteria.

Event-triggered protocol-based adaptive impulsive control for delayed chaotic neural networks

This article focuses on the synchronization problem of delayed chaotic neural networks via adaptive impulsive control. An adaptive impulsive gain law in a discrete-time framework is designed. The delay is handled skillfully by using the Lyapunov-Razumikhin method. To improve the flexibility of impulsive control, an event-triggered impulsive strategy to determine when the impulsive instant happens is designed. Additionally, it is proved that the event-triggered impulsive sequence cannot result in the occurrence of Zeno behavior. Some criteria are derived to guarantee synchronization for delayed chaotic neural networks. Eventually, an illustrative example is presented to empirically validate the effectiveness of the suggested strategy.

Event-triggered predictive control for cooperation-competition multi-agent systems under DoS attacks

This paper concerns the bipartite consensus problem of multi-agent systems(MASs) with competitive- cooperative network topology under denial-of-service (DoS) attacks. Firstly, this work extensively analyzes the competitive phenomena that may exist in the information interchange of agents in contrast to the single cooperative behavior between agents. Based on this, some necessary conditions are provided for the system to attain the bipartite consensus. In addition, the event-triggered mechanism (ETM) effectively lowers unnecessary information sharing between agents and eliminates Zeno behavior. Furthermore, the predictive method provides the system with exceptional resistance against common energy-limited DoS attacks and the ability to compensate for information loss caused by DoS attacks. Finally, a numerical simulation proves that the proposed approach is feasible.

Sampled-based adaptive event-triggered resilient control for multiagent systems with hybrid cyber-attacks

The multiagent systems have shared broad application in many practical systems including unmanned aircraft clusters, intelligent robots, and intelligent transportation. However, many unexpected cyber-attacks may disturb or disrupt the normal communication of the agents, thus reducing the interacting efficiency of multiagent systems. Ever since the cyber-attacks have been proposed, the resilient control problem for multiagent systems has been intensively explored in light of the communication network growth. However, most of the consequences only focused on denial-of-service (DoS) attacks or deception attacks independently. Distinguished from the existing resilient control mechanisms, the current investigation represents the first attempt at designing an adaptive resilient controller for multiagent systems according to the sampled-based adaptive event-triggered manner, where denial-of-service (DoS) attacks and deception attacks are both considered. First, the hybrid cyber-attacks model and its impact on the closed-loop system are addressed. And then, an adaptive event-triggered strategy is proposed to reduce network resource consumption and ease the communication burden, where the designed adaptive law can automatically adjust the triggering threshold. Finally, the consensus state of multiagent systems is capable of achieving via a series of reasonable control rules formulated through Lyapunov functional approach despite suffering hybrid cyber-attacks. And a simulation example is given to substantiate the feasibility of the proposed method.

Adaptive Event-Triggered Consensus of Multi-Agent Systems in Sense of Asymptotic Convergence

In this paper, the asymptotic consensus control of multi-agent systems with general linear agent dynamics is investigated. A neighbor-based adaptive event-triggering strategy with a dynamic triggering threshold is proposed, which leads to a fully distributed control of the multi-agent system, depending only on the states of the neighboring agents at triggering moments. By using the Lyapunov method, we prove that the states of the agents converge asymptotically. In addition, the proposed event-triggering strategy is proven to exclude Zeno behavior. The numerical simulation results illustrate that the agent states achieve consensus in sense of asymptotic convergence. Furthermore, the proposed strategy is shown to be scalable in case of variable agent numbers.

Dynamic Event-Triggered Formation Control for Heterogeneous Multiagent Systems With Nonautonomous Leader Agent

In this article, the time-varying output formation issue of heterogeneous multiagent systems is investigated by the event-triggered control scheme. Only the outputs of all agents, including leader agent and follower agents, are measurable. The leader agent contains an unknown input signal to generate flexible reference trajectory. Also, only a subset of follower agents have the direct access to the leader agent. First, for each follower, the leader-state compensator is designed to estimate the state of leader. Two kinds of dynamic event-triggered (DET) mechanisms, i.e., node- and edge-based event-triggered schemes, can be equipped on the compensator to save the communication bandwidth of leader-follower and follower-follower interactions, respectively. Then, the distributed formation controller is built to drive each follower achieving formation tracking. The presented control protocol consisting of the DET state compensator and formation controller is fully distributed, which is independent of the global information of communication topology, such as the eigenvalues of Laplacian matrix of communication topology and amount of whole agents. Finally, the numerical experiments and comparison experiments are exhibited to verify the effectiveness of the presented control protocol.

Topology-based dynamic event-triggered leader-following consensus of multi-agent systems under switching topologies

This paper is devoted to the topology-based dynamic event-triggered leader-following consensus issue of general linear multi-agent systems under switching topological structures. The novel topology-based distributed dynamic event-triggered rule is formed, in which a topology-based dynamic auxiliary variable is introduced to reduce the conservatism and save resources. Under novel triggering rules, topology-based distributed event-triggered controllers are constructed. Different control gains are designed for different topological structures. Compared with existing works, conservatism is further reduced. Then the leader-following consensus is achieved with a global exponential convergence rate. Moreover, the average dwell time method is adopted to relax restrictions on the switching speed of topological structures and an original analytical thought is put forward to rule out the Zeno phenomenon concisely and clearly. Finally, two numerical examples and a realistic mass-spring system are utilized to verify the feasibility and superiority of the proposed theory.

Formation Tracking Control for Heterogeneous Multiagent Systems With Multiple Nonautonomous Leaders via Dynamic Event-Triggered Mechanisms

This article considers the time-varying formation (TVF) tracking issue of heterogeneous multiagent systems (HMASs) with the dynamic event-triggered control. The HMASs contain heterogeneous multiple leaders, all of which have the input signals to generate flexible reference, and only the output information can be measured. All leaders do not have access to the same followers, that is, the well-informed follower assumption is removed in this article. In this setting, the adaptive multileader state compensator is designed for each follower to estimate the integrated state information of all leaders, which can equip with two kinds of dynamic event-triggered mechanisms, that is, node-based event-triggered mechanism and edge-based event-triggered mechanism, to save communication bandwidth. Then, the TVF controllers are built by some estimation values to regulate the followers to achieve and maintain the geometric shape while tracking the reference which is the convex combination of outputs of leaders. The event-triggered compensator and TVF controller constitute the control protocol of HMASs, which are independent of global information with the fully distributed manner. The stability analysis and numerical simulations are given to verify the presented control protocol.

Distributed Multiagent-Based Event-Driven Fault-Tolerant Control of Islanded Microgrids

This article proposes an observer-based event-driven fault-tolerant (OBEDFT) secondary control strategy for AC microgrids (MGs) to achieve load voltage regulation. First, the input-output feedback linearization method transforms the voltage regulation issue into an output feedback tracking problem for linear multiagent systems (MASs) with nonlinear dynamics. This transformation provides the necessary preprocessing for load voltage regulation. Then, an OBEDFT secondary control protocol that considers full-state immeasurability is proposed. The actuators of distributed generators (DGs) may experience partial loss of effectiveness (PLOE) and bias faults, and these fault parameters may be heterogeneous and time-varying. The protocol introduces adaptive techniques to avoid information related to fault parameters while using event-driven mechanisms to achieve discrete measurements of neighboring DG. Additionally, the protocol uses boundary layers to construct smooth controllers that prevent the chattering effect caused by nonsmooth controllers. Finally, simulation results confirm the effectiveness of this load voltage regulation strategy.

Asymptotical Neuro-Adaptive Consensus of Multi-Agent Systems With a High Dimensional Leader and Directed Switching Topology

We study the asymptotical consensus problem for multi-agent systems (MASs) consisting of a high-dimensional leader and multiple followers with unknown nonlinear dynamics under directed switching topology by using a neural network (NN) adaptive control approach. First, we design an observer for each follower to reconstruct the states of the leader. Second, by using the idea of discontinuous control, we design a discontinuous consensus controller together with an NN adaptive law. Finally, by using the average dwell time (ADT) method and the Barbǎlat's lemma, we show that asymptotical neuroadaptive consensus can be achieved in the considered MAS if the ADT is larger than a positive threshold. Moreover, we study the asymptotical neuroadaptive consensus problem for MASs with intermittent topology. Finally, we perform two simulation examples to validate the obtained theoretical results. In contrast to the existing works, the asymptotical neuroadaptive consensus problem for MASs is firstly solved under directed switching topology.

Robust Output Regulation of Linear Uncertain Systems by Dynamic Event-Triggered Output Feedback Control

In this article, the robust output regulation problem of the linear uncertain system is investigated by the event-triggered control approach. Recently, the same problem is addressed by an event-triggered control law where the Zeno behavior may happen when time tends to infinity. In comparison, a class of event-triggered control laws is developed to achieve output regulation exactly, and meanwhile, explicitly exclude the Zeno behavior for all time. In particular, a dynamic triggering mechanism is first developed by introducing a dynamic changing variable with specific dynamics. Then, by the internal model principle, a class of dynamic output feedback control laws is designed. Later, a rigorous proof is provided to show that the tracking error of the system converges to zero asymptotically while prohibiting the Zeno behavior for all time. Finally, we give an example to illustrate our control approach.

Fully Distributed Dynamic Event-Triggered Bipartite Formation Tracking for Multiagent Systems With Multiple Nonautonomous Leaders

Considering that cooperative interactions and antagonistic interactions between neighboring agents may exist simultaneously in practice, this article studies the bipartite time-varying output formation tracking (BTVOFT) problems for homogeneous/heterogeneous multiagent systems with multiple nonautonomous leaders under switching communication networks. First, a full-dimensional observer-based nonsmooth distributed dynamic event-triggered (DDET) output feedback control scheme is proposed to ensure that BTVOFT is achieved, and the Zeno behavior is excluded. Note that the nonsmooth distributed control scheme requires global communication network information and may cause unexpected chattering effect, and the design cost of full-dimensional observer is relatively high. Thus, a reduced-dimensional observer-based continuous fully DDET scheme is proposed. Compared with the existing event-triggered schemes, the dynamic event-triggered scheme can ensure larger interevent times by introducing an additional internal dynamic variable. Finally, the effectiveness and performance of the theoretical results are validated by numerical simulations.

Adaptive Time-Varying Formation Tracking Control for Multiagent Systems With Nonzero Leader Input by Intermittent Communications

The time-varying formation (TVF) tracking problem is studied for linear multiagent systems (MASs), where followers reach a preset TVF when tracking the leader's state. Followers are divided into the informed ones, which directly receive the leader's information, and uninformed ones. To alleviate communication requirements, trigger mechanisms are designed for the leader and all edges. Note that the designed trigger mechanisms enable the leader to send information intermittently and each follower to transmit information asynchronously when the corresponding trigger mechanism is satisfied. To address the TVF tracking problem, the node-event (for the leader) and (dynamic) edge-event triggered adaptive control strategy is proposed, which is fully distributed and has no relation to the system network's scale. Moreover, the MASs do not exhibit the Zeno behavior. Finally, a practice example is introduced to effectively illustrate the theoretical results.

Mean-square consensus of a semi-Markov jump multi-agent system based on event-triggered stochastic sampling

This paper focuses on achieving leader-follower mean square consensus in semi-Markov jump multi-agent systems. To effectively reduce communication costs and control updates, we propose an event-triggered protocol based on stochastic sampling. The stochastic sampling interval randomly switches between finite given values, while the event-triggered function depends on the stochastic sampled data from neighboring agents. Using the event-triggered strategy, we present sufficient conditions to ensure mean square consensus. Finally, we provide a numerical example demonstrating the effectiveness of the theoretical results.

Observer-Based Dynamic Event-Triggered Semiglobal Bipartite Consensus of Linear Multi-Agent Systems With Input Saturation

Observer-based dynamic event-triggered semiglobal bipartite consensus (SGBC) is investigated for linear multi-agent systems (MASs) with input saturation under a competitive network. Based on the estimated relative information and low-gain feedback technology, distributed dynamic event-triggered control (DETC) protocols are proposed for solving the observer-based SGBC problems for MASs under a fixed topology and a jointly connected topology, respectively. It is turned out that the SGBC of MASs can be achieved under the proposed protocols. By using gauge transformation and the Lyapunov theory, the bipartite consensus conditions are obtained. Moreover, Zeno behaviors will be excluded. Finally, two simulation examples are presented to verify the theoretical results efficiently.

Reset Event-Triggered Adaptive Fuzzy Consensus for Nonlinear Fractional-Order Multiagent Systems With Actuator Faults

This article studies the problem of event-triggered adaptive fault-tolerant fuzzy output feedback consensus tracking control for nonlinear fractional-order multiagent systems with actuator failures under a directed graph. Considering the fact that the actual system works near the equilibrium point most of the time, a novel dynamic event-triggering strategy with the reset mechanism is proposed, where the dynamic threshold can be actively adjusted according to the preset conditions, so that the resource utilization can be further reduced. Based on an improved event-based consensus error, the state estimator about the derivative of reference trajectory and the adaptive law about the information of graph are constructed, which makes distributed consensus tracking control achieved without obtaining global information. Then, by introducing two adaptive compensating terms to deal with actuator failures and event-triggered measurement errors, it is shown in the sense of fractional-order stability criterion that tracking errors can converge to a compact set even if the fault parameters and modes are completely unknown. Finally, the correctness of the presented method is verified by a simulation example.

Leader-Follower Asymptotic Consensus Control of Multiagent Systems: An Observer-Based Disturbance Reconstruction Approach

In this article, a leader-follower asymptotic consensus control strategy is developed for a class of linear multiagent systems (MASs) with unknown external disturbances and measurement noises. First, the preconditions, the minimum phase condition (MPC) and observer matching condition (OMC), are discussed in detail, and an equivalent result under these two preconditions is given. In this way, the corresponding results from Corless and Tu (1998) are improved. Meanwhile, a reduced-order observer is designed for a constructed augmented system to estimate the system states and noises of each agent. Next, with the help of a traditional interval observer, a novel unknown disturbance reconstruction method is developed, and the reconstruction can converge to the unknown disturbance asymptotically and decouple from the control input. The subsequent asymptotic consensus is accomplished by utilizing an observer-based control scheme, with its design satisfying the so-called separation principle. Finally, two simulation examples are given to verify the effectiveness and show the advantages of the proposed methods.

Dynamic Event-Triggered Output Feedback Control for Networked Systems Subject to Multiple Cyber Attacks

This article is concerned with the problem of the H_∞ output feedback control for a class of event-triggered networked systems subject to multiple cyber attacks. Two dynamic event-triggered generators are equipped at sensor and observer sides, respectively, to lower the frequency of unnecessary data transmission. The sensor-to-observer (STO) channel and observer-to-controller (OTC) channel are subject to deception attacks and Denial-of-Service (DoS) attacks, respectively. The aim of the addressed problem is to design an output feedback controller, with the consideration of the effects of dynamic event-triggered schemes (DETSs) and multiple cyber attacks. Sufficient condition is derived, which can guarantee that the resulted closed-loop system is asymptotically mean-square stable (AMSS) with a prescribed H_∞ performance. Moreover, we provide the desired output feedback controller design method. Finally, the effectiveness of the proposed method is demonstrated by an example.

Dynamic event-triggered adaptive command filtered control for nonlinear multi-agent systems with input saturation and disturbances

This paper investigates the dynamic event-triggered adaptive command filtered control for the nonlinear high-order multi-agent systems with input saturation and disturbances. By designing a novel dynamic event-triggered adaptive command filtered control, computational burdens have been removed comprehensively. First, a dynamic event-triggered mechanism is designed, which can dynamically adjust the update frequency of controllers to reduce the computational burdens caused by the continuous updates of controllers. Moreover, the proposed approach can save communication resources and improve control performances simultaneously. Second, the command filtered control is studied to remove the computational burdens caused by the repeated differentiation of virtual control signals. Furthermore, input saturation and disturbances are handled concurrently. Finally, simulation results are given to validate the efficacy of the proposed approach.

A Comment on and Correction to: Opinion Dynamics in the Presence of Increasing Agreement Pressure

We identify counterexamples to the consensus result given in Semonsen et al. (2018). We resolve the counterexamples by replacing Lemma 5 in the given reference with a novel variation of the Banach fixed-point theorem, which explains both the numerical results in the reference and the counterexample(s) in this note and provides a sufficient condition for consensus in systems with increasing peer-pressure. This work is relevant for other papers that have used the proof technique from Semonsen et al. and establishes the veracity of their claims assuming the new sufficient condition.

Finite-Time Heterogeneous Cyclic Pursuit With Application to Cooperative Target Interception

This article presents a finite-time heterogeneous cyclic pursuit scheme that ensures consensus among agents modeled as integrators. It is shown that for the proposed consensus scheme, even when the gains are nonidentical, consensus results within a finite time, provided all the gains are positive or even if one gain is negative, subject to a lower bound. An algorithm is presented to compute the consensus value and consensus time for a given set of positive gains and initial states of the agents. The set of values, where consensus can occur, by varying the gains, has been derived and a second algorithm aids in determining the positive gains that enable consensus at any point in the aforementioned set, at a given finite time. As an application, the finite-time consensus in line-of-sight rates, over a cycle digraph, for a group of interceptors is shown to be effective in ensuring co-operative collision-free interception of a target, for both constant speed as well as realistic time-varying-speed models of the interceptors. Simulations the theoretical results.

Secure Event-Triggered Consensus Control of Linear Multiagent Systems Subject to Sequential Scaling Attacks

This article investigates secure consensus of linear multiagent systems under event-triggered control subject to a scaling deception attack. Different from probabilistic models, a sequential scaling attack is considered, in which specific attack properties, such as the attack duration and frequency, are defined. Moreover, to alleviate the utilization of communication resources, distributed static and dynamic event-triggered control protocols are proposed and analyzed, respectively. This article aims at providing a resilient event-triggered framework to defend a kind of sequential scaling attack by exploring the relationship among the attack duration and frequency, and event-triggered parameters. First, the static event-triggered control is studied, and sufficient consensus conditions are derived, which impose constraints on the attack duration and frequency. Second, a state-based auxiliary variable is introduced in the dynamic event-triggered scheme. Under the proposed dynamic event-triggered control, consensus criteria involving triggering parameters, attack constraints, and system matrices are obtained. It proves that the Zeno behavior can be excluded. Moreover, the impacts of the scaling factor, triggering parameters, and attack properties are discussed. Finally, the effectiveness of the proposed event-triggered control mechanisms is validated by two examples.

Adaptive Event-Triggered Finite-Frequency Fault Detection With Zonotopic Threshold Analysis for LPV Systems

This article investigates a class of multiobjective optimization fault detection observer design problems for linear parameter varying (LPV) systems considering the unknown but bounded disturbance with an adaptive event-triggered scheme. In this study, the actuator faults are considered in the low-frequency domain. First, to save the communication bandwidth and improve communication efficiency, an adaptively adjusted event-triggered (AAET) mechanism is proposed. Then, in order to make the designed observer gain satisfy both fault sensitivity and disturbance robust conditions, an H_-/L_∞ multiobjective optimization problem is proposed and solved by appropriate linear matrix inequalities. Next, the upper and lower bounds of the generated residual are calculated by the zonotope method when considering the estimation uncertainty. Fault detection can be achieved by judging whether the zero value belongs to the generated range of the residual signal. Finally, a simulation case is used to verify the effectiveness of the proposed method.

Coordinated Planar Path-Following Control for Multiple Nonholonomic Wheeled Mobile Robots

This article is concerned with both consensus and coordinated path-following control for multiple nonholonomic wheeled mobile robots. In the design, the path-following control is decoupled into the longitudinal control (speed control) and the lateral control (heading control) for the convenience of implementation. Different from coordinated trajectory tracking control schemes, the proposed control scheme removes the temporal constraint, which greatly improves the coordination robustness. In particular, two new coordinated error variables describing a chasing-and-waiting strategy are introduced in the proposed coordinated path-following control for injective paths and circular paths, respectively. All the closed-loop signals have proved to be asymptotically stable in the Lyapunov sense. Finally, simulation results under three typical paths are presented to verify the proposed coordination controllers.

Resilient Event-Triggered Distributed State Estimation for Nonlinear Systems Against DoS Attacks

This article investigates the resilient event-triggered (ET) distributed state estimation problem for nonlinear systems under denial-of-service (DoS) attacks. Different from the existing results mainly considering linear or specified nonlinear systems, more general nonlinear systems are considered in this study. Moreover, the considered DoS attacks are able to compromise different communication links among estimators independently. In this context, by resorting to the techniques of incremental homogeneity, a nonlinear ET distributed estimation scheme is designed to estimate the states and regulate the data transmission. Under this scheme, the resilient state estimation is achieved by employing a multimode switching estimator, and the problem of efficiency loss of the ET mechanism caused by DoS attacks is solved by designing a dynamic trigger threshold with switched update laws. Then, based on the decay rates of the Lyapunov function corresponding to different communication modes, sufficient conditions are given to guarantee the stability of the estimation error system under DoS attacks. Finally, simulation results are provided to verify the effectiveness of the proposed method.

Fully distributed event-triggered secure consensus of general linear multi-agent systems under sequential scaling attacks

In this article, the secure consensus problem is studied for a general linear multi-agent system, where a fully distributed event-triggered scheme is introduced to increase the feasibility and improve the scalability of the control protocol. Firstly, an edge-based sequential scaling attack is formulated with constraints on the attack duration and the frequency, which includes multiplicative deception attacks and DoS attacks as a particular situation when the scaling factor is equal to 0. Then a fully distributed event-triggered control protocol is designed, in which the global information is no longer needed. Sufficient conditions related to triggering parameters, the scaling factor, the attack duration and attack frequency are derived ensuring the asymptotic consensus of MAS. Furthermore, the impact of the triggering parameters and the scaling factor on the attack duration and the attack frequency are also discussed. The Zeno behavior is proved not to happen. Finally, two simulation examples based on unmanned intelligent vehicles are conducted to verify the results.

Synchronization of Neural Networks via Periodic Self-Triggered Impulsive Control and Its Application in Image Encryption

In this article, a periodic self-triggered impulsive (PSTI) control scheme is proposed to achieve synchronization of neural networks (NNs). Two kinds of impulsive gains with constant and random values are considered, and the corresponding synchronization criteria are obtained based on tools from impulsive control, event-driven control theory, and stability analysis. The designed triggering protocol is simpler, easier to implement, and more flexible compared with some previously reported algorithms as the protocol combines the advantages of the periodic sampling and event-driven control. In addition, the chaotic synchronization of NNs via the presented PSTI sampling is further applied to encrypt images. Several examples are also utilized to illustrate the validity of the presented synchronization algorithm of NNs based on PSTI control and its potential applications in image processing.

Output-Based Event-Triggered Cooperative Robust Regulation for Constrained Heterogeneous Multiagent Systems

The output-based event-triggered cooperative output regulation problem is addressed for constrained linear heterogeneous multiagent system in this article. In light of the robust control theory, H_∞ leader-following consensus with respect to exogenous signals, including both disturbance to be rejected and reference state of leader to be tracked, is guaranteed. Meanwhile, the system performance alleviates degradation through a model recovery anti-windup technique while encountering input saturation. Furthermore, the follower's self-state observer, the leader-state observer, and the anti-windup auxiliary system are integrated into a comprehensive system, and a unified event-triggering mechanism of full states is addressed. A fixed lower bound of sampled interval is adopted such that the frequency of data transmission gets reduced and no Zeno-behavior happens. Both the input and output of the follower's controller and anti-windup compensator hold constant, respectively, during the event-triggered intervals such that the resulting output-based event-triggered controller can be directly implemented in a digital platform. Finally, a simulation example is provided to illustrate the effectiveness.

Designing Event-Triggered Observers for Distributed Tracking Consensus of Higher-Order Multiagent Systems

In this article, the asymptotic tracking consensus problem of higher-order multiagent systems (MASs) with general directed communication graphs is addressed via designing event-triggered control strategies. One common assumption utilized in most existing results on such tracking consensus problem that the inherent dynamics of the leader are the same as those of the followers is removed in this article. In particular, two cases that the dynamics of the leader are subjected, respectively, to bounded input and unknown nonlinearity are considered. To do this, distributed event-triggered observers are first constructed to estimate the state information of the leader. Then, local event-triggered tracking control protocols are designed for each follower to complete the goal of tracking consensus. One distinguishing feature of the present distributed observers lies in the fact that they could avoid the continuous monitoring for the states of the neighbors' observer states. It is also worth pointing out that the present tracking consensus control strategies are fully distributed as no global information related to the directed communication graph is involved in designing the strategies. Two simulation examples are finally presented to verify the efficiency of the theoretical results.

Adaptive Consensus Control for Nonlinear Multiagent Systems With Unknown Control Directions Using Event-Triggered Communication

In this article, under directed graphs, an adaptive consensus tracking control scheme is proposed for a class of nonlinear multiagent systems with completely unknown control coefficients. Unlike the existing results, here, each agent is allowed to have multiple unknown nonidentical control directions, and continuous communication between neighboring agents is not needed. For each agent, we design a group of novel Nussbaum functions and construct a monotonously increasing sequence in which the effects of our Nussbaum functions reinforce rather than counteract each other. With these efforts, the obstacle caused by the unknown control directions is successfully circumvented. Moreover, an event-triggering mechanism is introduced to determine the time instants for communication, which considerably reduces the communication burden. It is shown that all closed-loop signals are globally uniformly bounded and the tracking errors can converge to an arbitrarily small residual set. Simulation results illustrate the effectiveness of the proposed scheme.

A Unified Optimization for Resilient Dynamic Event-Triggering Consensus Under Denial of Service

This article proposes a resilient framework for optimized consensus using a dynamic event-triggering (DET) scheme, where the multiagent system (MAS) is subject to denial-of-service (DoS) attacks. When initiated by an adversary, DoS blocks the local and neighboring communication channels in the network. A distributed DET scheme is utilized to limit transmissions between the neighboring agents. A novel convex optimization approach is proposed that simultaneously co-designs all unknown control and DET parameters. The optimization is based on the weighted sum approach and increases the interevent interval for a predefined consensus convergence rate. In the presence of DoS, the proposed co-design framework is beneficial in two ways: 1) the desired level of resilience to DoS is included as a given (desired) input and 2) the upper bound for guaranteed resilience associated with the proposed co-design approach is less conservative (larger) compared to those obtained from other analytical solutions. A structured tradeoff between relevant features of the MAS, namely, the consensus convergence rate, frequency of event triggerings, and level of resilience to DoS attacks, is established. Simulations based on nonholonomic mobile robots quantify the effectiveness of the proposed implementation.

Reset Observer-Based Zeno-Free Dynamic Event-Triggered Control Approach to Consensus of Multiagent Systems With Disturbances

In this article, we investigate the observer-based event-triggered consensus problem of multiagent systems with disturbances. A reset observer consisting of a linear observer and reset element is proposed, the reset element endows the reset observer the ability to improve transient estimation performance compared with traditional linear observers. A hybrid dynamic event-triggering mechanism (ETM) is proposed, in which an internal timer variable is introduced to enforce a lower bound for the triggering intervals such that Zeno-free triggering can be guaranteed even in the presence of disturbances. Then, in order to describe the closed-loop system with both flow dynamics and jump dynamics, a hybrid model is constructed, based on which the Lyapunov-based consensus analysis and dynamic ETM design results are presented. In contrast with linear observer-based consensus protocols and the existing dynamic ETMs, the system performance can be improved and continuous communication between neighboring agents is not needed. Finally, a simulation example is provided to show the effectiveness of the proposed methods.

Event-Triggered Cooperative Predictive Control for Networked Multi-Agent Systems with Random Delays and Packet Dropouts

This paper addresses the cooperative output tracking control problem for a class of leader-following linear heterogeneous networked multi-agent systems subject to random network delays and packet dropouts in the feedback and forward channels of each agent. A state observer is established at the plant side of each agent, and an event-triggering transmission mechanism is introduced to decide which state estimate is transmitted to the corresponding controller so as to save the network resources of the feedback channel. To further compensate for the negative effects of those random communication constraints and the event trigger, a cooperative predictive control scheme with proportional and integral actions is proposed. Then, a necessary and sufficient condition is derived for the stability of the resulting closed-loop system. Finally, simulation results are given to show the effectiveness of the proposed scheme.