Distributed Adaptive Event-Triggered Fault-Tolerant Consensus of Multiagent Systems With General Linear Dynamics

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.

Distributed Adaptive Fault-Tolerant Control for Multiagent Systems via Virtual-Actuator-Based Reconfiguration

This article aims to develop a virtual-actuator-based control scheme for the consensus tracking problem of multiagent systems (MASs) against actuator faults and mismatched disturbances. The proposed scheme has a double-layer structure. In the cyber layer, the nominal controller is designed with neighboring information for the fault-free case. While in the physical layer, the fault compensator, working as the virtual actuator, is applied to reconfigure faulty plants adaptively. This design enjoys the advantages that the nominal controller needs no adjustment and all its properties can be preserved after failure. Moreover, the proposed control scheme is distinguished by the following features: 1) the commonly imposed rank condition on outage faults is removed; 2) the norm bound of the leader's input is allowed to be unknown even though the topologies are switching and directed; and 3) there is no need to use the estimates of faults in the virtual actuator design, which means the negative impacts caused by the inaccurate fault estimation can be avoided. Finally, a numerical example is given to validate the effectiveness of the theoretical results.

Formation Tracking of Multiagent Systems With Time-Varying Actuator Faults and Its Application to Task-Space Cooperative Tracking of Manipulators

This article is concerned with a fault-tolerant formation tracking problem of nonlinear systems under unknown faults, where the leader's states are only accessible to a small set of followers via a directed graph. Under these faults, not only the amplitudes but also the signs of control coefficients become time-varying and unknown. The current setting will enhance the investigated problem's practical relevance and at the same time, it poses nontrivial design challenges of distributed control algorithms and convergence analysis. To solve this problem, a novel distributed control algorithm is developed by incorporating an estimation-based control framework together with a Nussbaum gain approach to guarantee an asymptotic cooperative formation tracking of nonlinear networked systems under unknown and dynamic actuator faults. Moreover, the proposed control framework is extended to ensure an asymptotic task-space coordination of multiple manipulators under unknown actuator faults, kinematics, and dynamics. Lastly, numerical simulation results are provided to validate the effectiveness of the proposed distributed designs.

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.

H∞Bipartite Synchronization of Double-Layer Markov Switched Cooperation-Competition Neural Networks: A Distributed Dynamic Event-Triggered Mechanism

In this article, the H_∞ bipartite synchronization issue is studied for a class of discrete-time coupled switched neural networks with antagonistic interactions via a distributed dynamic event-triggered control scheme. Essentially different from most current literature, the topology switching of the investigated signed graph is governed by a double-layer switching signal, which integrates a flexible deterministic switching regularity, the persistent dwell-time switching, into a Markov chain to represent the variation of transition probability. Considering the coexistence of cooperative and antagonistic interactions among nodes, the bipartite synchronization of which the dynamics of nodes converge to values with the same modulus but the opposite signs is explored. A distributed control strategy based on the dynamic event-triggered mechanism is utilized to achieve this goal. Under this circumstance, the information update of the controller presents an aperiodic manner, and the frequency of data transmission can be reduced extensively. Thereafter, by constructing a novel Lyapunov function depending on both the switching signal and the internal dynamic nonnegative variable of the triggering mechanism, the exponential stability of bipartite synchronization error systems in the mean-square sense is analyzed. Finally, two simulation examples are provided to illustrate the effectiveness of the derived results.

Adaptive Bipartite Output Tracking Consensus in Switching Networks of Heterogeneous Linear Multiagent Systems Based on Edge Events

This article focuses on the problem of adaptive bipartite output tracking for a class of heterogeneous linear multiagent systems (MASs) by asynchronous edge-event-triggered communications under jointly connected signed topologies. By designing the observers to estimate the states of followers and the dynamic compensators to estimate the states of zero input and nonzero input leader, respectively, the fully distributed edge-event-triggered control protocol is presented. Moreover, it is proven that the bipartite output tracking problem is implemented, and the systems do not exhibit Zeno behavior under a fully distributed control strategy with edge-event-triggered mechanisms. Compared with the existing works, one of the highlights of this article is the design of triggering mechanisms, under which the leader avoids continuous information transmission and any pair of followers that make up the edge asynchronously transmit information through the edge. The methods greatly avoid unnecessary information transmission in the systems. Finally, several simulation examples are introduced to demonstrate the theoretical results obtained in this article.

Distributed Bipartite Adaptive Event-Triggered Fault-Tolerant Consensus Tracking for Linear Multiagent Systems Under Actuator Faults

This article considers the distributed bipartite adaptive event-triggered fault-tolerant consensus tracking issue for linear multiagent systems in the presence of actuator faults based on the output feedback control protocol. Both time-varying additive and multiplicative actuator faults are taken into account in the meantime. And the upper/lower bounds of actuator faults are not required to be known. First, the state observer is designed to settle the occurrence of unmeasurable system states. Two kinds of event-triggered mechanisms are then developed to schedule the interagent communication and controller updates. Next, with the developed event-triggered mechanisms, a novel observer-based bipartite adaptive control strategy is proposed such that the fault-tolerant control problem can be addressed. Compared with some related works on this topic, our control scheme can achieve the intermittent communication and intermittent controller updates, and the more general actuator faults and network topology are considered. It is proved that the exclusion of Zeno behavior can be realized. Finally, three illustrative examples are given to demonstrate the feasibility of the main theoretical findings.

Fully Distributed Adaptive Event-Triggered Control of Networked Systems With Actuator Bias Faults

In this article, the problem of distributed synchronization of networked systems with actuator bias faults is investigated. To effectively use the limited network bandwidth and avoid the requirement of global information, a novel adaptive event-triggered state feedback controller and a dynamic triggering law are designed jointly by employing a projection operator approach. The proposed synchronization scheme is different from existing ones that have focused on designing controllers and triggering laws independently. Besides, our scheme is extended to design an observer-based distributed adaptive event-triggered controller and corresponding dynamic triggering law when the system states are unmeasurable. Theoretical analysis shows that under the two different distributed event-triggered synchronization schemes, the following three results can be obtained: 1) fully distributed synchronization can be achieved without knowing global information associated with the underlying communication topology and node's scale; 2) continuous communication among adjacent nodes can be avoided for both designed controllers and dynamic triggering laws; and 3) exclusion of Zeno phenomenon is shown by contradiction. Finally, the effectiveness of the proposed algorithms is verified through three numerical examples.

Secure Finite-Horizon Consensus Control of Multiagent Systems Against Cyber Attacks

The problem of secure finite-horizon consensus control for discrete time-varying multiagent systems (MASs) with actuator saturation and cyber attacks is addressed in this article. A random attack model is first proposed to account for randomly occurring false data injection attacks and denial-of-service attacks, whose dynamics are governed by the random Markov process. The hybrid secure control scheme is developed to mitigate the influence of arbitrary cyber attacks on system performance. Specifically, this article proposes a hybrid control law containing multiple controllers, each of which is designed to counter different types of cyber attacks. By using the stochastic analysis approach, two sufficient criteria are provided to guarantee that the time-varying MASs satisfy the finite horizon H_∞ consensus performance. Then, the controller parameters are obtained by solving the recursive linear matrix inequality. The usefulness of the theoretic results presented is demonstrated via a numerical example that contains a performance comparison of different secure control schemes.

Adaptive NN-Based Consensus for a Class of Nonlinear Multiagent Systems With Actuator Faults and Faulty Networks

This article addresses the problem of fault-tolerant consensus control of a general nonlinear multiagent system subject to actuator faults and disturbed and faulty networks. By using neural network (NN) and adaptive control techniques, estimations of unknown state-dependent boundaries of nonlinear dynamics and actuator faults, which can reflect the worst impacts on the system, are first developed. A novel NN-based adaptive observer is designed for the observation of faulty transformation signals in networks. On the basis of the NN-based observer and adaptive control strategies, fault-tolerant consensus control schemes are designed to guarantee the bounded consensus of the closed-loop multiagent system with disturbed and faulty networks and actuator faults. The validity of the proposed adaptively distributed consensus control schemes is demonstrated by a multiagent system composed of five nonlinear forced pendulums.

Finite-time distributed event-triggered formation control for quadrotor UAVs with experimentation

This paper deals with the finite-time event-triggered formation control problem for multiple quadrotor unmanned aerial vehicles (UAVs) with unknown external disturbances. Novel adaptive distributed robust event-triggered controllers without/with finite-time extended state observer (FTESO) are developed based on adaptive terminal sliding mode (TSM) control method to save control update times and reduce chattering times simultaneously. It is proved that the proposed control strategies guarantee that all the closed-loop signals are practically finite-time stable. Moreover, the proposed controllers are fully distributed without the global information that is related to the communication topology matrix H. Meanwhile, the controller with FTESO is anti-disturbance. Zeno behavior is excluded by the strictly positive sampling intervals. Finally, the efficiency of the proposed control algorithms is illustrated by numerical simulations and three bebop2 quadrotor UAVs experimentation.

Event-Based Tracking Consensus for Multiagent Systems With Volatile Control Gain

This work investigates the tracking consensus problem of multiagent systems over directed networks, where the control gains follow certain volatile patterns. Some event-based consensus protocols are formulated so as to reduce the redundant execution of control. By using an extended differential inequality with a time-dependent coefficient, criteria for tracking consensus under time- and state-dependent triggering conditions are constructed, respectively. It is proved that the time average of the control gain, together with the agent dynamics, network topology, and triggering conditions, governs the consensus despite the fluctuation of control gain. The derived theorem can be utilized to ensure consensus with intermittent strategies aiming to lessen the burden in communications, including aperiodic on-off control with periodic perturbation and pulse-modulated on-off control. Unlike existing works, the requirement of a positive lower bound of control ratios is removed and, thus, a wide range of control gain patterns is possible, signifying higher flexibility in intermittent policy design. Finally, numerical examples are provided to further illustrate the theoretical results.

Cooperative Fault-Tolerant Control for a Class of Nonlinear MASs by Resilient Learning Approach

In this article, a learning-based resilient fault-tolerant control method is proposed for a class of uncertain nonlinear multiagent systems (MASs) to enhance the security and reliability against denial-of-service (DoS) attacks and actuator faults. With the framework of cooperative output regulation, the developed algorithm consists of designing a distributed resilient observer and a decentralized fault-tolerant controller. Specifically, by using the data-driven method, an online resilient learning algorithm is first presented to learn the unknown exosystem matrix in the presence of DoS attacks. Then, a distributed resilient observer is proposed working against DoS attacks. In addition, based on the developed observer, a decentralized adaptive fault-tolerant controller is designed to compensate for actuator faults. Moreover, the convergence of error systems is shown by using the Lyapunov stability theory. The effectiveness of our result is examined by a simulation example.

Guaranteed Cost for an Event-Triggered Consensus Strategy for Interconnected Two Time-Scales Systems With Structured Uncertainty

This article proposes the design of an event-triggered control strategy for consensus of interconnected two-time scales systems with structured uncertainty. The control design under consideration ensures also that consensus is achieved with an overall guaranteed cost. Since each system involves processes evolving on both fast and slow time scales, two Zeno-free event-triggered mechanisms are designed to independently decide the sampling and transmission instants for the slow and fast states, respectively. As the first step, we design an event-triggering consensus protocol in the ideal/nominal case when the interconnected systems are not affected by uncertainties and the interactions happen over a fixed interaction network. Next, the results are extended in order to take into account structured uncertainties affecting the systems' dynamics. At this step, we go further and we provide sufficient conditions for event-triggering consensus with a guaranteed overall cost. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Fully Distributed Adaptive Fault-Tolerant Sliding-Mode Control for Nonlinear Leader-Following Multiagent Systems With ANASs and IQCs

In this article, by combining the skills of the pseudo-PID sliding-mode control (SMC) method with adaptive control techniques, two novel fully distributed adaptive fault-tolerant control strategies are proposed to handle the leader-following consensus problem of nonlinear multiagent systems with integral quadratic constraints (IQCs) and actuator faults, with and without asymmetric nonlinear actuator saturations (ANASs). For the no-saturation case, the designed controller has a simple structure and low computation but requires the crude information of the system model. To overcome this weakness, for the saturation case, the controller is redesigned by introducing a novel anti-windup compensator and fuzzy-logic systems (FLSs), where the problem of reducing computational complexity is also considered. The controllers only need local neighbor information instead of global topology information and ensure the practical consensus of the leader-following systems in finite time. Finally, simulation results demonstrate the effectiveness of the proposed approaches.

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.

Observer-Based Fixed-Time Secure Tracking Consensus for Networked High-Order Multiagent Systems Against DoS Attacks

This article studies the secure tracking consensus problem of nonlinear multiagent systems (MASs) against denial-of-service (DoS) attacks. Two types of DoS attacks, i.e., connectivity-maintained attacks and connectivity-broken attacks, are considered. The resulting topologies caused by DoS attacks may destabilize the consensus performance of MASs. Especially under connectivity-broken attacks, the connectivity between agents is destroyed. To deal with these difficulties, a novel defense strategy consisting of distributed observation and decentralized control is proposed. First, a distributed fixed-time observer (DFTO) is prepared for the case of connectivity-maintained attacks, which can quickly and accurately estimate the leader's information for each follower. Besides, the adverse impact of DoS attacks is completely eliminated. Furthermore, to cope with the problem arising from connectivity-broken attacks, by using an online algorithm of updating label information, an improved resilient DFTO (RDFTO) is further developed, which can preserve those followers having directed paths from the leader to quickly and accurately estimate the leader's information, without being affected by DoS attacks. The developed DFTO and RDFTO have successfully eliminated or weakened the adverse effects caused by DoS attacks. Subsequently, based on the proposed DFTO/RDFTO with the power integrator technique, a fixed-time controller is finally constructed, which realizes the desired transient performance of consensus tracking in the finite-time interval. The effectiveness of the proposed defense strategy is verified by stability analysis and simulation examples.

Distributed Adaptive Consensus of Nonlinear Heterogeneous Agents With Delayed and Sampled Neighbor Measurements

In this article, the adaptive output consensus problem of high-order nonlinear heterogeneous agents is addressed using only delayed, sampled neighbor output measurements. A class of auxiliary variables is introduced which are n -times differentiable functions and include the agent's output along with delayed, sampled output neighbor measurements. It is proven that if these variables are bounded and regulated to zero then asymptotic consensus among all agent outputs is ensured. In view of this property, an adaptive distributed backstepping design procedure is presented that guarantees boundedness and regulation of the proposed variables. This design procedure ensures not only the desired asymptotic output consensus but also the uniform boundedness of all closed-loop variables. The main feature of our approach is that, in the proposed control law for each agent, the entire state vector of the neighbors is not needed and only delayed sampled measurements of the neighbors' outputs are utilized. The simulation results are also presented that verify our theoretical analysis.

T-S Fuzzy Model-Based Fault Detection for Continuous Stirring Tank Reactor

Continuous stirring tank reactors are widely used in the chemical production process, which is always accompanied by nonlinearity, time delay, and uncertainty. Considering the characteristic of the actual reaction of the continuous stirring tank reactors, the fault detection problem is studied in terms of the T-S fuzzy model. Through a fault detection filter performance analysis, the sufficient condition for the filtering error dynamics is obtained, which meets the exponential stability in the mean square sense and the given performance requirements. The design of the fault detection filter is transformed into one that settles the convex optimization issue of linear matrix inequality. Numerical analysis shows the effectiveness of this scheme.

Data-Driven State Prediction and Sensor Fault Diagnosis for Multi-Agent Systems with Application to a Twin Rotational Inverted Pendulum

When a multi-agent system is subjected to faults, it is necessary to detect and classify the faults in time. This paper is motivated to propose a data-driven state prediction and sensor fault classification technique. Firstly, neural network-based state prediction model is trained through historical input and output data of the system. Then, the trained model is implemented to the real-time system to predict the system state and output in absence of fault. By comparing the predicted healthy output and the measured output, which can be abnormal in case of sensor faults, a residual signal can be generated. When a sensor fault occurs, the residual signal exceeds the threshold, a fault classification technique is triggered to distinguish fault types. Finally, the designed data-driven state prediction and fault classification algorithms are verified through a twin rotational inverted pendulum system with leader-follower mechanism.

A Fully Distributed Protocol with an Event-Triggered Communication Strategy for Second-Order Multi-Agent Systems Consensus with Nonlinear Dynamics

This paper presents the communication strategy for second-order multi-agent systems with nonlinear dynamics. To address the problem of the scarcity of communication channel resources and get rid of using continuous signals among the followers in lead-follower multi-agent systems, a novel event-triggered communication mechanism is proposed in this paper. To avoid employing the centralized information that depends on the Laplacian matrix spectrum, a network protocol with updated coupling gains is proposed, as well as an event-triggered strategy with updated thresholds. To eliminate the ill effects of inter-node communicating noise, relative positions are employed by the protocol instead of absolute positions. By a Lyapunov-Krasovskii functional, it is rigorously proven that the leader-following consensus of MASs is achieved without Zeno behavior, under the control of the proposed protocol with an event-triggered mechanism communication. The effectiveness of the proposed protocol is verified through numerical examples.

Continuous-Time Distributed Policy Iteration for Multicontroller Nonlinear Systems

In this article, a novel distributed policy iteration algorithm is established for infinite horizon optimal control problems of continuous-time nonlinear systems. In each iteration of the developed distributed policy iteration algorithm, only one controller's control law is updated and the other controllers' control laws remain unchanged. The main contribution of the present algorithm is to improve the iterative control law one by one, instead of updating all the control laws in each iteration of the traditional policy iteration algorithms, which effectively releases the computational burden in each iteration. The properties of distributed policy iteration algorithm for continuous-time nonlinear systems are analyzed. The admissibility of the present methods has also been analyzed. Monotonicity, convergence, and optimality have been discussed, which show that the iterative value function is nonincreasingly convergent to the solution of the Hamilton-Jacobi-Bellman equation. Finally, numerical simulations are conducted to illustrate the effectiveness of the proposed method.

Fuzzy Adaptive Practical Fixed-Time Consensus for Second-Order Nonlinear Multiagent Systems Under Actuator Faults

This article concentrates upon the problem of practical fixed-time consensus for second-order nonlinear multiagent systems (MASs) under directed communication topology. The convergence time is independent of the initial condition. Both loss of effectiveness and bias fault are taken into account. Meanwhile, fuzzy-logic systems are introduced to approximate the unknown nonlinear functions. By the adding-a-power-integrator method, a distributed fuzzy adaptive practical fixed-time fault-tolerant control scheme is proposed. Then, the leader can be tracked in a settling time, and the consensus tracking errors converge to an adjustable neighborhood of the origin. Finally, two simulations are given to further illustrate the effectiveness of the theoretical result.

Neural Network Adaptive Tracking Control of Uncertain MIMO Nonlinear Systems With Output Constraints and Event-Triggered Inputs

This article is concerned with a neural adaptive tracking control scheme for a class of multiinput and multioutput (MIMO) nonaffine nonlinear systems with event-triggered mechanisms, which include the fixed thresholds, triggering control inputs, and decreasing functions of tracking errors. Unlike the existing results of nonaffine nonlinear controller decoupling, a novel nonlinear multiple control inputs separated design method is proposed based on the mean-value theorem and the Taylor expansion technique. By this way, a weaker condition of nonlinear decoupling is provided to instead of the previous ones. Then, introducing a prescribed performance barrier Lyapunov function (PPBLF) and using neural networks (NNs), the presented event-triggered controller can maintain better tracking performance and effectively alleviate the computation burden of the communication procedure. Furthermore, it is proved that all the closed-loop signals are bounded and the system output tracking errors are confined within the prescribed bounds. Finally, the simulation results are given to demonstrate the validity of the developed control scheme.

Finite-Horizon H∞ Fault-Tolerant Constrained Consensus for Multiagent Systems With Communication Delays

This article focuses on the fault-tolerant constrained consensus problem for multiagent systems with communication delays. The communication graphs are first assumed to be directed and fixed. Then, a novel delay-dependent fault-tolerant controller is designed such that, in the presence of communication delays and randomly occurring actuator failures, the influence of the projections and the initial states on the closed-loop system can be attenuated with a prespecified level. Based on the provided performance requirement, the initial state of each agent does not need to be identical. The proposed control algorithms ensure that sufficient conditions are met for the fault-tolerant constrained consensus to be achieved according to the prespecified performance index. After this, the controller gains are computed by employing an iterative linear matrix inequality scheme. Finally, a numerical example is provided to show the effectiveness of the proposed method.

Adaptive Cooperative Control With Guaranteed Convergence in Time-Varying Networks of Nonlinear Dynamical Systems

In this paper, we investigate the adaptive cooperative control problem with guaranteed convergence for a class of nonlinear multiagent systems with unknown control directions and time-varying topologies. A key lemma is first derived which involves dynamically changing interaction topologies, and then a new kind of distributed control algorithms with Nussbaum-type functions are proposed based on this lemma. It is proven that if the topologies are time varying with integral weight uniform upper bound and reciprocity, then convergence is guaranteed with the proposed algorithms for nonlinear multiagent systems with nonidentical unknown control directions. An important feature of this paper is that, under time-varying topologies, the designed algorithms can deal with nonidentical unknown control directions by using classical Nussbaum-type functions. Moreover, with the proposed algorithms, we extend the adaptive cooperative control results to the case of δ -connected graphs. In particular, the adaptive leaderless consensus of high-order nonlinear agents with nonidentical unknown control directions and a directed graph having a spanning tree is also tackled as a special case. Finally, theoretical results are illustrated by a group of Genesio-Tesi systems with distributed control algorithms under time-varying topologies and some special network topologies.

Robust Adaptive Fault-Tolerant Tracking Control for Nonaffine Stochastic Nonlinear Systems With Full-State Constraints

In this article, the adaptive fault-tolerant tracking control problem of nonaffine stochastic nonlinear systems with actuator failures and full-state constraints is studied. To surmount the design difficulty from nonaffine nonlinear term with multi-input and single-output (MISO) faulty modes, a novel nonlinear fault compensation function with adjustable parameter factor is first introduced to establish a standard adaptive fault-tolerant control (AFTC) strategy based on the mean-value theorem. Then, the remaining nonlinear function, including the partial loss of effectiveness, outage, and stuck cases, together with the constructed compound nonlinear function can be approximated by using the suitable fuzzy-logic system (FLS). Moreover, it is shown that all the states of nonaffine stochastic nonlinear systems are not violating the preset constraint bounds by employing the barrier Lyapunov functions (BLFs). Also, the given adaptive controller can guarantee all the closed-loop signals are uniformly ultimately bounded (UUB) in probability in the sense of fourth-moment within the appropriate compact sets. Finally, two simulation examples are given to demonstrate the validity of the proposed method.

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

This paper is concerned with event-triggered consensus of general linear multiagent systems (MASs) in leaderless and leader-following networks, respectively, in the framework of adaptive control. A distributed dynamic event-triggered strategy is first proposed, in which an auxiliary parameter is introduced for each agent to regulate its threshold dynamically. The time-varying threshold ensures less triggering instants, compared with the traditional static one. Then under the proposed event-triggered strategy, a distributed adaptive consensus protocol is formed including the updating law of the coupling strength for each agent. Some criteria are derived to guarantee leaderless or leader-following consensus for MASs with general linear dynamics, respectively. Moreover, it is proved that the triggering time sequences do not exhibit Zeno behavior. Finally, the effectiveness of the proposed dynamic event-triggered control mechanism combined with adaptive control is validated by two examples.

Distributed Secure Control Against Denial-of-Service Attacks in Cyber-Physical Systems Based on K-Connected Communication Topology

In this article, the security problem in cyber-physical systems (CPSs) against denial-of-service (DoS) attacks is studied from the perspectives of the designs of communication topology and distributed controller. To resist the DoS attacks, a new construction algorithm of the k -connected communication topology is developed based on the proposed necessary and sufficient criteria of the k -connected graph. Furthermore, combined with the k -connected topology, a distributed event-triggered controller is designed to guarantee the consensus of CPSs under mode-switching DoS (MSDoS) attacks. Different from the existing distributed control schemes, a new technology, that is, the extended Laplacian matrix method, is combined to design the distributed controller independent on the knowledge and the dwell time of DoS attack modes. Finally, the simulation example illustrates the superiority and effectiveness of the proposed construction algorithm and a distributed control scheme.

Distributed Fixed-Time Consensus Tracking Control of Uncertain Nonlinear Multiagent Systems: A Prioritized Strategy

This paper focuses on the fixed-time consensus tracking problem for uncertain high-order nonlinear multiagent systems (MASs) under switching topologies. Unlike the traditional methods using the given original topology directly, a prioritized strategy is first proposed to assign a priority to the topological network such that the information from the leader is delivered to each agent in a least transit route (LTR). For each agent, only parts of its received information are used to design controller, which reduces the computing burden and complexity in the design process. According to the proposed prioritized strategy, the consensus tracking problem is transformed into general tracking problem. By utilizing the power integration technique, the uncertainties of nonlinear functions in MASs are dealt with. Finally, the distributed fixed-time control protocols are developed to ensure all the followers achieve the consensus with the leader under different topological cases. Rigorous stability analysis has been given and simulation results verify the effectiveness of the proposed method.

Semiglobal Observer-Based Non-Negative Edge Consensus of Networked Systems With Actuator Saturation

The observer-based edge-consensus problem of networked continuous-time dynamical systems with edge state non-negative constraint and actuator saturation is considered in this paper. Based on line graph theory, low-gain output-feedback technique and algebraic Riccati equation (ARE)-based method, two edge-consensus algorithms are designed to achieve the observer-based edge consensus, in which the specific mathematical expressions of the two algorithms are obtained. Meanwhile, sufficient conditions are obtained to meet the bounded inputs and the non-negative edge states by combining with the ARE-based low-gain output-feedback technique and the positive system theory. Moreover, the feedback-gain and observer-gain matrices which must meet the sufficient conditions at the same time are existed and easy to obtain. Finally, two simulation cases are introduced to show the effectiveness of the theoretical results.

Summation Detector for False Data-Injection Attack in Cyber-Physical Systems

In this paper, from the perspectives of defenders, we consider the detection problems of false data-injection attacks in cyber-physical systems (CPSs) with white noise. The false data-injection attacks usually modify the sensor data to make CPSs unstable and keep stealth for the χ² detector. To guarantee system security, a novel detector, that is, the summation (SUM) detector, is proposed to detect the false data-injection attacks. Different from the χ² detector, the SUM detector not only utilizes the current compromise information but also collects all historical information to reveal the threat. Its evaluation value also satisfies χ² distribution when no attacks compromise the systems, and the false alarm rate can be restricted to less than any given value by choosing the proper threshold value. Furthermore, an improved false data-injection attack with a time-variable increment coefficient is introduced based on the existing approaches. The effects of the SUM detector are also verified for the traditional and the improved false data-injection attacks, respectively. Finally, some simulation results are given to demonstrate the effectiveness and superiority of the SUM detector.

Distributed Control of Nonlinear Multiagent Systems With Unknown and Nonidentical Control Directions via Event-Triggered Communication

In this paper, the leader-following output consensus problem for a class of uncertain nonlinear multiagent systems with unknown control directions is investigated. Each agent system has nonidentical dynamics and is subject to external disturbances and uncertain parameters. The agents are connected through a directed and jointly connected switching network. A novel two-layer distributed hierarchical control scheme is proposed. In the upper layer, to save the communication resources and to handle the switching networks, an event-triggered communication scheme is proposed, and a Zeno-free event-triggered mechanism is designed for each agent to generate the asynchronous triggering time instants. Furthermore, to avoid the continuous monitoring of the system states, a Zeno-free self-triggering algorithm is proposed. In the lower layer, to handle the unknown control directions problem and to achieve the output tracking of the local references generated in the upper layer, the Nussbaum-type function-based technique is combined with internal model principle. With the proposed two-layer distributed hierarchical controller, the leader-following output consensus is achieved. The obtained result is further extended to the formation control problem. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Fault-Tolerant Consensus Tracking Control for Linear Multiagent Systems Under Switching Directed Network

In this paper, for linear leader-follower networks with multiple heterogeneous actuator faults, including partial loss of effectiveness fault and actuator bias fault, a cooperative fault-tolerant control (CFTC) approach is developed. Assume that the interaction network topology among all nodes is a switching directed graph. To address the difficulty of designing the distributed compensation control laws under the time-varying asymmetrical network structure, a novel distributed-reference-observer-based fault-tolerant tracking control approach is established, under which the global tracking errors are proved to be asymptotically convergent in the presence of actuator failures. First, by constructing a group of distributed reference observers based on neighborhood state information, all followers can estimate the leader's state trajectories directly. Second, a decentralized adaptive fault-tolerant tracking controller via local estimation is designed to achieve the global synchronization. Furthermore, the reliable coordination problem under switching directed topology with intermittent communications is solved by utilizing the presented CFTC approach. Finally, the effectiveness of the proposed coordination control protocol is illustrated by its applications to a networked aircraft system.

Event-Based Multiagent Consensus Control: Zeno-Free Triggering via Lp Signals

In this paper, we develop some new event-triggered algorithms for achieving distributed consensus for a multiagent system that guarantees fully Zeno-free triggerings for all the agents. In the proposed framework, each agent updates its control input only at its own triggering instants by using local measurements (i.e., relative states) with respect to neighboring agents, and such local measurements can be done in a local coordinate frame. For all agents, a positive L^p signal function is embedded in the event detector functions, which aims to avoid the possible comparison of an event error term to a zero threshold that may happen in a zero-crossing scenario. We further propose a Zeno-free self-triggered algorithm to achieve multiagent consensus, which enables discrete-time measurements and thus avoids continuous measurements between the neighboring agents. We also show that the proposed event-based consensus algorithms guarantee less frequent triggered events in a bounded time interval compared to the conventional algorithm without L^p signals. Simulations and comparisons are provided to validate the performance and effectiveness of the proposed event-based consensus schemes.