Event/Self-Triggered Control for Leader-Following Consensus Over Unreliable Network With DoS Attacks

Distributed Adaptive Output Feedback Consensus for Nonlinear Stochastic Multiagent Systems by Reference Generator Approach

This article investigates the distributed leader-following consensus for a class of nonlinear stochastic multiagent systems (MASs) under directed communication topology. In order to estimate unmeasured system states, a dynamic gain filter is designed for each control input with reduced filtering variables. Then, a novel reference generator is proposed, which plays a key role in relaxing the restriction on communication topology. Based on the reference generators and filters, a distributed output feedback consensus protocol is proposed by a recursive control design approach, which incorporates adaptive radial basis function (RBF) neural networks to approximate the unknown parameters and functions. Compared with existing works on stochastic MASs, the proposed approach can significantly reduce the number of dynamic variables in filters. Furthermore, the agents considered in this article are quite general with multiple uncertain/unmatched inputs and stochastic disturbance. Finally, a simulation example is given to demonstrate the effectiveness of our results.

Secure output consensus for multi-agent systems under edge-based event-trigger against denial-of-service

This paper is concerned with the secure output consensus problem for the heterogeneous multi-agent systems under the event-triggered scheme in the presence of the denial-of-service attack. Without detecting the attack, the hold-input controller update strategy is adopted when some transmission data may be lost due to the effect of the attack. Based on the tolerable duration of the attack, a novel edge-based event-triggered scheme is developed. The scheme can avoid continuous communication and exclude Zeno behavior. With the aid of the switched system theory, output consensus is preserved. An example shows the effectiveness.

Sampled-Data-Based Secure Synchronization Control for Chaotic Lur'e Systems Subject to Denial-of-Service Attacks

This article investigates the sampled-data-based secure synchronization control problem for chaotic Lur'e systems subject to power-constrained denial-of-service (DoS) attacks, which can block data packets' transmission in communication channels. To eliminate the adverse effects, a resilient sampled data control scheme consisting of a secure controller and communication protocol is designed by considering the attack signals and periodic sampling mechanism simultaneously. Then, a novel index, i.e., the maximum anti-attack ratio, is proposed to measure the secure level. On this basis, a multi-interval-dependent functional is established for the resulting closed-loop system model. The main feature of the developed functional lies in that it can fully use the information of resilient sampling intervals and DoS attacks. In combination with the convex combination method, discrete-time Lyapunov theory, and some inequality estimate techniques, two sufficient conditions are, respectively, derived to achieve sampled-data-based secure synchronization of drive-response systems against DoS attacks. Compared with the existing Lyapunov functionals, the advantages of the proposed multi-interval-dependent functional are analyzed in detail. Finally, a synchronization example and an application to secure communication are provided to display the effectiveness and validity of the obtained results.

Output Feedback-Based Consensus for Nonlinear Multiagent Systems: The Event-Triggered Communication Strategy

The current investigation explores the leader-following consensus problem for nonlinear multiagent systems under the output feedback control mechanism and the event-triggered communication mechanism. Owing to the physical instrument constraints, a significant portion of the state variables is not readily available. Therefore, this article put forward a distributed event-based leader-following consensus protocol only using agents' relative output measurements and underlying neighbors. Furthermore, this article develops two event-triggered mechanisms simultaneously, one is the event-triggered communication mechanism in the sensor-to-controller channel, and another is the event-triggered controller update in the controller-to-actuator track. Besides that, it is proven that the developed event-triggered control protocol can settle the leader-following consensus problem of the nonlinear multiagent systems, and the Zeno behavior is excluded in both the channels. Finally, we perform two simulation examples to illustrate the efficacy of the obtained results.

Outlier-Resistant State Estimation for Singularly Perturbed Complex Networks With Nonhomogeneous Sojourn Probabilities

This study investigates an outlier-resistant state estimation problem for singularly perturbed complex networks (SPCNs) with sojourn probabilities and randomly occurring coupling strengths. Aiming at better describing the dynamic behavior of the network topology for SPCNs, a novel switching law associated with the time-varying sojourn probabilities is developed, and the variation of sojourn probabilities is arranged by a high-level deterministic switching signal. Meanwhile, a sequence of mode-dependent variables is employed to describe the randomly occurring coupling strength. Subsequently, to alleviate the side effects from possible measurement outliers, a dynamic saturation function-based state estimator is designed, whose saturation level is adaptively varying based on previous estimation errors. In virtue of Lyapunov theory and mode-dependent average dwell-time strategy, it can be verified that the resulting dynamics is stochastic H∞ finite-time bounded. To this end, a simulation example is presented to show the validity of the proposed estimator design method.

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.

Learning-Based DoS Attack Power Allocation in Multiprocess Systems

We study the denial-of-service (DoS) attack power allocation optimization in a multiprocess cyber-physical system (CPS), where sensors observe different dynamic processes and send the local estimated states to a remote estimator through wireless channels, while a DoS attacker allocates its attack power on different channels as interference to reduce the wireless transmission rates, and thus degrading the estimation accuracy of the remote estimator. We consider two attack optimization problems. One is to maximize the average estimation error of different processes, and the other is to maximize the minimal one. We formulate these problems as Markov decision processes (MDPs). Unlike the majority of existing works where the attacker is assumed to have complete knowledge of the CPS, we consider an attacker with no prior knowledge of the wireless channel model and the sensor information. To address this uncertainty issue and the curse of dimensionality, we provide a learning-based attack power allocation algorithm stemming from the double deep Q-network (DDQN) method. First, with a defined partial order, the maximal elements of the action space are determined. By investigating the characteristic of the MDP, we prove that the optimal attack allocations of both problems belong to the set of these elements. This property reduces the entire action space to a smaller subset and speeds up the learning algorithm. In addition, to further improve the data efficiency and learning performance, we propose two enhanced attack power allocation algorithms which add two auxiliary tasks of MDP transition estimation inspired by model-based reinforcement learning, i.e., the next state prediction and the current action estimation. Experimental results demonstrate the versatility and efficiency of the proposed algorithms in different system settings compared with other algorithms, such as the conventional value iteration, double Q-learning, and deep Q-network.

Adaptive prescribed settling time periodic event-triggered control for uncertain robotic manipulators with state constraints

In this paper, an adaptive prescribed settling time periodic event-triggered control (APST-PETC) is investigated for uncertain robotic manipulators with state constraints. In order to economize network bandwidth occupancy and reduce computational burden, a periodic event-triggered control (PETC) strategy is proposed to reduce the update frequency of the control signal and avoid unnecessary continuous monitoring. Besides, considering that the maneuverable space of the actual robotic manipulators is often limited, the barrier Lyapunov function (BLF) is applied to deal with the influence of the constraint characteristics on the robotic manipulators. Further, based on the one-to-one nonlinear mapping function of the system tracking error, an adaptive prescribed settling time control (APSTC) is designed to ensure that the system tracking error reaches the predetermined precision residual set within the prescribed settling time. Finally, theoretical analysis and comparative experiments are given to verify its feasibility.

Observer-based model predictive control for uncertain NCS subject to hybrid attacks via interval type-2 T-S fuzzy model

In this study, an observer-based model predictive control (MPC) algorithm is addressed for an uncertain discrete-time nonlinear networked control system (NCS) subject to hybrid malicious attacks by using interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy theory. Hybrid malicious attacks, including two typical attacks, i.e., denial-of-service (DoS) attacks and false data injection (FDI) attacks, are considered in the communication networks. Under DoS attacks, the control signals will be interfered, which cause the degradation of signal-to-interference-plus-noise ratio, then lead to packets loss. Under FDI attacks, the false signals are injected and output signals are modified so that the system performance is deteriorated. For the NCS subject to hybrid attacks, a secure observer that can resist FDI attacks is devised and a fuzzy MPC algorithm that can solve the controller gains is proposed. Besides, by updating the bound of augmented estimation error, the recursive feasibility can be guaranteed. Finally, illustrative examples are given to show the effectiveness of proposed scheme.

Resilient Consensus Control for Multi-Agent Systems: A Comparative Survey

Due to the openness of communication network and the complexity of system structures, multi-agent systems are vulnerable to malicious network attacks, which can cause intense instability to these systems. This article provides a survey of state-of-the-art results of network attacks on multi-agent systems. Recent advances on three types of attacks, i.e., those on DoS attacks, spoofing attacks and Byzantine attacks, the three main network attacks, are reviewed. Their attack mechanisms are introduced, and the attack model and the resilient consensus control structure are discussed, respectively, in detail, in terms of the theoretical innovation, the critical limitations and the change of the application. Moreover, some of the existing results along this line are given in a tutorial-like fashion. In the end, some challenges and open issues are indicated to guide future development directions of the resilient consensus of multi-agent system under network attacks.

Adaptive Neural Event-Triggered Control of Networked Markov Jump Systems Under Hybrid Cyberattacks

This article is concerned with the neural network (NN)-based event-triggered control problem for discrete-time networked Markov jump systems with hybrid cyberattacks and unmeasured states. The event-triggered mechanism (ETM) is used to reduce the communication load, and a Luenberger observer is introduced to estimate the unmeasured states. Two kinds of cyberattacks, denial-of-service (DoS) attacks and deception attacks, are investigated due to the vulnerability of cyberlayer. For the sake of mitigating the impact of these two types of cyberattacks on system performance, the ETM under DoS jamming attacks is discussed first, and a new estimation of such mechanism is given. Then, the NN technique is applied to approximate the injected false information. Some sufficient conditions are derived to guarantee the boundedness of the closed-loop system, and the observer and controller gains are presented by solving a set of matrix inequalities. The effectiveness of the presented control method is demonstrated by a numerical example.

Resilient Output Synchronization of Heterogeneous Multiagent Systems With DoS Attacks Under Distributed Event-/Self-Triggered Control

This article investigates the resilient output synchronization problem of a class of linear heterogeneous multiagent systems subjected to denial-of-service (DoS) attacks. Two types of control mechanisms, namely, event- and self-triggered control mechanisms, are presented so as to cut down unnecessary information transmission. Both of these two mechanisms are distributed, and thus, only local information of each agent and its neighboring agents is adopted for the event condition design. The DoS attacks are considered to be aperiodic, and the quantitative relationship between the attributes of the DoS attacks and the synchronization is also revealed. It is shown that the output synchronization can be achieved exponentially in the presence of DoS attacks under the proposed control mechanisms. The validness of the provided mechanisms is certified by a simulation example.

Event-Triggered Recursive State Estimation for Stochastic Complex Dynamical Networks Under Hybrid Attacks

In this article, the event-based recursive state estimation problem is investigated for a class of stochastic complex dynamical networks under cyberattacks. A hybrid cyberattack model is introduced to take into account both the randomly occurring deception attack and the randomly occurring denial-of-service attack. For the sake of reducing the transmission rate and mitigating the network burden, the event-triggered mechanism is employed under which the measurement output is transmitted to the estimator only when a preset condition is satisfied. An upper bound on the estimation error covariance on each node is first derived through solving two coupled Riccati-like difference equations. Then, the desired estimator gain matrix is recursively acquired that minimizes such an upper bound. Using the stochastic analysis theory, the estimation error is proven to be stochastically bounded with probability 1. Finally, an illustrative example is provided to verify the effectiveness of the developed estimator design method.

Event-triggered prescribed settling time consensus control of uncertain nonlinear multiagent systems with given transient performance

Multiagent systems (MASs) are usually used in unmanned aerial vehicle formations, multi-manipulator coordinated, traffic vehicle control and other fields, which have attracted a lot of attention from scholars. In this research, with the help of the designed performance function, the nonlinear transformation of synchronization error is realized. And the synchronization error of MASs with given transient performance could converge to the predefined interval. According to the designed transformation function, a prescribed setting time consensus control is investigated with the advantages of Radial Basis Function Neural Networks (RBFNNs) in dealing with unknown functions. It guarantees that the MASs under consideration are uniformly bounded convergent. Furthermore, event-triggered mechanism is applied to relieve pressure of MASs' communication resources. Simulation results demonstrate its effectiveness.

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.

Edge-Based Decentralized Adaptive Pinning Synchronization of Complex Networks Under Link Attacks

This article studies the pinning synchronization problem with edge-based decentralized adaptive schemes under link attacks. The link attacks considered here are a class of malicious attacks to break links between neighboring nodes in complex networks. In such an insecure network environment, two kinds of edge-based decentralized adaptive update strategies (synchronous and asynchronous) on coupling strengths and gains are designed to realize the security synchronization of complex networks. Moreover, by virtue of the edge pinning technique, the corresponding secure synchronization problem is considered under the case where only a small fraction of coupling strengths and gains is updated. These designed adaptive strategies do not require any global information, and therefore, the obtained results in this article are developed in a fully decentralized framework. Finally, a numerical example is provided to verify the availability of the achieved theoretical outcomes.

On Consensus of Second-Order Multiagent Systems With Actuator Saturations: A Generalized-Nyquist-Criterion-Based Approach

In this article, a frequency-domain approach is developed to deal with the global consensus problem for a class of general second-order multiagent systems (MASs) subject to actuator saturations. By employing the describing function and the generalized Nyquist criterion, the global consensus problem is thoroughly investigated for both undirected and directed topologies. First, the describing function is introduced to characterize the actuator saturations in the s -plane, and the inherent representation error is quantitatively analyzed from a frequency-domain perspective. Then, by means of the Kronecker product, the addressed consensus problem of the MAS is transformed into a corresponding stability analysis problem for a certain multi-input-multi-output (MIMO) system and, consequently, the generalized Nyquist criterion for MIMO systems is exploited to derive the condition for the global consensus of the MAS where the impact from the actuator saturation is explicitly reflected. Finally, numerical simulations are provided to illustrate the validity of the proposed theoretical result.

Consensus of Positive Networked Systems on Directed Graphs

This article addresses the distributed consensus problem for identical continuous-time positive linear systems with state-feedback control. Existing works of such a problem mainly focus on the case where the networked communication topologies are of either undirected and incomplete graphs or strongly connected directed graphs. On the other hand, in this work, the communication topologies of the networked system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Specifically, the problem involves complex eigenvalues, the Hurwitzness of complex matrices, and positivity constraints, which make analysis difficult in the Laplacian matrix. First, a necessary and sufficient condition for the consensus analysis of directed networked systems with positivity constraints is given, by using positive systems theory and graph theory. Unlike the general Riccati design methods that involve solving an algebraic Riccati equation (ARE), a condition represented by an algebraic Riccati inequality (ARI) is obtained for the existence of a solution. Subsequently, an equivalent condition, which corresponds to the consensus design condition, is derived, and a semidefinite programming algorithm is developed. It is shown that, when a protocol is solved by the algorithm for the networked system on a specific communication graph, there exists a set of graphs such that the positive consensus problem can be solved as well.

Switching cluster synchronization control of networked harmonic oscillators subject to denial-of-service attacks

This paper is concerned with the average cluster synchronization control problem of networked harmonic oscillators under denial-of-service (DoS) attacks. Different from some existing DoS attack models that often necessitate specific statistical characteristics, only the worse-case duration bound of the DoS attacks is required during the control design procedure, which represents the least a priori knowledge of realistic DoS attacks. Then, a novel switching cluster synchronization control scheme, which leverages a position-based feedback control protocol under a non-small delay and a position velocity-based feedback control protocol with a small delay, is developed such that the above two control protocols are selected based on the occurrence of the DoS attacks. Via formulating the resultant synchronization system as a switched time-delay system, a complete-type Lyapunov-Krasovskii functional (LKF) method is further proposed to establish sufficient controller design criteria associated with the duration and frequency of attacks for both synchronous and asynchronous DoS attacks among clusters. Furthermore, an iterative algorithm is designed to calculate the control gain matrices by solving a set of nonlinear matrix inequalities (NLMIs). Finally, a multi-vehicle cooperative control system is presented to demonstrate the validity of the proposed control scheme.

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.

Networked Multiagent Systems: Antagonistic Interaction, Constraint, and its Application

In this article, we study the consensus problem in the framework of networked multiagent systems with constraint where there exists antagonistic information. A major difficulty is how to characterize the communication among the interacting agents in the presence of antagonistic information without resorting to the signed graph theory, which plays a central role in the Altafini model. It is shown that the proposed control protocol enables us to solve the consensus problem in a node-based viewpoint where both cooperative and antagonistic interactions coexist. Moreover, the proposed setup is further extended to the case of input saturation, leading to the semiglobal consensus. In addition, the consensus region associated with antagonistic information among participating individuals is also elaborated. Finally, the deduced theoretical results are applied to the task distribution problem via unmanned ground vehicles.

Sigmoid-like Event-Triggered Security Cruise Control under Stochastic False Data Injection Attacks

This paper presents a Sigmoid-like event-triggered scheme (Sigmoid-like ETS) for security cruise control systems (CCSs) under stochastic false data injection (FDI) attacks. In order to improve the sensitivity of the ETS, a Sigmoid-like function is first proposed to adjust the event-triggered threshold, dynamically. In what follows, by considering a class of stochastic FDI attacks which obey Bernoulli distribution, the Sigmoid-like event-triggered security control strategy is proposed to ensure both the security and resource saving of the CCSs. Thus, a sufficient stability and stabilization criterion is well derived to present the co-design of an H∞ control and event-triggered parameter. Finally, some simulation experiments are conducted to verify the effectiveness of the proposed Sigmoid-like event-triggered security cruise control for networked vehicles.

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.

Resilient Cooperative Control for Networked Lagrangian Systems Against DoS Attacks

In this article, we study the distributed resilient cooperative control problem for directed networked Lagrangian systems under denial-of-service (DoS) attacks. The DoS attacks will block the communication channels between the agents. Compared with the existing methods for the linear networked systems, the considered nonlinear networked Lagrangian systems with asymmetric channels under DoS attacks are more challenging and still not well explored. In order to solve this problem, a novel resilient cooperative control scheme is proposed by using the sampling control approach. Sufficient conditions are first derived in the absence of DoS attacks according to a multidimensional small-gain scheme. Then, in the presence of DoS attacks, the proposed resilient scheme works in a switching manner. Inspired by multidimensional small-gain techniques, the Lyapunov approach is used to analyze the closed-loop system, which enables us to establish sufficient stability conditions for the control gains in terms of the duration and frequency of the DoS attacks.

Cooperative Output Tracking of Unknown Heterogeneous Linear Systems by Distributed Event-Triggered Adaptive Control

This article addresses the cooperative output tracking problem of a class of linear minimum-phase multiagent systems, where the agent dynamics are unknown and heterogeneous. A distributed event-triggered model reference adaptive control strategy is developed. It is shown that under the proposed event-triggered control strategy, the outputs of all the agents synchronize to the output of the leader asymptotically. It is also shown that Zeno behavior can be excluded with the proposed novel event triggering mechanism. In addition, the proposed adaptive control strategy is fully distributed in the sense that no prior knowledge of some global information, such as the eigenvalues of the associated Laplacian matrix and the number of the agents is required. Finally, an example is given to demonstrate the effectiveness of the proposed control strategy.

Cooperative Output-Feedback Secure Control of Distributed Linear Cyber-Physical Systems Resist Intermittent DoS Attacks

This article studies a cooperative output-feedback secure control problem for distributed cyber-physical systems over an unreliable communication interaction, which is to achieve coordination tracking in the presence of intermittent denial-of-service (DoS) attacks. Under the switching communication network environment, first, a distributed secure control method for each subsystem is proposed via neighborhood information, which includes the local state estimator and cooperative resilient controller. Second, based on the topology-dependent Lyapunov function approach, the design conditions of secure control protocol are derived such that cooperative tracking errors are uniformly ultimately bounded. Interestingly, by exploiting the topology-allocation-dependent average dwell-time (TADADT) technique, the stability analysis of closed-loop error dynamics is presented, and the proposed coordination design conditions can relax time constraints on interaction topology switching. Finally, two numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Finite-Horizon H∞ Bipartite Consensus Control of Cooperation-Competition Multiagent Systems With Round-Robin Protocols

This article focuses on the finite-horizon H_∞ bipartite consensus control problem for a class of discrete time-varying cooperation-competition multiagent systems (DTV-CCMASs) with the round-robin (RR) protocol. The cooperation-competition relationship among agents is characterized by a signed graph, whose edges are with positive or negative connection weights. Specifically, a positive weight corresponds to an allied relationship between two agents and a negative one means an adversary relationship. The data exchange between each agent and its neighbors is orchestrated by an RR protocol, where only one neighboring agent is authorized to transmit the data packet at each time instant, and therefore, the data collision is prevented. This article aims to design a bipartite consensus controller for DTV-CCMASs with the RR protocol such that the predetermined H_∞ bipartite consensus is satisfied over a given finite horizon. A sufficient condition is first established to guarantee the desired H_∞ bipartite consensus by resorting to the completing square method. With the help of an auxiliary cost combined with the Moore-Penrose pseudoinverse method, a design scheme of the bipartite consensus controller is obtained by solving two coupled backward recursive Riccati difference equations (BRRDEs). Finally, a simulation example is given to verify the effectiveness of the proposed scheme of the bipartite consensus controller.

Simplifying Complex Network Stability Analysis via Hierarchical Node Aggregation and Optimal Periodic Control

In this study, the stability of a hierarchical network with delayed output is discussed by applying a kind of optimal periodic control. To reduce the number of the nodes of the original hierarchical network, an aggregation algorithm is first presented to take some nodes with the same information as an aggregated node. Furthermore, the stability of the original hierarchical network can be guaranteed by the optimal periodic control of the aggregated hierarchical network. Then, an optimal control scheme is proposed to reduce the bandwidth waste in information transmission. In the control scheme, the time sequence is separated into two parts: the deterministic segment and the dynamic segment. With the optimal control scheme, two targets are achieved: 1) the outputs of the original and aggregated hierarchical system are both asymptotically stable and 2) the nodes with slow convergent rate can catch up with the convergence speeds of other nodes.

Distributed Secure Consensus Control With Event-Triggering for Multiagent Systems Under DoS Attacks

Consensus control of multiagent systems (MASs) has applications in various domains. As MASs work in networked environments, their security control becomes critically desirable in response to various cyberattacks, such as denial of service (DoS). Efforts have been made in the development of both time- and event-triggered consensus control of MASs. However, there is a lack of precise calculation of control input during the attacking periods. To address this issue, a distributed secure consensus control with event triggering is developed for linear leader-following MASs under DoS attacks. It is designed with a dual-terminal event-triggered mechanism, which schedules information transmission through two triggered functions for each follower: one on the measurement channel (sensor-to-controller) and the other on the control channel (controller-to-actuator). To deal with DoS attacks, the combined states in the triggered functions are replaced by their estimations from an observer. Sufficient conditions are established for the duration and frequency of DoS attacks. To remove continuous monitoring of the measurement errors, a self-triggered secure control scheme is further developed, which combines the system states and other information at past triggered instants. Theoretical analysis shows that the followers in MASs under DoS attacks are able to track the leader and meanwhile the Zeno behavior is excluded. Case studies are conducted to demonstrate the effectiveness of our distributed secure consensus control of MASs.

Adaptive Event-Triggered Consensus Control of a Class of Second-Order Nonlinear Multiagent Systems

This paper addresses an adaptive event-triggered consensus control problem for a class of second-order nonlinear multiagent systems (MASs) in an undirected communication topology. A novel adaptive distributed event-triggered consensus control scheme is presented for the MAS with unknown functions based on the definition of an auxiliary state, and the coefficient of the triggered function can be regulated adaptively with dependence on the auxiliary state error to ensure not only the control performance but also the efficiency of the network interactions. Furthermore, two self-triggered algorithms are developed for two cases, known functions and unknown ones, by the current state and information at the previous event time instant instead of the requirement for continuous monitoring auxiliary state errors. In theory, the stability of the resulting closed-loop system is rigorously investigated, and it is proven that all signals in the closed-loop system are bounded and the Zeno behavior is ruled out. Finally, two simulation examples, both real-time and numerical ones, are provided to verify the theoretical claims.

State-Saturated Recursive Filter Design for Stochastic Time-Varying Nonlinear Complex Networks Under Deception Attacks

This article tackles the recursive filtering problem for a class of stochastic nonlinear time-varying complex networks (CNs) suffering from both the state saturations and the deception attacks. The nonlinear inner coupling and the state saturations are taken into account to characterize the nonlinear nature of CNs. From the defender's perspective, the randomly occurring deception attack is governed by a set of Bernoulli binary distributed white sequence with a given probability. The objective of the addressed problem is to design a state-saturated recursive filter such that, in the simultaneous presence of the state saturations and the randomly occurring deception attacks, a certain upper bound is guaranteed on the filtering error covariance, and such an upper bound is then minimized at each time instant. By employing the induction method, an upper bound on the filtering error variance is first constructed in terms of the solutions to a set of matrix difference equations. Subsequently, the filter parameters are appropriately designed to minimize such an upper bound. Finally, a numerical simulation example is provided to demonstrate the feasibility and usefulness of the proposed filtering scheme.

Dynamic event-based state estimation for delayed artificial neural networks with multiplicative noises: A gain-scheduled approach

This study is concerned with the state estimation issue for a kind of delayed artificial neural networks with multiplicative noises. The occurrence of the time delay is in a random way that is modeled by a Bernoulli distributed stochastic variable whose occurrence probability is time-varying and confined within a given interval. A gain-scheduled approach is proposed for the estimator design to accommodate the time-varying nature of the occurrence probability. For the sake of utilizing the communication resource as efficiently as possible, a dynamic event triggering mechanism is put forward to orchestrate the data delivery from the sensor to the estimator. Sufficient conditions are established to ensure that, in the simultaneous presence of the external noises, the randomly occurring time delays with time-varying occurrence probability as well as the dynamic event triggering communication protocol, the estimation error is exponentially ultimately bounded in the mean square. Moreover, the estimator gain matrices are explicitly calculated in terms of the solution to certain easy-to-solve matrix inequalities. Simulation examples are provided to show the validity of the proposed state estimation method.

Consensus via event-triggered strategy of nonlinear multi-agent systems with Markovian switching topologies

The consensus problem via event-triggered strategy of nonlinear multi-agent systems (MASs) with Markovian switching topologies is addressed in this paper. To simplify information transmission, a distributed event-triggered mechanism (ETM) is designed. By combining the Markovian switching topologies and ETM, an appropriate consensus control protocol is presented. Considering the impact of delay on systems stability, the system model is transformed by the delay system approach. By choosing a Lyapunov-Krasovskii function and applying linear matrix inequalities technique, sufficient conditions are obtained to ensure the consensus stability with H_∞ norm bound of the MASs. A numerical simulation is given to confirm the effectiveness of the designed method.

Distributed Secure Cooperative Control Under Denial-of-Service Attacks From Multiple Adversaries

This paper develops a fully distributed framework to investigate the cooperative behavior of multiagent systems in the presence of distributed denial-of-service (DoS) attacks launched by multiple adversaries. In such an insecure network environment, two kinds of communication schemes, that is, sample-data and event-triggered communication schemes, are discussed. Then, a fully distributed control protocol with strong robustness and high scalability is well designed. This protocol guarantees asymptotic consensus against distributed DoS attacks. In this paper, "fully" emphasizes that the eigenvalue information of the Laplacian matrix is not required in the design of both the control protocol and event conditions. For the event-triggered case, two effective dynamical event-triggered schemes are proposed, which are independent of any global information. Such event-triggered schemes do not exhibit Zeno behavior even in the insecure environment. Finally, a simulation example is provided to verify the effectiveness of theoretical analysis.

Ship Security Relative Integrated Navigation with Injected Fault Measurement Attack and Unknown Statistical Property Noises

In this work, the ship relative integrated navigation approaches are studied for the navigation scenarios with the measurements disturbed by unknown statistical property noises and with the injected fault measurement attacks. On the basis of the limited energy property of system noises, the navigation states are estimated by the local finite horizon H∞ filter to satisfy the performance index function. Then, the local estimates are fused in the relative integrated navigation system with the weight fusion parameters obtained by using the local estimate error measurements. Further, the injected fault measurement attacks are considered in the relative integrated navigation systems. Due to the system noises and the measurement noises having unknown statistical property, the classical Chi-square test can hardly be utilized to detect the injected fault measurements. Therefore, a secure relative integrated navigation method is proposed with a distance-based clustering detector. The finial simulation results illustrate the effectiveness of the proposed relative integrated navigation approach and the proposed secure relative integrated navigation approach.