A Decentralized Event-Triggered Dissipative Control Scheme for Systems With Multiple Sensors to Sample the System Outputs

Global attractive set for quaternion-valued neural networks with neutral items

This paper investigated the global attractive set for quaternion-valued neural networks (QVNNs) with leakage delay, time-varying delay, and neutral items. Based on various basic conditions of activation function, the global attractive set and global exponential attractive set of QVNNs are given combined with novel analytical techniques and Lyapunov theory. The QVNNs are studied by a direct method, without any decomposition. The time delay can be non-differential, which makes the results more pragmatic. Restrictions on the activation function of the neutral item are relaxed. The neutral activation function can be bounded or unbounded, which makes the results more practical. Two simulation examples are given to verify the validity of the theory results.

Memory-Based Event-Triggered Output Regulation for Networked Switched Systems With Unstable Switching Dynamics

This article studies an event-triggered asynchronous output regulation problem (EAORP) for networked switched systems (NSSs) with unstable switching dynamics (USDs) including all modes unstable and partial switching instants destabilization, which means that the Lyapunov function increases both on the activation intervals of all subsystems and at some switching instants. First, a memory-based mode-compared event-triggered mechanism for switched systems is proposed to effectively shorten asynchronous intervals, which employs historical sampled outputs and compares the mode of the current sampled instant and the adjacent sampled instant. Then, the maximum average dwell time for a novel switching signal is derived with a constraint on the ratio of total destabilizing switchings to total stabilizing switchings, which relaxes the requirement of the regular arrangement of destabilizing and stabilizing switchings. Moreover, with the help of different coordinate transformations in the EAORP, the discretized Lyapunov functions are no longer needed when synthesizing the NSSs with USDs, and the asynchronous switching situation is also discussed. Afterward, by designing a dynamic output feedback controller, sufficient conditions are given to solve the EAORP for NSSs with USDs subject to network-induced delays, packet disorders, and packet losses. Finally, the effectiveness of the proposed methods is verified via a switched RLC circuit.

Event-Triggered ILC for Optimal Consensus at Specified Data Points of Heterogeneous Networked Agents With Switching Topologies

In this article, the optimal consensus problem at specified data points is considered for heterogeneous networked agents with iteration-switching topologies. A point-to-point linear data model (PTP-LDM) is proposed for heterogeneous agents to establish an iterative input-output relationship of the agents at the specified data points between two consecutive iterations. The proposed PTP-LDM is only used to facilitate the subsequent controller design and analysis. In the sequel, an iterative identification algorithm is presented to estimate the unknown parameters in the PTP-LDM. Next, an event-triggered point-to-point iterative learning control (ET-PTPILC) is proposed to achieve an optimal consensus of heterogeneous networked agents with switching topology. A Lyapunov function is designed to attain the event-triggering condition where only the control information at the specified data points is available. The controller is updated in a batch wise only when the event-triggering condition is satisfied, thus saving significant communication resources and reducing the number of the actuator updates. The convergence is proved mathematically. In addition, the results are also extended from linear discrete-time systems to nonlinear nonaffine discrete-time systems. The validity of the presented ET-PTPILC method is demonstrated through simulation studies.

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.

Predictor-Based Periodic Event-Triggered Control for Dual-Rate Networked Control Systems With Disturbances

This article considers the problem of periodic event-triggered control design for dual-rate networked control systems subject to nonvanishing disturbance. The plant considered in this article is a kind of dual-rate networked control system, where the sensor samples the measurement output at a slow rate and the actuator updates the control input at a fast rate. Despite the slow-rate sampling of the sensor, a new output predictor-based observer is proposed to accurately estimate system state and disturbance in the intersample time interval, and an active anti-disturbance controller that updates at a fast rate is accordingly proposed, such that the desirable control performance and disturbance rejection performance can be achieved. At each fast-rate updating time instant, we use the prediction technique to generate a data packet, including the computed current control input and the predicted values of the control inputs for the future finite steps, and design a new periodic event-triggered mechanism to determine whether to transmit the data packet via a communication network or not. The proposed control method is easily implemented in digital platform since it has a discrete-time form. To verify the effectiveness of the proposed control method, we finally present the simulation results of a practical speed control system.

Fuzzy Fault Detection for Markov Jump Systems With Partly Accessible Hidden Information: An Event-Triggered Approach

This article addresses the design issue of fuzzy asynchronous fault detection filter (FAFDF) for a class of nonlinear Markov jump systems by an event-triggered (ET) scheme. The ET scheme can be applied to cut down the transmission times from the system to FAFDF. It is assumed that the system modes cannot be obtained synchronously by the filter, and instead, there is a detector that can measure the estimated modes of the system. The asynchronous phenomenon between the system and the filter is characterized via a hidden Markov model with partly accessible mode detection probabilities. Applying the Lyapunov function methods, sufficient conditions for the presence of FAFDF are obtained. Finally, an application of a wheeled mobile manipulator with hybrid joints is employed to clarify that the devised FAFDF can detect the faults without any incorrect alarm.

Consensus for Second-Order Multiagent Systems Under Two Types of Sampling Mechanisms: A Time-Varying Gain Observer Method

This article considers the consensus of second-order multiagent systems (MASs) under a directed communication topology. By introducing time-varying gains into observers, two types of novel continuous-discrete-time observers are presented to estimate state information of agents under two sampling mechanisms, respectively, namely: 1) a synchronous nonuniform sampling (SNS) mechanism and 2) an asynchronous nonuniform sampling (ANS) mechanism. A new design method of the time-varying gain observer is proposed, in that it can allow for one to select a consensus protocol with lower cost observers to attain the consensus task. Only sampled position information needs to be transmitted in designing consensus protocols for the MSAs, and neither velocity information nor control input information is required. Under the SNS mechanism, a consensus condition is obtained and it is shown that the introduction of time-varying gains in the observers indeed can improve their convergence. Under the ANS mechanism, the corresponding consensus protocol allows the sampling and transmission of different agents to be asynchronous and aperiodic, which means that each agent may sample and transmit its information in line with its own sampling requirements. Furthermore, each sampling period can be arbitrarily selected within a certain range while ensuring the consensus of the MASs. Finally, numerical examples are given to illustrate the effectiveness of the obtained results.

Finite-Time Asynchronous Event-Triggered Formation of UAVs with Semi-Markov-Type Topologies

In this paper, the finite-time formation problem of UAVs is investigated with consideration of semi-Markov-type switching topologies. More precisely, finite-time passivity performance is adopted to overcome the dynamical effect of disturbances. Furthermore, an asynchronous event-triggered communication scheme is proposed for more efficient information exchanges. The mode-dependent formation controllers are designed in terms of the Lyapunov-Krasovskii method, such that the configuration formation can be accomplished. Finally, simulation results are given to demonstrate the validity of the proposed formation approach.

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.

Event-Triggered Distributed State Estimation for Cyber-Physical Systems Under DoS Attacks

This article investigates the event-triggered distributed state estimation problem for a class of cyber-physical systems (CPSs) with multiple transmission channels under denial-of-service (DoS) attacks. First, an observer-based event-triggered transmission scheme is proposed to improve the transmission efficiency, and the corresponding distributed Kalman filter is designed to estimate the system states. Under the collective observability condition, a relationship between estimation error covariance, attack intensity, and transmission efficiency is established by utilizing the covariance intersection fusion method and the property of matrix congruent transformation rank. The important features that distinguish our work from others are that the considered DoS attacks compromise each channel independently and do not have to satisfy the probabilistic property of the packet loss process. Furthermore, an event-triggered communication scheme is considered to improve the utilization of network resources between filters, and a sufficient condition for the parameter design is given which takes into account the influence of DoS attacks. Finally, simulation results are provided to verify the effectiveness of the proposed methods.

Line Integral Approach to Extended Dissipative Filtering for Interval Type-2 Fuzzy Systems

This article is concerned with the problems of extended dissipativity analysis and filter design for interval type-2 (IT2) fuzzy systems. Based on the line integral Lyapunov function, a sufficient condition of asymptotic stability and extended dissipativity of the systems under consideration is established. A LMI-based equivalent condition to the obtained one in a nonlinear form is provided by combining congruence transformation with change of variables. This LMI condition obtained is more general than the one which is based on the common quadratic Lyapunov function. Meanwhile, in terms of parameterization, the extended dissipative filter is developed which guarantees the asymptotic stability and extended dissipativity for the filtering error system. Furthermore, our filter obtained by the parameterization method includes the one obtained by the equivalent transformation method as a special case. Two simulation examples are provided to show the merits and effectiveness of the proposed approach.

Effects of Communication Signal Delay on the Power Grid: A Review

Communication plays a huge role in the operation of modern power systems. It permits a real-time monitoring coordination and control of the transmission, generation and distribution of electrical energy. As the modern grid grows towards an increased reliance on communication systems for the protection, metering and monitoring for as well as data acquisition for planning; there is a need to understand the challenge in the powers’ system communication and their impact on the uninterrupted supply of electrical energy. Communication delays are one of the challenges that might affect the performance of the power system and lead to power losses and equipment damage, it is important to investigate the causes and the mitigation options available. Thus, this paper the state of arts on the cause, the effect and mitigation of communication delays in the power system. Furthermore, in this paper an analysis of different causes of the delays for different network configurations and communication systems used; a comparative analysis of different latency mitigation methods and system performance simulations of a given compensation algorithm is tested against the existing methods. The pros and cons of these control strategies are illustrated in this paper. The summary and assessment of those methods of control in this review offer scholars and utilities valuable direction-finding to design superior communication energy control systems in the future.

Event-Triggered Output Feedback Synchronization of Master-Slave Neural Networks Under Deception Attacks

The problem of event-triggered synchronization of master-slave neural networks is investigated in this article. It is assumed that both communication channels from the sensor to controller and from controller to actuator are subject to stochastic deception attacks modeled by two independent Markov processes. Two discrete event-triggered mechanisms are introduced for both channels to reduce the number of data transmission through the communication channels. To comply with practical point of view, static output feedback is utilized. By employing the Lyapunov-Krasovskii functional method, some sufficient conditions on the synchronization of master-slave neural networks are derived in terms of linear matrix inequalities, which make it easy to design suitable output feedback controllers. Finally, a numerical example is presented to show the effectiveness of the proposed method.

Reset Control for Consensus of Multiagent Systems with Event-Triggered Communication

In the existing literature, reset control has been shown to have great potential to improve transient performance of linear systems, but reset-induced jump dynamics bring difficulties for stability analysis, especially under the network environment. In this article, we apply reset control to the consensus of multiagent systems (MASs) with event-triggered communication, and a novel reset mechanism (RM) and a hybrid event-triggering mechanism (ETM) are proposed with guaranteed Zeno-freeness. The state space is decomposed into multiple flow sets and jump sets according to the RM and ETM, and a hybrid model of the MASs is constructed such that the reset induced and event-trigger induced jump dynamics can be handled in a unified framework. Based on the hybrid model, a novel hybrid systems framework is presented for consensus analysis and co-design of RM and ETM. Finally, the proposed design is verified with a simulation example.

Outlier-Resistant Recursive Filtering for Multisensor Multirate Networked Systems Under Weighted Try-Once-Discard Protocol

In this article, a new outlier-resistant recursive filtering problem (RF) is studied for a class of multisensor multirate networked systems under the weighted try-once-discard (WTOD) protocol. The sensors are sampled with a period that is different from the state updating period of the system. In order to lighten the communication burden and alleviate the network congestions, the WTOD protocol is implemented in the sensor-to-filter channel to schedule the order of the data transmission of the sensors. In the case of the measurement outliers, a saturation function is employed in the filter structure to constrain the innovations contaminated by the measurement outliers, thereby maintaining satisfactory filtering performance. By resorting to the solution to a matrix difference equation, an upper bound is first obtained on the covariance of the filtering error, and the gain matrix of the filter is then characterized to minimize the derived upper bound. Furthermore, the exponential boundedness of the filtering error dynamics is analyzed in the mean square sense. Finally, the usefulness of the proposed outlier-resistant RF scheme is verified by simulation examples.

Periodic Event-Triggered Output-Feedback Stabilization for Stochastic Systems

This article is devoted to explore the periodic event-triggered stabilization for continuous-time stochastic systems, and to develop analysis tools/methods for stochastic periodic event-triggered control. Notably, without real-time monitoring of system behavior as in the scenario with continuous event evaluation, it is critical to delicately estimate and govern the execution/sampling error to achieve the desired system performance. This, under stochastic effects, would be substantially challenging, since the behavior of the stochastic system is hard to predict and is disparate between trials even with the same initial conditions. In this article, a framework of global stabilization via periodic event-triggered output-feedback is established: 1) a criterion condition based on the ISS-Lyapunov function is presented for the feasibility of the desired event-triggered stabilization; 2) both the asymptotic stabilization and exponential stabilization are achieved for the systems, with delicately specifying the periodic event-triggering mechanism; and 3) the involved analysis, without applying the well-known Lyapunov theorems, can serve as a pattern from estimating sampling and execution errors to assess the closed-loop stability for stochastic periodic event-triggered control. Moreover, based on the established framework, we contribute the stabilizing controller design via periodic event-triggered output-feedback for a class of stochastic nonlinear systems.

H∞ Static Output Feedback for Low-Frequency Networked Control Systems With a Decentralized Event-Triggered Scheme

This paper investigates an H_∞ static output feedback for a low-frequency (LF) networked control system (NCS). A decentralized event-triggered scheme (DETS) is proposed to reduce the network communication loads. The LF NCS with the DETS is modeled as a time-delay system with an LF constraint. With this model, H_∞ performance analysis is developed via an LF integral quadratic constraint method and a generalized Kalman-Yakubovich-Popov lemma. Furthermore, a detailed controller design algorithm is presented to obtain an H_∞ static output feedback controller for the LF NCS with the DETS via a two-stage approach. The numerical results are provided to demonstrate the effectiveness and superiority of the proposed techniques.

Position-Based Synchronization of Networked Harmonic Oscillators With Asynchronous Sampling and Communication Delays

This paper is concerned with position-based synchronization of networked harmonic oscillators. Note that synchronization cannot be achieved via current-position-based protocols. The objective of this paper is to investigate the positive effects of network-induced delays on the synchronization of networked harmonic oscillators. That is, if taking network-induced delays into account, the motion of harmonic oscillators can be really synchronized via a proper position-based control protocol. In doing so, the harmonic oscillators are connected via a shared digital communication network. Different from some existing results, system measurements from oscillator nodes are sampled in an asynchronous way; and network-induced delays are assumed to be time varying and bounded, and they do not need to be synchronous with those from the other communication channels. At each oscillator node, a buffer is embedded into the controller to store the newest sampled-data packets transmitted from its neighboring nodes through communication channels. Then, based on the store of the buffer, the controller computes its control signal with its own period. As a result, the overall synchronization error system is modeled as a linear system with multiple interval time-varying delays. By employing the discretized Lyapunov-Krasovskii functional method, a sufficient condition on synchronization of networked harmonic oscillators is derived, which can ensure that the synchronization error system is asymptotically stable for network-induced delays falling into a certain closed interval whose lower bound is a positive real number. This condition is thus used to design suitable control protocols in terms of linear matrix inequalities with several tuning parameters. Finally, a multirobot platform is given to demonstrate the effectiveness of the proposed method.

Event-Triggered/Self-Triggered Leader-Following Control of Stochastic Nonlinear Multiagent Systems Using High-Gain Method

In this article, the event-triggered and self-triggered leader-following output-feedback control problems are investigated for a class of high-order stochastic nonlinear multiagent systems (MASs) under an undirected graph. First, using the high-gain method, the observer is designed to estimate the unmeasured state variables of the given nonlinear system. Then, by introducing an internal dynamic variable, a distributed Zeno-free dynamic event-triggered controller is constructed. Compared with the static event-triggering results, the interevent time of the proposed dynamic event-triggering mechanism is shown to be prolonged and, thus, the advantages of the event-triggered control approaches can be enhanced. Further, to avoid continuously monitoring the states, a Zeno-free self-triggering mechanism is given. It is shown that the expectations of the output tracking errors converge to an arbitrarily small set if the diffusion terms are different for all agents, and that the expectations of all state tracking errors converge to an arbitrarily small set if the diffusion terms are the same for all agents. Finally, simulation studies are given to illustrate the effectiveness of the proposed methods.

Event-Triggered Output Feedback Control of Switched Nonlinear Systems With Input Saturation

This article is concerned with the event-triggered output feedback control problem for a class of switched nonlinear strict-feedback systems subject to asymmetric input saturation. The nonlinear terms are assumed to be bounded by a continuous function of the output multiplied by unmeasured states. The hyperbolic tangent function is employed to process the error caused by the event-triggered scheme, and an indicator function of the saturation degree is used to analyze the influence generated by the asymmetric input saturation. By adopting the common Lyapunov function method and the dynamic gain control design approach, a new design procedure based on a reduced-order observer is proposed to construct an output feedback controller. It is proved by the Lyapunov analysis that the proposed event-triggered control scheme can ensure that all the signals of the closed-loop system are globally bounded. Furthermore, the output can be converged to a bounded region around the origin, and this region can be tuned to be small by adjusting the design parameters. Different from typical existing results on the switched nonlinear strict-feedback systems, the celebrated backstepping method is not employed in this article. The continuous stirred tank reactor is finally used to demonstrate the effectiveness of the proposed control scheme.

Observer-Based Event-Driven Control for Discrete-Time Systems With Disturbance Rejection

In this article, the problem of disturbance rejection control is studied for discrete-time systems within an event-driven control framework. Through a predefined event-driven scheduler, both full- and reduced-order extended state observer (ESO)-based output feedback controllers are designed. With the proposed ESOs, both the disturbance and the system states are estimated, and the controllers are constructed with the estimated disturbance and states. Then, the stability and disturbance rejection analyses are conducted. It can be found that with the established event-driven control approaches, the updating frequency of the controller can be prominently reduced, and the disturbance can also be compensated in the output channels of the systems. Finally, the validity of the established control approaches is illustrated by the numerical simulations.

Distributed Event-Triggered Formation Control of Multiagent Systems via Complex-Valued Laplacian

Event-triggered formation control of multiagent systems under an undirected communication graph is investigated using complex-valued Laplacian. Both continuous-time and discrete-time models are considered. The dynamics of each agent is described by complex-valued differential or difference equations. For each agent, only the discrete-time information of its neighbors is used in the design of formation controllers and event triggers. Triggering time instants for any agent are determined by certain events that depend on the states of its neighboring agents. Continuous updating of controllers and continuous communication among neighboring agents are avoided. The obtained results show that formation can reach specific but arbitrary formation shape. Furthermore, it is shown that the closed-loop system does not exhibit the Zeno phenomenon for the continuous-time dynamics case or the Zeno-like behavior for the discrete-time dynamics case. Finally, numerical simulations for both the continuous-time and the discrete-time dynamics cases are presented to illustrate the effectiveness of the proposed distributed event-triggered control methods.

A Comprehensive Review of the Evolution of Networked Control System Technology and Its Future Potentials

Networked control systems (NCSs) are attracting the attention of control system engineers. The NCS has created a paradigm shift in control system technology. An NCS consists of control loops joined through communication networks in which both the control signal and the feedback signal are exchanged between the system and the controller. However, its materialization faces several challenges as it requires the integration of advanced control and communication techniques. This paper presents an extensive review of NCSs from the perspective of control system design. The evolution of NCSs is broadly divided in three phases, namely NCSs prior to 2000, NCSs during 2001–2010, and NCSs from 2011 onwards. This division corresponds to the initial status, intermediate status, and the recent status of the developments in the design of NCSs. The advancement of different control techniques during these phases has been discussed comprehensively. This paper also describes the transition of control systems form continuous domain to networked domain, which makes it better than the traditional control systems. Some important practical applications, which have been implemented using NCSs, have also been discussed. The thrust areas for future research on NCS have also been identified.

Periodic Event-Triggered Suboptimal Control With Sampling Period and Performance Analysis

In this paper, the periodic event-triggered suboptimal control (PETSOC) method is developed for continuous-time linear systems. Different from event-triggered control, where the triggering condition is monitored continuously, the developed PETSOC method only verifies the triggering condition periodically at sampling instants, which further reduces computational resources. First, the control gain of the PETSOC is designed based on the algebraic Riccati equation. Subsequently, the periodic event-triggering condition is proposed for the suboptimal control method, which is only verified at sampling instants periodically. The sampling period is determined and analyzed based on the continuous form of the triggering condition. Moreover, the stability and the performance upper bound of the closed-loop system with the PETSOC are proved. Finally, the effectiveness of the developed PETSOC is validated through simulation on an unstable batch reactor.

Distributed Dynamic Self-Triggered Impulsive Control for Consensus Networks: The Case of Impulse Gain With Normal Distribution

This paper investigates a distributed static and dynamic self-triggered impulsive control for nonlinear multiagent systems (MASs) where the impulsive gains follow a normal distribution, respectively. By integrating the distributed self-triggered control scheme with the impulsive control approach, a novel distributed impulsive controller is developed. The goal of the consensus of MASs can be realized using the proposed methods and several consensus criteria are obtained. Our schemes have some distinct superiorities, including the impulsive gains obeying a normal distribution, avoiding the continuous communication, and reducing the sampling frequency. Hence, compared with the existing literature, the conservativeness coming from the limitation of impulse gain and the sampling frequency is degraded, and it effectively extends the generality of the method in the practical application. Finally, the effectiveness of the theoretical results is demonstrated by two simulations.

Bit-Rate Conditions for the Consensus of Quantized Multiagent Systems With Network-Induced Delays Based on Event Triggering

This paper is mainly concerned with bit-rate conditions to guarantee the consensus of unstable scalar multiagent systems by event-triggering strategies. In such systems, state information is quantized and transmitted among agents through digital communication networks which suffer from network-induced delays. In order to save communication resources, we implement a periodic event-triggering scheme, under which agents quantize and transmit their own states when a predefined event is triggered. By introducing a well-designed internal saturation function, the proposed strategy can place a priori bounds on the control inputs of agents and guarantee the asymptotic consensus of agents at a finite bit rate, even under network-induced delays. By extracting extra information from the receive time instants of data packets, our strategy can require less information carried by data packets and a lower bit rate to maintain the desired asymptotic consensus than some state-of-the-art time-triggered consensus strategies. Under our strategy, the obtained bit-rate conditions depend on the network-induced delays, the unstable eigenvalue of agent dynamics, and the network topology. The simulation results are provided to illustrate the effectiveness of these bit-rate conditions.

Decentralized Event-Triggered Control for a Class of Nonlinear-Interconnected Systems Using Reinforcement Learning

In this article, we propose a novel decentralized event-triggered control (ETC) scheme for a class of continuous-time nonlinear systems with matched interconnections. The present interconnected systems differ from most of the existing interconnected plants in that their equilibrium points are no longer assumed to be zero. Initially, we establish a theorem to indicate that the decentralized ETC law for the overall system can be represented by an array of optimal ETC laws for nominal subsystems. Then, to obtain these optimal ETC laws, we develop a reinforcement learning (RL)-based method to solve the Hamilton-Jacobi-Bellman equations arising in the discounted-cost optimal ETC problems of the nominal subsystems. Meanwhile, we only use critic networks to implement the RL-based approach and tune the critic network weight vectors by using the gradient descent method and the concurrent learning technique together. With the proposed weight vectors tuning rule, we are able to not only relax the persistence of the excitation condition but also ensure the critic network weight vectors to be uniformly ultimately bounded. Moreover, by utilizing the Lyapunov method, we prove that the obtained decentralized ETC law can force the entire system to be stable in the sense of uniform ultimate boundedness. Finally, we validate the proposed decentralized ETC strategy through simulations of the nonlinear-interconnected systems derived from two inverted pendulums connected via a spring.

Real-Time H∞ Control of Networked Inverted Pendulum Visual Servo Systems

Aiming at the challenges of networked visual servo control systems, which rarely consider network communication duration and image processing computational cost simultaneously, we here propose a novel platform for networked inverted pendulum visual servo control using H_∞ analysis. Unlike most of the existing methods that usually ignore computational costs involved in measuring, actuating, and controlling, we design a novel event-triggered sampling mechanism that applies a new closed-loop strategy to dealing with networked inverted pendulum visual servo systems of multiple time-varying delays and computational errors. Using the Lyapunov stability theory, we prove that the proposed system can achieve stability whilst compromising image-induced computational and network-induced delays and system performance. In the meantime, we use H_∞ disturbance attenuation level γ for evaluating the computational errors, whereas the corresponding H_∞ controller is implemented. Finally, simulation analysis and experimental results demonstrate the proposed system performance in reducing computational errors whilst maintaining system efficiency and robustness.

Maneuvering Target Tracking With Event-Based Mixture Kalman Filter in Mobile Sensor Networks

In this paper, the distributed remote state estimation problem for conditional dynamic linear systems in mobile sensor networks with an event-triggered mechanism is investigated. The distributed mixture Kalman filtering method is proposed to track the state of the maneuvering target, which uses particle filtering to estimate the nonlinear variables and apply Kalman filtering to estimate the linear variables. An event-based distributed filtering scheme is designed, which is an energy-efficient way to transmit data between sensors and estimators. In addition, by using the mutual information theory, an optimal control problem is formed to control the position of sensors so that the target tracking process can be achieved quickly. Finally, a simulation example about the maneuvering target tracking is provided to corroborate the effectiveness of the filtering method and the control performance for sensors.

Distributed Sliding-Mode Tracking Control of Second-Order Nonlinear Multiagent Systems: An Event-Triggered Approach

The event-triggered tracking control problem of second-order multiagent systems in consideration of system nonlinearities is investigated by utilizing the distributed sliding-mode control (SMC) approach. An event-triggered strategy is proposed to decrease the controller sampling frequency and save the network communication resources; the triggering condition is then established for leader-following multiagent systems. In this article, by utilizing the distributed event-based sliding-mode controller, the system state of second-order multiagent systems with system nonlinearities is capable of approaching the integral sliding-mode surface in finite time. A novel integral sliding-mode surface is constructed in this article to guarantee the consensus tracking performance in the existence of system nonlinearities as the state trajectories of second-order integrator systems move on the constructed sliding manifold. By employing the Lyapunov approach, sufficient conditions are deduced to ensure that the consensus tracking performance is obtained for the closed-loop system. Furthermore, it is presented that the triggering scheme can effectively reduce state updates and eliminate the Zeno behavior. A simulation example is provided to testify the validity of our proposed methodology.

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.

Resilient Control Design Based on a Sampled-Data Model for a Class of Networked Control Systems Under Denial-of-Service Attacks

This article is concerned with designing resilient state feedback controllers for a class of networked control systems under denial-of-service (DoS) attacks. The sensor samples system states periodically. The DoS attacks usually prevent those sampled signals from being transmitted through a communication network. A logic processor embedded in the controller is introduced to not only receive sampled signals but also capture information on the duration time of each DoS attack. Note that the duration time of DoS attacks is usually both lower and upper bounded. Then the closed-loop system is modeled as an aperiodic sampled-data system closely related to both lower and upper bounds of duration time of DoS attacks. By introducing a novel looped functional, which caters for the N -order canonical Bessel-Legendre inequalities, some N -dependent stability criteria are presented for the resultant closed-loop system. It is worth pointing out that a number of identity formulas are uncovered, which enable us to apply the notable free-weighting matrix approach to derive less conservative stability criteria. A linear-matrix-inequality-based criterion is provided to design stabilizing state-feedback controllers against DoS attacks. A satellite control system is given to demonstrate the effectiveness of the proposed method.

Distributed Event-Triggered Consensus of Multiagent Systems With Communication Delays: A Hybrid System Approach

This paper investigates the leader-following consensus problem for multiagent systems (MASs) with communication delays. A novel hybrid event-triggered control scheme is developed and a hybrid system approach is proposed to design the event-triggering condition. Meanwhile, by means of temporal regularization, a strictly positive lower bound on the interevent times can be guaranteed, that is, Zeno-freeness can be guaranteed. The MASs are first described as a closed-loop system with both flow dynamics and jump dynamics, where the jump dynamics is induced from the triggering events and communication delays. Then, a hybrid model of the MASs is constructed under a hybrid systems framework. Based on this hybrid model, how to construct the Lyapunov function is given and the event-triggering condition design is also developed, such that the asymptotic consensus is achieved. Finally, an example is provided to show the effectiveness of the proposed approach.

Event-Triggered Consensus of Linear Multiagent Systems With Time-Varying Communication Delays

In this paper, the event-triggered consensus problem of linear multiagent systems with time-varying communication delays is addressed. Different from the existing event-triggered consensus results with communication delays, more general nonuniform time-varying communication delays are considered. To avoid the asynchronous phenomenon caused by nonuniform delays, a novel periodic switching controller is developed. Based on this controller, the resulting consensus error system can be modeled as a periodic switching system. Furthermore, the exponential stability of the consensus error system is derived by utilizing the Lyapunov approach and the dwell-time analysis method. Finally, an illustrative example is presented to demonstrate the effectiveness of the developed method.

Network-Based Modeling and Proportional-Integral Control for Direct-Drive-Wheel Systems in Wireless Network Environments

This paper focuses on the network-based modeling and proportional-integral (PI) control for a continuous-time direct-drive-wheel system in a wireless network environment. The developed system can simplify configuration, reduce bus cables, and realize vehicle height adjustment. A novel network-based model is first established by constructing a PI control system and taking network-induced delays and stochastic packet dropouts into account. By using two different artificial delays to characterize the update of proportional and integral control signals, the network-based PI control system is modeled as a stochastic impulsive system with two input delays and reset equations at updating instants. Then, through involving the reset states and the relationship among two delayed states and the current state in the discontinuous Lyapunov-Krasovskii functional and actively introducing the upper bounds of nonzero network-induced delays, some exponential mean-square stability and H_∞ performance conditions with less conservatism are derived in terms of tractable linear matrix inequalities. An algorithm is presented to determine the minimum H_∞ performance and the corresponding PI control parameters by combining a particle swarm optimization technique with the performance condition. These results can be extended to a network-based PI control of general continuous-time linear systems. A ZigBee-based network simulation platform is finally built and some simulation results are provided to validate the proposed methods.

Output-Based Dynamic Event-Triggered Mechanisms for Disturbance Rejection Control of Networked Nonlinear Systems

This paper proposes a new output-based dynamic event-triggered mechanism (ETM) for disturbance rejection control of a class of networked nonlinear uncertain systems subject to additive time-varying disturbance. In the proposed control method, a new robust output feedback controller is first designed based on a generalized proportional-integral observer to attenuate/compensate the undesirable influence of nonlinear uncertainties and disturbances. Different from the static ETM, two new dynamic variables are defined, and thereafter, two kinds of different discrete-time dynamic ETMs are developed only using the sampled-data output signal, such that a better tradeoff between the communication properties and the control properties can be obtained. It is shown that under the proposed control methods, the global bounded stability of the closed-loop hybrid system can be guaranteed by choosing some appropriate parameters. Finally, the numerical simulations of a single link robot arm are conducted to demonstrate the feasibility and efficacy of the proposed control approach.

Distributed Event-Triggered Estimation Over Sensor Networks: A Survey

An event-triggered mechanism is of great efficiency in reducing unnecessary sensor samplings/transmissions and, thus, resource consumption such as sensor power and network bandwidth, which makes distributed event-triggered estimation a promising resource-aware solution for sensor network-based monitoring systems. This paper provides a survey of recent advances in distributed event-triggered estimation for dynamical systems operating over resource-constrained sensor networks. Local estimates of an unavailable state signal are calculated in a distributed and collaborative fashion based on only invoked sensor data. First, several fundamental issues associated with the design of distributed estimators are discussed in detail, such as estimator structures, communication constraints, and design methods. Second, an emphasis is laid on recent developments of distributed event-triggered estimation that has received considerable attention in the past few years. Then, the principle of an event-triggered mechanism is outlined and recent results in this subject are sorted out in accordance with different event-triggering conditions. Third, applications of distributed event-triggered estimation in practical sensor network-based monitoring systems including distributed grid-connected generation systems and target tracking systems are provided. Finally, several challenging issues worthy of further research are envisioned.

Adaptive Event-Triggered Transmission Scheme and H∞ Filtering Co-Design Over a Filtering Network With Switching Topology

This paper addresses the distributed adaptive event-triggered H_∞ filtering problem for a class of sector-bounded nonlinear system over a filtering network with time-varying and switching topology. Both topology switching and adaptive event-triggered mechanisms (AETMs) between filters are simultaneously considered in the filtering network design. The communication topology evolves over time, which is assumed to be subject to a nonhomogeneous Markov chain. In consideration of the limited network bandwidth, AETMs have been used in the information transmission from the sensor to the filter as well as the information exchange among filters. The proposed AETM is characterized by introducing the dynamic threshold parameter, which provides benefits in data scheduling. Moreover, the gain of the correction term in the adaptive rule varies directly with the estimation error and inversely with the transmission error. The switching filtering network is modeled by a Markov jump nonlinear system. The stochastic Markov stability theory and linear matrix inequality techniques are exploited to establish the existence of the filtering network and further derive the filter parameters. A co-design algorithm for determining H_∞ filters and the event parameters is developed. Finally, some simulation results on a continuous stirred tank reactor and a numerical example are presented to show the applicability of the obtained results.

Decentralized event-triggered output feedback control for a class of interconnected large-scale systems

This paper is concerned with the problem of decentralized event-triggered dynamic output feedback control for large-scale systems with unknown interconnections. By using a modified cyclic-small-gain condition and introducing a free-matrix-based integral inequality, a novel sufficient condition is derived to ensure that the overall closed-loop system is asymptotically stable with a prescribed H_∞ performance. Based on this condition, a convex condition is presented to design the controller gains and the event-triggered parameters simultaneously. In contrast with the existing event-triggered results, the derived stability criterion can be applied to the large-scale systems with unmatched unknown interconnections. The effectiveness of the proposed control strategy is demonstrated by a double-inverted pendulum model.

Input-to-State Stabilization in Probability for Nonlinear Stochastic Systems Under Quantization Effects and Communication Protocols

In this paper, the observer-based stabilization problem is investigated for a class of discrete-time nonlinear stochastic networked control systems (NCSs) with exogenous disturbances. The signal transmission from the sensors to the observer is implemented via a shared digital network, in which both uniform quantization effect and stochastic communication protocol (SCP) are taken into account to reflect several network-induced constraints. The notion of input-to-state stability in probability is introduced to describe the dynamical behaviors of the closed-loop stochastic NCS that is effectively characterized by a general nonlinear stochastic difference equation with Markovian jumping parameters. A theoretical framework is first established to felicitate the dynamics analysis of the closed-loop system in virtue of the switched Lyapunov function method and the stochastic analysis techniques. By making full use of the quantized measurement output under the scheduling of the SCP, the existence conditions for an observer-based controller are established under which the closed-loop system is input-to-state stable in probability. Then, the explicit expression of the gain matrices of the desired controller is given by resorting to a set of feasible solutions of certain matrix inequalities. The effectiveness of the theoretical results is demonstrated by a numerical simulation example.

Near-Optimal Resilient Control Strategy Design for State-Saturated Networked Systems Under Stochastic Communication Protocol

In this paper, the near-optimal resilient control strategy design problem is investigated for a class of discrete time-varying system in simultaneous presence of stochastic communication protocols (SCPs), gain perturbations, state saturations, and additive nonlinearities. In the sensor-to-controller network, only one sensor is permitted to get access to the communication media so as to avoid possible data collisions. Described by a Markov chain, the SCP is employed to determine which sensor should obtain the access to the network at a certain time. Furthermore, two kinds of well-recognized complexities (i.e., state saturations and additive nonlinearities) are considered in the system model and the phenomenon of controller gain perturbation is also taken into special consideration. Accordingly, the resilient control strategy is designed by: 1) deriving a certain upper bound on the associate cost function of underlying systems and 2) minimizing such an upper bound through the utilization of the completing-the-square technique and the Moore-Penrose pseudo inverse. The resilient control strategy is obtained in an iterative manner by solving a set of coupled backward Riccati-like recursions. Furthermore, based on the proposed control strategies, the infinite horizon case is considered and the corresponding upper bound of the cost function is explicitly provided. Finally, numerical simulations are carried out on power systems in order to verify the validity of the proposed resilient control algorithms.

Observer-Based Event-Triggered Control for Nonlinear Systems With Mixed Delays and Disturbances: The Input-to-State Stability

In this paper, the input-to-state stabilization problem is investigated for a class of nonlinear delayed systems with exogenous disturbances. The model under consideration is general that covers for both mixed time-delays and Lipschitz-type nonlinearities. An observer-based controller is designed such that the closed-loop system is stable under an event-triggered mechanism. Two separate event-triggered strategies are proposed in sensor-to-observer (S/O) and controller-to-actuator (C/A) channels, respectively, in order to reduce the updating frequencies of the sensor and the controller with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to characterize the performance of the controlled system that caters for the influence from both disturbances and event-triggered schemes. The estimates of the upper bounds of the delayed states and two measurement errors are employed to analyze and further exclude the Zeno behavior resulting from the proposed event-triggered schemes in S/O and C/A channels. The controller gain matrices and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.

Model-Based Edge-Event-Triggered Containment Control Under Directed Topologies

This paper investigates the containment control problem of multiagent systems with double integrator dynamics under directed topologies. A model-based edge-event-triggered control protocol is proposed, in which the control input to each agent only contains edge information and its own velocity information. Continuous detection is avoided by the establishment of a predictive model and each controller is only updated at its own event time instants. The theoretical results show that, under our control protocol, the containment control problem can be solved and the Zeno behavior is excluded. The effectiveness is further illustrated by simulation results.