Event-triggered Parameters Research Articles

Observer-Based Event-Triggered Control for Networked Linear Systems Subject to Denial-of-Service Attacks.

This paper is concerned with the observer-based event-triggered control for a continuous networked linear system subject to denial-of-service (DoS) attacks, where the attacks are launched periodically to block the data transmission in control channels. First, a new observer state-based resilient event-triggering scheme is developed in the presence of DoS attacks. Second, a novel event-based switched system model is established by considering the effect of the event-triggering scheme and DoS attacks simultaneously. By virtue of this new model combined with a piecewise Lyapunov-Krasovskii functional method, the sufficient conditions are derived to guarantee exponential stability of the resulting switched system. It is shown that the proposed results can establish a quantitative relationship among the launching/sleeping periods of the attacks, the event-triggering parameters, the sampling period, and the exponential decay rate. Third, criteria for designing a desired observer-based event-triggered controller are provided and expressed in terms of a set of linear matrix inequalities. Finally, an offshore structure model is presented to illustrate the efficiency of the developed control method.

Event-triggered quantized [formula omitted] control for networked control systems in the presence of denial-of-service jamming attacks

The problem of event-triggered quantized H∞ control of networked control systems (NCSs) under denial-of-service (DoS) jamming attacks is investigated in this paper. Firstly, a new resilient event-triggering transmission scheme is proposed to lighten the load of computing and communications while offsetting the DoS jamming attacks imposed by power-constrained Pulse-Width Modulated (PWM) jammers. Secondly, a new switched system model is established, which characterizes the effects of the event-triggering scheme, quantization and DoS jamming attacks within a unified framework. Thirdly, linear matrix inequality (LMI)-based sufficient conditions for ensuring the exponential stability of the resulting switched system under the DoS jamming attacks are derived by using the piecewise Lyapunov functional method. Moreover, if the obtained LMIs are feasible, the co-design of the event-triggering parameter and the feedback gain matrix can be obtained. Finally, a satellite yaw angle control system is given to verify the effectiveness and feasibility of the developed theoretical 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.

Event-triggered state estimation for T-S fuzzy affine systems based on piecewise Lyapunov-Krasovskii functionals

This paper investigates the problem of event-triggered H∞ state estimation for Takagi-Sugeno (T-S) fuzzy affine systems. The objective is to design an event-triggered scheme and an observer such that the resulting estimation error system is asymptotically stable with a prescribed H∞ performance and at the same time unnecessary output measurement transmission can be reduced. First, an event-triggered scheme is proposed to determine whether the sampled measurements should be transmitted or not. The output measurements, which trigger the condition, are supposed to suffer a network-induced time-varying and bounded delay before arriving at the observer. Then, by adopting the input delay method, the estimation error system can be reformulated as a piecewise delay system. Based on the piecewise Lyapunov-Krasovskii functional and the Finsler’s lemma, the event-triggered H∞ observer design method is developed. Moreover, an algorithm is proposed to co-design the observer gains and the eventtriggering parameters to guarantee that the estimation error system is asymptotically stable with a given disturbance attenuation level and the signal transmission rate is reduced as much as possible. Simulation studies are given to show the effectiveness of the proposed method.

Resilient H∞ Filtering for Event-Triggered Networked Systems Under Nonperiodic DoS Jamming Attacks

This paper focuses on the resilient ${H_{\infty }}$ filter design for event-triggered networked systems subject to nonperiodic denial-of-service (DoS) jamming attacks. In this paper, a new resilient event-triggered transmission strategy is first proposed to improve the efficiency of network resource utilization while counteracting the nonperiodic DoS jamming attacks. Then, by using a time-delay approach, the filtering error system is modeled as a switched system, which characterizes the effects of the event-triggering scheme and nonperiodic DoS jamming attacks simultaneously. Based on the established model, by using the piecewise Lyapunov–Krasovskii functional method, linear matrix inequality (LMI)-based sufficient conditions are formulated to achieve the globally exponential stability as well as the weighted ${H_{\infty }}$ performance of the resulting switched system under the DoS jamming attacks. Consequently, the co-design method for the desired filter parameters and event-triggering parameters can be formulated provided that the above LMIs are feasible. Finally, the effectiveness of the proposed method is demonstrated by a practical example.

Dynamic output feedback control for stochastic networked control systems based on a periodic event-triggered mechanism

In this paper, the event-triggered dynamic output feedback control for stochastic networked control systems is investigated. The measurement output signal is periodically sampled but aperiodically transmitted. The time-delay system method is utilized to model the stochastic networked control system under the periodic event-triggered mechanism, then the corresponding stability criteria are obtained. Based on the stability criteria, the suitable output-based controller and event-triggered parameters are co-designed. Two air vehicle systems are presented to illustrate the efficiency of the proposed control method.

Event-triggered group consensus for multi-agent systems subject to input saturation

This paper investigates group consensus for leaderless multi-agent systems with non-identical dynamics. The consensus protocol is put forward in the form of the distributed event-triggered control subject to saturation, which depends on information from neighboring agents at event-triggered instants. In order to exclude the Zeno behavior and save resources, the given event-triggered condition is detected only at discrete sampling times, where the sampling intervals can be variable. Based on the graph theory, Lyapunov–Krasovskii functional method and by adopting the free-weighting matrix technique, some sufficient group consensus criteria in terms of linear matrix inequalities are derived. Furthermore, optimization problems aiming at maximizing the event-triggered parameter and the consensus region are proposed. Finally, numerical simulations illustrate the effectiveness of the theoretical results.

H∞ observer-based event-triggered sliding mode control for a class of discrete-time nonlinear networked systems with quantizations

This paper investigates the problem of H∞ observer-based event-triggered sliding mode control (SMC) for a class of uncertain discrete-time Lipschitz nonlinear networked systems with quantizations occurring in both input and output channels. The event-triggered strategy is used to save the limited network bandwidth. Then, based on the zero-order-hold (ZOH) measurement, a state observer is designed to reconstruct the system state, which facilitates the design of the discrete-time sliding surface. Considering the effects of quantizations, networked-induced constraints and event-triggered scheme, the nonlinear state error dynamics and sliding mode dynamics are converted into a unified linear parameter varying (LPV) time-delay system with the aid of a reformulated Lipschitz property. By using the Lyapunov-Krasovskii functional and free weighting matrix, a new sufficient condition is derived to guarantee the robust asymptotic stability of the resulting closed-loop system with prescribed H∞ performance. And then the observer gain, event-triggering parameter and sliding mode parameter are co-designed. Furthermore, a novel SMC law is synthesized to force the trajectories of the observer system onto a pre-specified sliding mode region in a finite time. Finally, a single-link flexible joint robot example is utilized to demonstrate the effectiveness of the proposed method.

Remote Nonlinear State Estimation With Stochastic Event-Triggered Sensor Schedule.

This paper concentrates on the remote state estimation problem for nonlinear systems over a communication-limited wireless sensor network. Because of the non-Gaussian property caused by nonlinear transformation, the unscented transformation technique is exploited to obtain approximate Gaussian probability distributions of state and measurement. To reduce excessive data transmission, uncontrollable and controllable stochastic event-triggered scheduling schemes are developed to decide whether the current measurement should be transmitted. Compared with some existing deterministic event-triggered scheduling schemes, the newly developed ones possess a potential superiority in maintaining Gaussian property of innovation process. Under the proposed schemes, two nonlinear state estimators are designed based on the unscented Kalman filter. Stability and convergence conditions of these two estimators are established by analyzing behaviors of estimation error and error covariance. It is shown that an expected compromise between communication rate and estimation quality can be achieved by properly tuning event-triggered parameter matrix. Numerical examples are provided to testify the validity of the proposed results.

Event-triggered [formula omitted] filtering of discrete-time switched linear systems

In this paper, the event-triggered H∞ filtering problem for discrete-time switched linear systems is addressed. The filter and the system are connected via a communication network, and the transmitted information of system output and switching signal is determined by an event-triggered transmission scheme, which contains system mode dependent parameters. Consequently, the asynchronous switching between the filter and the system occurs, and the filtering error system is modeled as a switched system with augmented switching signal by using the merging switching signal technique. Then, by the multiple Lyapunov function method, a new sufficient condition is obtained such that the filtering error system is exponentially asymptotically stable and satisfies the weighted H∞ performance. Finally, the design method for the filter and event-triggered parameters is proposed by solving a set of linear matrix inequalities. Numerical simulations illustrate the effectiveness of the proposed approach.

Event-triggered control of discrete-time switched linear systems with packet losses

The event-triggered control problem for discrete-time switched linear systems with packet losses is addressed in this paper. It is assumed that, at each event-triggered instant transmitted successfully, the controller can only access the transmitted information of system state and mode. In both cases of packet losses and no packet losses, mode dependent event-triggered transmission schemes are proposed. And the closed-loop system is modeled as a switched system with augmented switching signal. Then, based on the multiple Lyapunov function method, in the case of packet losses, exponential stability conditions are given with constraint of the maximum allowable number of successive packet losses, and design methods for state feedback controller gains and mode dependent event-triggered parameters are obtained. Finally, the effectiveness and improvement of the proposed approach are illustrated by a numerical example.

Robust event-triggered control for networked control systems

This paper is concerned with event-triggered dynamic output feedback control for networked control systems subject to communication delays. Two event-triggered conditions are predefined independently to check in an asynchronous matter if sampled signals from the sensor and control input signals from the controller should be transmitted to the controller and the actuator, respectively. As a result, communication resources can be further saved. Then, under the proposed framework, the closed-loop system is modeled as a switched system with a time-delay, based on which a novel exponential stability criterion is derived. This criterion is of less conservatism due to that the chosen Lyapunov–Krasovskii functional is not necessarily decreased. Moreover, the control gains and event-triggered parameters can be co-designed if the related linear matrix inequalities are feasible. The effectiveness of the proposed method is demonstrated via two numerical examples.

Decentralized Event-Triggered Control for Large-Scale Networked Fuzzy Systems

This paper addresses event-triggered data transmission in a class of large-scale networked nonlinear systems with transmission delays and nonlinear interconnections. Each nonlinear subsystem in the considered large-scale system is represented by a Takagi–Sugeno model, and exchanges its information through a digital channel. We propose an event-triggering mechanism, which determines when the premise variables and system states should be transmitted to the controller. Our goal is to design a decentralized event-triggered state-feedback fuzzy controller, such that the resulting closed-loop fuzzy control system is asymptotically stable while the measured information is transmitted to the controller as little as possible. By using the input delay and perturbed system approaches, the closed-loop sampled-data fuzzy system with event-triggered control is first reformulated into a continuous-time system with time-varying delay and extra disturbance. Then, based on the new model, we introduce a Lyapunov–Krasovskii functional with virtue of Wirtinger's inequality, where not all of the Lyapunov matrices are required to be positive definite. The codesign result is derived to obtain simultaneously the controller gains, sampled period, network delay, and event-triggered parameter in terms of a set of linear matrix inequalities. Finally, two simulation examples are provided to validate the advantage of the proposed method.

Event-triggered [formula omitted] filter design for Markovian jump systems with quantization

The problem of event-triggered H∞ filter design for Markov jump systems with output quantization is investigated in this paper. A dynamic event-triggered communication scheme is introduced to detect whether or not transmit the newly sampled data to the quantizer for different jumping modes. Time interval analysis approach is used to unify the Markov jump system, the event-triggered scheme and network-induced delays into a new Markov jump filtering error system with time-delay. Based on reciprocally convex approach, conditions are derived to guarantee the networked Markov jump system mean-square stable with an H∞ norm bound. The correspondent H∞ filter and the event-triggered parameters are also co-designed. Two numerical examples are given to show the effectiveness and better performance of the proposed analysis and design techniques.

Event-Triggered Based Reliable Control of Vehicle Active Suspension System Under Actuator Faults

This paper addresses the problem of reliable control of a vehicle active suspension system under actuator faults.The methodology based on event-triggering scheme is employed to design the controller and the proposed results are expressed in the form of linear matrix inequalities (LMIs). The motivation for introducing event-triggering control is to reduce the amount of data transmission in the system. The problem is contrived as a co-design problem to find both controller gain and event-triggering parameters. Finally, the efficacy of the proposed results is demonstrated for the system under fault through a simulation example. Also, a comparison is drawn between the sampled-data control and the proposed event-triggered control strategy.

Exponential Synchronization of Chaotic Lur’e Systems Using an Adaptive Event-Triggered Mechanism

This paper investigates event-triggered exponential synchronization of master-slave chaotic Lur'e systems (CLSs). First, in order to save communication resources, a novel event-based transmission strategy is developed using continuous-time measurements while a positive minimum inter-event time can be ensured. Second, an adaptive law is adopted to adjust dynamically the event-triggered threshold parameter. Compared with some existing static event-triggered mechanisms, the proposed event-triggered mechanism can provide a better tradeoff between communication resource saving and desired synchronization performance. Third, a switched Lyapunov-Krasovskii functional (LKF) is introduced, which is continuous at the switching instants but not necessarily positive definite at sampling intervals. This LKF is employed to derive a less conservative synchronization criterion for CLSs, based on which, the synchronization controller gain and the event-triggered parameters can be co-designed in terms of linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to illustrate the efficiency of the proposed method.

Event-triggered non-fragile control for linear systems with actuator saturation and disturbances

This paper investigates the problem of event-triggered non-fragile dynamic output feedback controller design for linear systems with actuator saturation and disturbances. The controller to be designed is supposed to include additive gain variations. By using Lyapunov stability theory and adding slack matrix variables, new sufficient conditions are derived to design the event-triggered parameters and the controller gains. Compared with the existing non-fragile dynamic output feedback controller design methods, the structural restriction on the Lyapunov matrix is relaxed. The effectiveness of the proposed method is demonstrated by two examples.

Event-Triggered Nonsynchronized $\mathcal {H}_{\infty }$ Filtering for Discrete-Time T–S Fuzzy Systems Based on Piecewise Lyapunov Functions

This paper is concerned with the design of ${\mathcal {H}_{\infty }}$ event-triggered filter for a class of Takagi–Sugeno fuzzy systems. Based on the proposed communication strategy, only the measured outputs of the physical plant that violate a predefined triggering condition will win the right for transmission in the shared communication channel. Considering that the implementation of the filter may not be synchronized with the plant trajectories due to the asynchronous premise variables in network environment, a novel observer-based piecewise fuzzy filter is proposed. By adopting the idea of input delay method, the filtering error dynamics is reformulated as a new event-triggered piecewise fuzzy system. By applying a piecewise Lyapunov–Krasovskii functional and some techniques on matrix convexification, a method of event-triggered ${\mathcal {H}_{\infty }}$ piecewise filter design is developed for the filtering error system concerned to be asymptotically stable with a given disturbance attenuation level and reduced transmission rate. Moreover, a co-design algorithm to derive the filter gains and the event triggering parameters is proposed. Illustrative examples are finally given to show the effectiveness of the developed method.

Event-based consensus for second-order multi-agent systems with actuator saturation under fixed and Markovian switching topologies

This paper studies the event-based consensus problem of second-order multi-agent systems with actuator saturation under fixed topology and Markovian switching topologies. By a model transformation, the consensus problem is first converted into the stability problem of the error system. Using discontinuous Lyapunov functional approach, two sufficient conditions on the consensus are derived for second-order multi-agent systems with fixed topology and Markovian switching topologies, respectively. The discontinuous Lyapunov functions take full account of the characteristics of the sawtooth delay, and thus lead to a less conservative consensus criterion. It is shown that the consensus condition depends on the parameters of sampling period, Laplacian matrix, and event-triggered parameter. In addition, this paper provides an effective method to co-design both the consensus controller and the event-triggered parameter. Finally, two numerical examples are provided to illustrate the effectiveness and feasibility of the proposed algorithm.

Event-triggered H∞ filtering of continuous-time switched linear systems

This paper considers the event-triggered H∞ filtering problem for continuous-time switched linear systems. It is assumed that only the information of system output and switching signal is available to the filter at each event-triggered sampling instant. Based on a mode dependent event-triggered sampling scheme, the filtering error system is modeled as a switched system with augmented switching signal. Then, by the average dwell time technique and multiple Lyapunov function method, a new sufficient condition is obtained such that the filtering error system is exponentially asymptotically stable and satisfies the weighted H∞ performance. The design method for the filter and event-triggered parameters is formulated by solving a set of linear matrix inequalities. Finally, the effectiveness of the proposed approach is illustrated by two numerical examples.