Event-triggered Stabilization Research Articles

Robust H∞ consensus for uncertain linear multi-agent systems on directed topologies: A dynamic event-triggered strategy

Considering the asymmetry of the system matrix caused by directed communication networks, a dynamic event-triggered control protocol for the robust [Formula: see text] consensus of uncertain linear multi-agent systems accompanied by external disturbances on directed topologies is proposed. Through the introduction of the controlled output and generalized algebraic connectivity for directed graphs, the consensus problem is converted to the event-triggered stabilization of the uncertain linear closed-loop system with disturbance. On the basis of the relative state of neighbor agents at event-times and the introduced dynamic variables, a dynamic event-triggered control protocol is put forward, and the linear matrix inequality sufficient conditions for the system to achieve robust [Formula: see text] consensus are obtained after a rigorous proof. Then, linear matrix inequalities are further decoupled to greatly reduce the computational complexity, and the parameters of the control protocol are determined by solving the decoupled linear matrix inequalities. Finally, simulations are applied for the verification of conclusions.

Event-triggered boundary control of an unstable reaction diffusion PDE with input delay

In chemical, biological, or population (epidemiological) processes the feedback action may be considerably delayed by time-consuming chemical measurements or biological tests. With such large delays on the control action in mind, and motivated by the fact that in some of these systems only piecewise-constant inputs can be applied between time instants at which measurements trigger changes in control, we consider the problem of event-triggered stabilization of 1-D reaction–diffusion PDE systems with input delay. The approach relies on reformulating the delay problem as an actuated transport PDE which cascades into the reaction–diffusion PDE, and on the emulation of backstepping control. The paper proposes a static (state-dependent) triggering condition which establishes the time instants at which the control value needs to be updated. It is shown that under the proposed event-triggered boundary control, there exists a minimal dwell-time (independent of the initial conditions) between two triggering times which allows to guarantee the well-posedness of the closed-loop system, and the exponential stability. The stability analysis is based on Input-to-State stability theory for PDEs and small-gain arguments. A simulation example is presented to validate the theoretical results.

The positivity and event-triggered stabilization of Takagi-Sugeno fuzzy systems with actuator saturation

The positivity and event-triggered stabilization of Takagi-Sugeno fuzzy systems with actuator saturation are investigated in this paper. Different from the existing quadratic event-triggered mechanism (ETM), a linear ETM is constructed, which can be reduced to a time-triggered mechanism (TTM). Based on parallel distribution compensation, an event-triggered fuzzy controller is designed, and sufficient conditions under the estimation of a certain domain of attraction are proposed to ensure the ETM-based and TTM-based closed-loop systems are positive and stable. The controller gain is solved directly by the proposed conditions. And then these sufficient conditions are extended to the conditions under the estimation of the largest domain of attraction by establishing an optimization problem. Furthermore, the linear ETM is proved to exclude the Zeno behavior of the system. Finally, two simulation examples are utilized to verify the effectiveness of the proposed event-triggered control scheme.

Adaptive Periodic Event-Triggered Stabilization of Switched Neural Networks Under the Merging Signal Scheme

Adaptive Periodic Event-Triggered Stabilization of Switched Neural Networks Under the Merging Signal Scheme

Adaptive event-triggered dissipative control for semi-Markovian jump systems with stochastic deception attack

This paper addresses the adaptive event-triggered (AET) stabilization problem for semi-Markovian jump systems (SMJSs) with deception attack. In the proposed AET control scheme, the threshold is adaptively updated unlike the existing event-triggered (ET) mechanisms, which can reduce communication pressure. By resorting to a mode-dependent Lyapunov functional, the stochastic stability and dissipative performance of SMJSs are guaranteed. In addition, according to stability conditions, the corresponding mode-dependent gain parameters are designed. At last, two numerical examples are given to demonstrate the effectiveness and applicability of the proposed theoretic results.

A hybrid event-triggered stabilization approach for switched systems under asynchronous switching and its application

This paper investigates the stabilization problem of switched systems with mismatched modes by an event-triggered control approach. A hybrid event-triggered scheme (HETS) with a dynamically adjustable threshold is newly proposed, which combines periodic sampling, continuous event-trigger and slow switching. It is assumed that the modes and states of the controller are updated only at each triggering instant, so the situation of asynchronous switching could arise. Compared with the control strategy under static HETS, the proposed hybrid event-triggered control strategy has the advantage of potentially speeding up the stabilization while reducing the communication burden. To ease the analysis, the closed-loop system is accordingly represented as a combination of the switched system with a periodically sampled control input and the one with a continuously event-triggered control input. By considering input delay information in the construction of multiple Lyapunov–Krasovskii functional (LKF), a discontinuous and non-positive definite LKF is developed to establish sufficient conditions on the exponential stability for the closed-loop switched system. The design method of the desired controller and HETS is then provided. Finally, the result obtained in this paper is applied to a networked continuous stirred tank reactors system.

Finite-Time Event-Triggered Stabilization for Discrete-Time Fuzzy Markov Jump Singularly Perturbed Systems.

The finite-time event-triggered stabilization is studied for a class of discrete-time nonlinear Markov jump singularly perturbed models with partially unknown transition probabilities (TPs). T-S fuzzy strategy is adopted to characterize the related nonlinear Markov jump singularly perturbed models. The control objective is to make sure that the system states remain within a bounded domain during a fixed-time interval. First, a mode-dependent event-triggered scheme is constructed to reduce the communication burden and save the network bandwidth. On that basis, by using a new Lyapunov function, a developed finite-time stability criterion is derived for the corresponding system to avoid an ill-conditioned issue due to a small singular perturbation parameter. Moreover, the mode-dependent fuzzy controller gain and the event-triggered parameter are co-designed under the framework of partially unknown TPs. Finally, the feasibility of the main results is provided to verify the finite-time event-triggered control strategy.

Aperiodic switching event-triggered stabilization of continuous memristive neural networks with interval delays

The stabilization problem is studied for memristive neural networks with interval delays under aperiodic switching event-triggered control. Note that, most of delayed memristive neural networks models studied are discontinuous, which are not the real memristive neural networks. First, a real model of memristive neural networks is proposed by continuous differential equations, furthermore, it is simplified to neural networks with interval matrix uncertainties. Secondly, an aperiodic switching event-trigger is given, and the considered system switches between aperiodic sampled-data system and continuous event-triggered system. Thirdly, by constructing a time-dependent piecewise-defined Lyapunov functional, the stability criterion and the feedback gain design are obtained by linear matrix inequalities. Compared with the existing results, the stability criterion is with lower conservatism. Finally, two neurons are taken as examples to ensure the feasibility of the results.

有限データレート信号と通信時刻情報を用いた離散時間線形システムの安定化

Event-triggered stabilization of a discrete-time system via a data-rate limited channel is studied. We concern the data rate required for stabilizability and provide a sufficient number of bits transmitted from the sensor to the controller at each event. When the controller receives a packet, it can extract information on the plant state from the reception timing and the event-triggering condition in addition to the bits carried by the packet. While the amount of the information is impaired by the communication delay and the discrete-time manner of the sampling, we show that for some systems the required data rate becomes lower than that obtained by the well-known data-rate theorem established for time-triggered systems.

Resilient event-triggered stabilization for uncertain Markovian jump delayed neural networks under time-window-based aperiodic DoS attacks

In this paper, the problem of robustly stable in mean square of uncertain Markovian jump neural networks (UMJNNs) with time-varying delays under time-window-based aperiodic denial-of-service (DoS) attacks is investigated. First, a new class of portrayal is proposed for DoS attacks, that is, fixed time-window-based non-periodic DoS attacks. In addition, a resilient event-triggered communication scheme (RETCS) is designed between sensors and controllers to reduce “unnecessary” waste of network resources under the proposed non-periodic DoS attack. Then, a new model of UMJNNs with time-varying delays considering non-periodic DoS attacks is developed on this basis. Second, a new single Lyapunov function is constructed in this paper for non-periodic DoS attacks. In addition, the stability criteria of UMJNNs with time-varying delays are obtained based on Lyapunov stability theory and the linear matrix inequality technique. Then, the criterion for co-designing the trigger parameters of RETCS and the gain matrix of the controller is proposed. Finally, the validity of the obtained result is illustrated by two examples.

Event-triggered stabilization of linear input-delay systems with state quantization and unknown time-varying delay: A Razumikhin stability theorem-based approach

Benefiting from the input-to-state stability (ISS) version of the Razumikhin stability theorem, this paper deals with the stabilization of continuous linear input-delay systems with state quantization and without any knowledge about the delay. An event-triggered delay independent truncated predictor feedback (ET-DITPF) controller with a switched feedback control law is proposed to guarantee the globally uniformly asymptotic stability (GUAS)/globally uniformly exponential stability (GUES) of the closed-loop system. As a prominent feature, this controller uses no information about the time delay (neither its value nor its upper bound). In the proposed event-triggered framework, a lower bound for each two consecutive events is derived to show the non-occurrence of the Zeno behavior. Numerical simulations confirm the effectiveness of the obtained theoretical results.

Decentralized observer-based event-triggered control for an interconnected fractional-order system with stochastic Cyber-attacks

<abstract> <p>The problem of decentralized observer-based event-triggered stabilization for an interconnected fractional-order system subject to stochastic cyber-attacks is studied. To address this issue, the decentralized event-triggered mechanism is proposed for the interconnected fractional-order system, where the event-triggered schemes are designed based on the states of fractional-order observers, and the stochastic attacks are considered both on control inputs and observer outputs. By combining decentralized observers and decentralized event-triggered controllers, we aim to achieve decentralized control with reduced amplifying error and use local signals to improve overall system performance. By utilizing the diffusive representation of the fractional-order system, the interconnected fractional-order system is transformed into an equivalent integer-order one to simplify the analysis and control design. Employing the Lyapunov indirect approach, a sufficient condition is obtained to guarantee the stochastic asymptotically stability of the augmented system. Additionally, by the singular value decomposition technique, the approach of simultaneously computing the decentralized observer gains and controller gains is presented. Finally, a simulation example is provided to validate the theoretical findings.</p> </abstract>

Event-Triggered Stabilization of Linear Time-Delay Systems via Halanay-Type Inequality

Event-Triggered Stabilization of Linear Time-Delay Systems via Halanay-Type Inequality

Event-triggered stabilisation of switched nonlinear systems with actuator saturation: a Hamiltonian approach

This paper presents a Hamiltonian approach to study the event-triggered stabilisation problem of switched affine nonlinear systems with actuator saturation. The key idea is to obtain an event-triggered control strategy by developing a constant Hamiltonian realisation method, an average dwell time (ADT) scheme and a nonlinear sector method. The proposed strategy can ensure the asymptotic stability of the plant without violating actuator saturation, even if there exists asynchronous phenomenon between the subsystems and their candidate controllers. The results presented in this paper remove the common assumption that the system's mode and controller's mode have to be synchronised and that the triggering condition has to be monitored continuously. This extends available results for switched nonlinear systems and reduces energy consumptions. Finally, an example is provided to verify the validity of the proposed results.

Event-triggered stabilisation for stochastic delayed differential systems with exogenous disturbances

In this paper, the practically input-to-state stabilization issue is considered for the stochastic delayed differential systems (SDDSs) with exogenous disturbances. To reduce the transmission frequency of the feedback control signal, the proposed SDDSs are stabilized by an event-triggered strategy. The concept of the practically input-to-state stability (ISS) is used to describe the dynamic performance of control target in the event-triggered schemes and exogenous disturbances. Besides, the considered SDDSs is stabilized by an event-triggered feedback controller which is represented by linear matrix inequalities. Moreover, lower bound of the interaction time of the event-triggered control method is obtained to avoid the Zeno behavior of the proposed event-triggering scheme. Finally, the effectiveness of the conclusion is verified by a numerical example.

Event-triggered stabilisation of sampled-data singular systems: a hybrid control approach

This paper provides a design of event-triggered feedback stabilisation scheme for a class of sampled-data singular systems, in which the input matrix corresponding to the algebraic equation is not full column rank. First, unlike the conventional piecewise-constant sampled-data feedback controller, a novel hybrid impulsive and sampled-data state feedback controller is designed, which can effectively match with the algebraic equation at sampling instants. An improved discrete event-triggering mechanism with checking period is proposed to achieve exponential stabilisation. Based on these, by applying the input delay approach and defining a new input-delay dependent Lyapunov functional, a sufficient stability condition is presented which ensures that the solution of the event-triggered control system exists and is unique, and the system is exponentially stable with definite decay rate. The estimate of decay coefficient is also given explicitly. Then, an optimisation-based method is developed to jointly design the hybrid controller gains and the event parameters. Finally, two simulation examples including a linearised 2-generator and 6-bus power network system are given to illustrate the validity of the new approach.

Stabilization of Memristor-Based Chua’s Circuits via Dynamic Event-Triggered Mechanism

This brief is concerned with the event-triggered stabilization for a memristor-based Chua’s circuits. A dynamic-periodic event-triggered approach is proposed, whose distinguishing feature is the introduction of two periodic triggering thresholds. One of the thresholds is an exponential decay function, and the other is an internal dynamic variable. Both thresholds contribute to the reduction of events. By Lyapunov theory, a concise criterion is developed for the stabilization of memristor-based Chua’s circuits. Simulation results are offered to support the theoretical results.

Event-triggered stabilization of uncertain scalar switched linear systems with bounded network delay

This paper aims to stabilize an uncertain scalar switched linear system whose feedback information is transmitted over a digital communication network. The system has a scalar state. That network can only supply a finite data rate to represent the state and suffers from time-varying bounded network delay. Due to the unknown mode switch time and the unknown network delay, mode mismatch between the plant and the controller is unavoidable. By applying reachable set approximation and propagation approaches, this paper quantitatively investigates the effects of mode mismatch and model uncertainty on the system’s stability and designs communication and control strategies to guarantee the desired stability. Moreover, it proposes some novel event-triggered sampling strategies, under which the required stabilizing bit rate can be lower than that required by traditional periodic sampling strategies. Simulations are done to verify the obtained results.

Dynamic event-triggered stabilization for the Schrödinger equation

The paper presents a dynamic event-triggering mechanism for the constant and the localized damped linear Schrödinger equation. The following results are tackled: the existence of solution to the closed-loop event-triggered control system; the avoidance of the Zeno behavior due to the absence of any accumulation point of the sequence of time instants and the exponential stability based on energy estimate through the observability inequality. A simulation example based on the one-dimensional Schrödinger equation is presented to validate the theoretical results.

Event-triggered stabilization for networked control systems under random occurring deception attacks.

This paper copes with event-triggered stabilization for networked control systems subject to deception attacks. A new switched event-triggered scheme (ETS) is designed by introducing a term regarding the last triggering moment in the trigger condition. This increases the difficulty of triggering, thus reducing trigger times compared to some existing ETSs. Furthermore, to cater for actual deception attack behavior, the occurrence of deception attacks is assumed to be a time-dependent stochastic variable that obeys the Bernoulli distribution with probability uncertainty. By means of a piecewise-defined Lyapunov function, a sufficient condition is developed to assure that the close-loop system under deception attacks is exponentially stable in regards to mean square. On the basis of this, a joint design of the desired trigger and feedback-gain matrices is presented. Finally, a simulation example is given to confirm the validity of the design method.