Event-triggered Feedback Control Research Articles

Stabilization for a class of fractional-order nonlinear reaction–diffusion systems with time-varying delay: Event-triggered boundary control approach

Based on the hybrid event-triggered mechanism (HETM), the boundary stabilization issue for fractional-order nonlinear reaction–diffusion systems (FNRDSs) with time-varying delay is studied by using two kinds of measurements. First, when the system state is measurable, a event-triggered feedback controller (ETFC) is designed directly based on the average measured output. Secondly, for the case that the state is unmeasurable, an event-triggered feedback controller based on observer framework is constructed through the boundary point measurement information. Utilizing the Lyapunov method and Wirtinger’s inequality, sufficient conditions for the asymptotic stability of the system are given in the form of linear matrix inequalities (LMIs), respectively, in which the Razumikhin theorem is used to deal with time-varying delay. Meanwhile, it is proved that Zeno behavior can be excluded by the designed HETM. Finally, numerical simulations demonstrate the validity and feasibility of the proposed control scheme.

Admissible and dissipative synchronisation of fractional order singular systems with time delay using event-triggered feedback control

The purpose of this work is to study the admissible and dissipative synchronisation of fractional order singular systems with time delay. The key goal is to use as few network resources as possible while retaining the desired closed-loop performance. An event-triggered control method is used to accomplish this. The Lyapunov function method, linear matrix inequality approach, and mathematical techniques are used to develop new synchronisation criteria that assure the synchronisation error system is Mittag–Leffler stable. Because fractional order differential equations have memory characteristics, which are very different from ordinary differential equations, leading to difficulties in preventing Zeno behaviour related to the event-triggered mechanism of fractional order systems, especially of delayed fractional order singular systems. To solve this issue, we propose a new theoretical framework and a new condition to preclude Zeno behaviours. This derived conditions use inequality techniques and take advantage of a number of fundamental aspects of fractional order calculus. Furthermore, the dissipative synchronous problem of delayed fractional order singular systems is also solved for the first time using the suggested stable criterion in conjunction with some auxiliary characteristics of fractional calculus. Two numerical examples are provided to demonstrate the usefulness of the proposed strategy.

Event-Triggered Feedback Control for Nonlinear Parabolic Distributed Parameter Systems With Time-Varying Delays

Event-Triggered Feedback Control for Nonlinear Parabolic Distributed Parameter Systems With Time-Varying Delays

Event-Triggered Adaptive Fuzzy Optimal Control for a Class of Strict-Feedback Nonlinear Systems With External Disturbances

In this paper, the problem of the event-triggered optimal control for a class of strict-feedback nonlinear systems with external disturbances is investigated. Firstly, by introducing proper low-pass filters to the steps of backstepping design, the problem of “jump of the error surfaces” is avoided. What's more, it facilitates the design of a fuzzy hybrid-mode-triggered feedforward controller, which aims to transform the original controlled nonlinear strict-feedback system into an equivalent nonlinear system in affine form. Secondly, by utilizing the adaptive dynamic programming theory, an event-triggered feedback controller is developed for the equivalent affine nonlinear system. Differing from the existing methods, the real control input consists of two event-triggered terms, which can be updated synchronously under the proposed composite error-based triggering condition. Moreover, it is proven that all the closed-loop signals are bounded. At last, by taking a second-order nonlinear system and missile integrated guidance and control system as examples, simulation results demonstrate the effectiveness of the proposed approach.

Finite-time decentralized event-triggered feedback control for generalized neural networks with mixed interval time-varying delays and cyber-attacks

<abstract><p>This article investigates the finite-time decentralized event-triggered feedback control problem for generalized neural networks (GNNs) with mixed interval time-varying delays and cyber-attacks. A decentralized event-triggered method reduces the network transmission load and decides whether sensor measurements should be sent out. The cyber-attacks that occur at random are described employing Bernoulli distributed variables. By the Lyapunov-Krasovskii stability theory, we apply an integral inequality with an exponential function to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). We present new sufficient conditions in the form of linear matrix inequalities. The main objective of this research is to investigate the stochastic finite-time boundedness of GNNs with mixed interval time-varying delays and cyber-attacks by providing a decentralized event-triggered method and feedback controller. Finally, a numerical example is constructed to demonstrate the effectiveness and advantages of the provided control scheme.</p></abstract>

Practical stability of continuous-time stochastic nonlinear system via event-triggered feedback control

This paper develops new practical stability criteria for continuous-time stochastic nonlinear system with uncertainties and external disturbances. Two cases of the system are considered: the system with state-dependent disturbance and the system with state-independent disturbance. Based on the event-triggered mechanism and Lyapunov function, we establish the input-to-state practical exponential stability in mean square for each case of the system. The obtained results improve some previous works in the literature. Finally, several examples are given to show the effectiveness and practicability of the main 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.

An Improved Design of Event-Triggered Feedback Controllers for Linear Systems Based on Fast and Slow Dynamics

In this article, an event-triggered technique is proposed to implement state feedback controllers for continuous-time linear systems. Toward this end, the closed-loop dynamic is decomposed into the fast and slow subsystems. Then, two individualized event-triggered mechanisms (ETMs) are designed to compute two sequences of updates. The first ETM determines when the fast subsystem should be sampled and its measured data should be sent to the controller. The second ETM decides the execution times for sampling all the system states, including both the fast and slow states. The proposed event-triggered technique leads to sampling policies in which the data of the slow states are sent to the controller with long interevent intervals whereas the fast dynamics are simultaneously allowed to be sampled with relatively shorter interevent intervals. In comparison with conventional methods with one ETM, the proposed event-triggered technique, equipped with an extra degree of freedom, leads to better results both in achieving smoother closed-loop responses and reducing the number of the transmitted packages from the system to the controller. Theoretical aspects of the proposed method including the boundedness of the system and its Zeno free property are investigated. Two simulation and experimental case studies are provided to show the effectiveness of the proposed event-triggered controller.

Adaptive Event-Triggered Control of Uncertain Nonlinear Systems Using Intermittent Output Only

Although rich collection of research results on event-triggered control exist, no effort has ever been made in integrating state/output triggering and controller triggering simultaneously with backstepping control design. The primary objective of this article is, by using intermittent output signal only, to build a backstepping adaptive event-triggered feedback control for a class of uncertain nonlinear systems. To do so, we need to tackle three technical obstacles. First, the nature of the event triggering makes the transmitted output signal discontinuous, rendering the regular recursive backstepping design method inapplicable as the repetitive differentiation of virtual control signals is literally undefined. Second, the effects arisen from the event-triggering action must be properly accommodated, but the current compensating method only works for systems in normal form, thus a new method needs to be developed in order to handle nonnormal form systems. Third, as only intermittent output signal is available, and at the same time, the impacts of certain terms containing unknown parameters (arising from event triggering) need to be compensated, it is rather challenging to design a suitable state observer. To circumvent these difficulties, we employ the dynamic filtering technique to avoid the differentiation of virtual control signals in the backstepping design, construct a new compensation scheme to deal with the effects of output triggering, and build a new form of state observer to facilitate the development of output feedback control. It is shown that, with the derived adaptive backstepping output-triggered control, all the closed-loop signals are ensured bounded and the transient system performance in the mean square error sense can be adjusted by appropriately adjusting design parameters. The benefits and effectiveness of the proposed scheme are also validated by numerical simulation.

Stability of Stochastic Delayed Differential Equations with Exogenous Disturbances via Event-Triggered Scheme

This paper discusses the input-to-state practically stabilization (ISpS) issue for stochastic delayed differential equations (SDDEs) 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 input-to-state practically stabilization is used to describe the dynamic performance of control target in the event-triggered schemes and exogenous disturbances. Making use of stochastic control theory, we demonstrate that the considered SDDEs is ISpS via an event-triggered feedback controller represented by linear matrix inequalities (LMIs). Moreover, lower bound of interaction time of control task is obtained to avoid the Zeno behavior. Compared with the large number of results for discrete-time stochastic systems, event-triggered control of continuous-time stochastic systems only yields a few results.

Dynamic Event-triggered Quantitative Feedback Control for Switched Affine Systems

Dynamic Event-triggered Quantitative Feedback Control for Switched Affine Systems

Toward Embedded System Resources Relaxation Based on the Event-Triggered Feedback Control Approach

The paper describes an event-triggered nonlinear feedback controller design. Event triggering is a real-time controller implementation technique which reduces embedded system utilization and relaxes task scheduling of the real-time system. In contrast to classic time implementation techniques, the event-triggered execution is validated regarding the introduced triggering policy. The triggering rule is a boundary, where the last task value is preserved until the rule is violated. In the given paper, two different event-triggered strategies are designed for the class of dynamic systems with integral behavior. Both methods are based on sliding mode controller design, where the triggering rule of the first design involves only a partial state vector, which is a direct consequence of the triggering rule derivation throughout the Lyapunov stability analysis. In the second approach, the sliding mode controller is designed upon prior stabilized systems with the additional term, which enables derivation of the triggering rule based on the whole state vector. The second approach offers better closed-loop performance and higher relaxation of the system utilization. The selection of triggering boundary is related closely to the derived minimal inter-event time, which impacts the computational burden of the real-time system and closed-loop performance directly. The derived controllers are compared with the classic sample and hold implementation techniques. The real-time results are presented, and system performances are confirmed regarding embedded system task relaxation, lowering the computational intensity and preserving closed-loop dynamics.

Asymptotical Synchronization of Drive-Response Networks by Sample-Data-Based Event-Triggered Control with Quantization and Cyber-Attacks

This paper addresses the asymptotic synchronization problem for a kind of drive-response complex networks (DRCNs) under cyber-attacks by using network control systems (NCSs). In order to reduce the pressure of communication and save the communication bandwidth on NCSs, some sampled-data-based event-triggered synchronization feedback controllers and logarithmic quantizers are designed by taking into account the effect of the NCSs’ transmission delays. Using Lyapunov stability theories, several sufficient conditions are obtained to guarantee the existence of sampleddata- based event-triggered synchronization controllers for the DRCNs with distributed-delay. Then, the state feedback gains are obtained by solving certain linear matrix inequalities (LMIs). Finally, a numerical example is provided to illustrate the effectiveness of the sampled-data-based eventtriggered control scheme.

Event-Triggered Distributed H∞ Constrained Control of Physically Interconnected Large-Scale Partially Unknown Strict-Feedback Systems

In this paper, an event-triggered distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> constrained control algorithm is designed for physically interconnected large-scale partially unknown strict-feedback systems with constrained-input and external disturbance. The advantage of both physical interconnection and communication is synchronously exploited for the scheme. First, an event-triggered feedforward control policy is proposed to transform control of physically interconnected large-scale systems into equivalent event-triggered control of decoupled multiagent systems. Then, an event-triggering condition and an event-triggered feedback control algorithm are designed to learn the optimal control policy and the disturbance policy in the worst case. The algorithm eliminates identifier, actor, and disturber neural networks and also relaxes the persistent excitation condition. It guarantees that the closed-loop dynamics is stabilized and the cost function is converged to the bounded <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain optimal value while the Zeno phenomenon is excluded. Finally, the effectiveness of the proposed algorithm is verified through simulation results of event-triggered distributed control of a physically interconnected constrained-torques multimobile robot system.

Event-triggered feedback control for discrete-time piecewise-affine systems subject to input saturation and bounded disturbance

The problem of event-triggered control for discrete-time piecewise-affine systems subject to input saturation and bounded disturbance is investigated in this paper. An LMI-based event-triggered controller is designed to guarantee the local asymptotic stability by introducing auxiliary feedback matrices to handle input saturation. In addition, the region of attraction is well estimated. Meanwhile, by synthesising the feedback control gains and the given event-triggering condition, an optimisation problem for maximising the region of attraction is formulated in LMIs. For input-saturated piecewise-affine systems with bounded disturbance, our control objective is to reduce the influence of disturbance while reducing communication in order to guarantee that the system is uniformly ultimately bounded. The effectiveness and advantages of the proposed approaches are demonstrated by simulations.

Stabilization and Event-Triggered Control of Stochastic Delay Systems With Markovian Jump Parameters

This article is concerned with the problem of delay-dependent stabilization for a class of stochastic Markov systems with event-triggered feedback control. An event-triggered mechanism (ETM) is proposed with the purpose of effectively reducing the transmissions of redundant massages, in which the generation of sensor sampling and control actuation is not periodic but only when some event-driven conditions are satisfied. In the meanwhile, a novel Lyapunov-Krasovskii functional (LKF) is applied to the closed-loop systems to establish the criterion of practically exponential mean-square stability. And a positive lower bound on the inter-execution times is guaranteed, that is, the Zeno behavior will not happen under this ETM. Furthermore, the event-triggered feedback controller can be constructed by solving the relevant linear matrix inequalities (LMIs). In the end, a numerical example displays the feasibility of our results.

Observer-based event-triggered control for semilinear time-fractional diffusion systems with distributed feedback

This paper is concerned with the observer-based distributed event-triggered feedback control for semilinear time-fractional diffusion systems under the Robin boundary conditions. To this end, an extended Luenberger-type observer is presented to solve the limitations caused by the impossible availability of full-state information that is needed for feedback control in practical applications due to the difficulties of measuring. With this, we propose the distributed output feedback event-triggered controllers via backstepping technique under which the considered systems admit Mittag–Leffler stability. It is shown that the given event-triggered control strategy could significantly reduce the amount of transmitted control inputs while guaranteeing the desired system performance with the Zeno phenomenon being excluded. A numerical illustration is finally presented to illustrate our theoretical results.

Quantized Event-triggered feedback control under fuzzy system with time-varying delay and Actuator fault

This paper is concerned to address the problem of quantized event-based H∞ control for networked control systems (NCS’s) under time-varying delay with actuator fault. The feedback NCS’s has been demonstrated as a nonlinear system with time-varying. Event-triggered communication scheme and a quantization scheme are also co-designed to overcome the bandwidth utilization. According to this scheme, data will only transmit when it reaches the threshold value. Furthermore a T–S fuzzy delay model is employed to approximate the nonlinear dynamics of the NCS’s. In addition a novel Lyapunov function is introduced to establish H∞ performance index in the term of linear matrix inequalities (LMIs). Finally, a truck-trailer example is provided to demonstrate the advantage and effectiveness of the anticipated results.

Stabilization of Stochastic Nonlinear Delay Systems With Exogenous Disturbances and the Event-Triggered Feedback Control

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.

Event-triggered uniform ultimate bound control for linear systems with time-varying delay

This paper investigates an effective event-triggered control for linear systems with time-varying delay. For reducing the sampled data transmission amount, a novel event-trigger is proposed wherein a state-independent threshold is involved. For guaranteeing uniformly ultimately bounded stability, an event-triggered feedback control law is proposed. By aid of a new free-weight matrix technique, the event-trigger and control co-design method is conveniently obtained. By pre-specifying the threshold of the event-trigger, the event-triggered frequency and the ultimate state convergence region can be simultaneously regulated. In addition, the convergence rate of closed-loop system is pre-specifiable as well. More significantly, the minimal event-triggering time interval is given. During that time interval, the event-trigger can not be violated, thus the Zeno phenomena is excluded naturally. Numerical examples are provided to demonstrate the effectiveness of the proposed method.