Event-triggered Feedback Research Articles

H∞ adaptive ETF control for degenerate jump systems under actuator faults and impulsive deception attacks with application to DCMIP device

This article considers the issue of H∞ adaptive event-triggered feedback control for degenerate jump systems under actuator faults and impulsive deception attacks. Based on periodic sampling strategy, a mode-dependent adaptive event-triggered scheme is developed, which can save communication resources, avoid the Zeno phenomenon and take full advantage of Markovian mode information. By constructing the neoteric Lyapunov-Krasovskii (L-K) functional containing piecewise linear impulsive auxiliary functions and applying singular value decomposition (SVD) technique, the fresh stochastic admissibility conditions for degenerate Markovian jump systems under actuator faults and impulsive deception attacks are obtained under the framework of linear matrix inequalities (LMIs), and then the adaptive event-triggered scheme with weighted matrices and feedback controller are designed simultaneously. By applying freedom weight matrix method and the property that the network-induced delay derivative is one, the non-strict LMI conditions are transformed into strict ones, such that the stochastic admissibility of the degenerate jump systems and state feedback controller gains are realized adequately. Finally, a direct current motor-controlled inverted pendulum (DCMIP) device is used to confirm the feasibility of the presented approach.

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

A co-design condition for dynamic event-triggered feedback linearization control

This paper presents a novel approach for dynamic event-triggered feedback linearization control of nonlinear systems. Two main aspects should be accounted for in this context: the internal perturbation induced by the sampling error and the stability of the internal dynamics. To deal with the first aspect, a trigger function is designed to cancel out the influence of the internal perturbation completely. Concerning the second one, a sufficient stability analysis condition is derived by representing the internal dynamics as a polytopic differential inclusion. These two ingredients allow for performing the co-design of dynamic event-triggered feedback linearization controllers. A multi-objective optimization problem with linear matrix inequality constraints is formulated to achieve the maximization of the estimate of the region of attraction and the minimization of the number of transmissions. Numerical examples illustrate the effectiveness of the proposed approach.

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.

Event-Triggered Control Under Unknown Input and Unknown Measurement Delays Using Interval Observers

We provide a new input-to-state stabilizing event-triggered feedback design for linear systems with unknown input delays, unknown measurement delays, and unknown additive disturbances. Our trigger times are computed using only the matrices defining the system and time-lagged sampled state values. We use the theory of positive systems, interval observers, and a vector version of Halanay’s inequality. We illustrate our method using a marine robotic model.

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.

Event-triggered feedback stabilization of switched linear systems via dynamic logarithmic quantization

Event-triggered feedback stabilization of switched linear systems via dynamic logarithmic quantization

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.

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.

Periodic event-triggered modified repetitive control with equivalent-input-disturbance estimator based on T-S fuzzy model for nonlinear systems

In this paper, the periodic signal tracking and the disturbance rejection problems are considered for a class of time-varying delay nonlinear systems with unknown exogenous disturbances under limited communication resources. The Takagi–Sugeno (T-S) fuzzy model is used to approximate the nonlinear system. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection effectiveley. This can be operated by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC) scheme. Moreover, a fuzzy periodic event-triggered feedback observer (FPETFO) is proposed for the purpose of reducing the computational burden, energy consumption and saving communication resources. The periodic event-triggered technique is designed to observe the occurrence of an event which is described by an error signal. When this error signal exceeds a prescribed threshold, the event occurs and the current data are transmitted; otherwise, there is a zero-order hold to keep data unchanged. The overall system consists of MRC, EID and FPETFO based on a T-S fuzzy model. Then, some sufficient conditions are derived to gurantee the asymptotic stability of the overall system subjected to unknown disturbances using the Lyapunov–Krasovskii functional (LKF) stability theory and linear matrix inequalities (LMIs). The fuzzy state feedback controller and observer gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme with comparative study.

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.

Dynamic Event-Triggered Feedback Fusion Estimation for Nonlinear Multi-Sensor Systems With Auto/Cross-Correlated Noises

This paper aims to solve the distributed fusion estimation problem for a nonlinear system with auto/cross-correlated noises. An equivalent nonlinear system with uncorrelated noises is obtained by means of a de-correlation method. Due to the nonlinear characteristics, the order of de-correlation affects whether the noises are completely uncorrelated or not. In order to improve accuracy of fusion estimation while avoiding the increase of communication burden, fusion predictions are fed back to local filters according to a dynamic event-triggered scheduling (DETS). The feedback frequency is reduced by introducing real-time adjusted offset variables into the DETS, which makes the event-triggered scheduling more strict. Subsequently, a local filter in the form of unscented Kalman filter (UKF) is designed using the measurement and received feedback information. Based on the Kalman-like fusion strategy, a distributed fusion estimation algorithm subject to auto/cross-correlated noises is developed, and boundedness of the fusion error covariance as well as complexity of the fusion algorithm are analyzed. Finally, performance of the proposed fusion estimation algorithm is verified by a numerical simulation.

Nonlinear integral control with event-triggered feedback: Unknown decay rates, zeno-freeness, and asymptotic convergence

This paper studies the event-triggered implementation of integral control laws for nonlinear uncertain systems. It is assumed that the plant already admits an integral control law such that the closed-loop system is input-to-state stable (ISS) with respect to the state sampling errors and admits an ISS-Lyapunov function. The unknown offset between the plant equilibrium and the set point means that one may not find a uniform lower bound for all the possible decay rates of the ISS-Lyapunov function, which however is usually required in the existing results. The design in this paper is based on a sequence of lower bound estimates of the decay rate, and the proposed dynamic event trigger guarantees that the intersampling intervals are lower bounded by a positive constant, and the asymptotic convergence property of integral control is retained even with event-triggered feedback. The theoretical result is physically validated by a pendulum control system.