Event-triggered Control Problem Research Articles

Event-Triggered Output Feedback Control for Leader–Follower Consensus of Feedforward Nonlinear Multiagent Systems

This article addresses the event-triggered output feedback control problem for feedforward nonlinear multiagent systems. A novel time-varying gain control method for the design of distributed consensus protocol is presented by means of a directed communication topology. An improved gain function is introduced to establish the relative threshold strategy and compensators. The distributed controllers are constructed such that the leader–follower consensus errors converge to a bounded region that is adjustable. The main advantage of the proposed method is that the consensus performance and event inter-execution intervals are taken into account. This strategy greatly accelerates the convergence rates of consensus errors and avoids the Zeno-behavior. The simulation results show the effectiveness of the established consensus protocol.

Observer-Based Event-Triggered Containment Control for MASs Under DoS Attacks.

This article studies the observer-based event-triggered containment control problem for linear multiagent systems (MASs) under denial-of-service (DoS) attacks. In order to deal with situations where MASs states are unmeasurable, an improved separation method-based observer design method with less conservativeness is proposed to estimate MASs states. To save communication resources and achieve the containment control objective, a novel observer-based event-triggered containment controller design method based on observer states is proposed for MASs under the influence of DoS attacks, which can make the MASs resilient to DoS attacks. In addition, the Zeno behavior can be eliminated effectively by introducing a positive constant into the designed event-triggered mechanism. Finally, a practical example is presented to illustrate the effectiveness of the designed observer and the event-triggered containment controller.

Event-triggered model-free adaptive control for unknown multiple input and multiple output nonlinear system under denial of service attacks

The event-triggered model-free adaptive control problem for a class of multiple input and multiple output (MIMO) nonlinear system under denial of service (DoS) attacks is investigated in this paper. To economize the limited bandwidth resources, an event-triggered mechanism is designed between the sensor and controller. First, intermittent denial of service attack is modeled, which is described as limited by frequency and duration, without more specific assumptions about the structure of attacks strategies. Then, with the help of the dynamic linearization method, a novel event-triggered model-free adaptive control algorithm is designed. The predictive output increments in the algorithm are used to compensate for the influence of DoS attacks on the system. Subsequently, the stability of the system is analyzed by using the Lyapunov method to determine the convergence of the tracking error. Finally, two simulation examples illustrate the validity of the design.

A new event-triggered adaptive tracking controller for nonlinear systems with unknown virtual control coefficients

This paper investigates the adaptive event-triggered tracking control problem for nonlinear systems with virtual control coefficients being unknown nonlinear functions. Firstly, different from approximators using fuzzy logics/neural networks or Nussbaum gain technique, a new transformation with less computation is introduced based on a monotone decreasing positive continuous function to handle uncertain virtual control coefficients (UVCCs). Furthermore, a novel event-triggered threshold scheme is firstly developed, which can switch between the fixed and relative threshold strategies smoothly. Finally, an adaptive event-triggered tracking controller is constructed, whose effectiveness is verified by both theoretical analysis and simulations.

Event-triggered-based online integral reinforcement learning for optimal control of unknown constrained nonlinear systems

For unknown nonlinear systems with actuator saturation, an online policy iteration-based algorithm is employed to solve the optimal event-triggered control problem. To learn the system dynamics, a novel identifier is proposed to make the estimation error converge quickly and the experience replay technique is employed to release the persistence of the excitation condition. To approximate the cost function and the event-triggered control law, we present event-triggered-based critic and actor networks, whose weights are updated only at triggered instants. During the policy iteration process, an event-triggered-based integral reinforcement learning method is proposed to solve the Hamilton–Jacobi–Bellman equation. By utilising the integral reinforcement learning, the network resource is saved and learning efficiency is improved. Based on the Lyapunov method, stability for the closed-loop system and estimation errors for the three networks are analysed. At last, simulation results of two numerical examples are used to show the effectiveness of the proposed method.

Event-Triggered MFAC of Nonlinear NCSs Against Sensor Faults and DoS Attacks

The event-triggered model-free adaptive control (ET-MFAC) problem for nonlinear networked control systems (NNCSs) with presence of sensor faults and denial-of-service (DoS) attacks is investigated. The attack occured in sensor-to-controller networked channels is supposed to obey the Bernoulli distribution. While sensor faults are formulated as unknown functions which could be approximated by a radial basis function-based neural networks (RBF-NNs). Then an ET-MFAC algorithm is constructed to ensure the tracking performance under sensor faults and DoS attacks based on adaptive estimations. The designed control algorithm is independent with the system structure and only uses the system input and output data. An example with comparison is given to demonstrate the validity of the new ET-MFAC algorithm.

Finite-Time Dynamic Event-Triggered Fuzzy Output Fault-Tolerant Control for Interval Type-2 Fuzzy Systems

The finite-time dynamic event-triggered fuzzy output feedback fault-tolerant control problem is studied in this article for the interval type-2 (IT2) Takagi–Sugeno fuzzy system with parameter uncertainties and actuator faults. A fuzzy state observer is first developed to solve the immeasurable state problem. Second, by using the sampled estimating states and measured output signals, a dynamic event-triggered mechanism is formulated via integrating sensor-to-observer with observer-to-controller. Third, an observer-based finite-time event-triggered fuzzy fault-tolerant controller is synthesized via the nonparallel distribution compensation design principle. Consequently, the finite-time stable conditions of the addressed IT2 fuzzy system are established by constructing an appropriate Lyapunov function. Furthermore, an output feedback control design algorithm of solving control and observer gains is given in terms of the established sufficient finite-time stable conditions. Finally, a practical example of a nonlinear tunnel diode circuit system is provided to verify the effectiveness of the proposed IT2 fuzzy control scheme.

Adaptive Event-Triggered Control for Uncertain High-Order Fully Actuated System

In this brief, the adaptive event-triggered control problem is investigated for a class of uncertain high-order fully actuated (HOFA) systems. Different from the existing works on HOFA systems, this brief considers the unknown control matrix function, which only requires its maximum and minimum eigenvalues to be unknown a priori. To deal with the problem, the adaptive technique is applied to estimate the unknown parameters. To save the energy in signal transmission, the controller and its event-triggered mechanism are co-designed. By means of the Lyapunov stability theory, it is rigorously proved that the proposed controller can render that all signals of the closed-loop system are bounded. Finally, the effectiveness of the theoretical result is demonstrated on the basis of the numerical simulation on the RLC circuit.

Small-gain technique-based adaptive output constrained control design of switched networked nonlinear systems via event-triggered communications

This paper investigates the problem of event-triggered tracking control for switched networked nonlinear systems with asymmetric time-varying output constraints. To handle the output constraints, an output-dependent generic constraint function is constructed to describe relationship between the output and the performance requirement. Meanwhile, an event-triggering rule is designed to reduce communication frequency between the controller and the actuator, thereby reducing the burden of the network communication. Based on the common Lyapunov function method and event-triggered control strategy, an adaptive control method is designed, which can guarantee that the closed-loop signals are bounded and avoid the Zeno behavior. Different from existing results considering constraints, the proposed scheme not only relaxes the restricted condition of constraint boundaries but also both the cases with and without output constraints can be addressed simultaneously. Furthermore, the stability of the system can be guaranteed by the small-gain technique. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed scheme.

Distributed event-triggered affine formation control for multiple underactuated marine surface vehicles

This article focuses on the distributed event-triggered affine formation control problem for multiple underactuated marine surface vehicles (UMSVs) considering affine transformation and communication energy consumption under a directed interaction topology. Firstly, the affine transformation mechanism is adopted to improve the flexibility and maneuverability of the formation. The proposed technique allows a rich collection of collective motions such as translation, rotation, scaling, and the combination of these transformations. Then, unlike the event-triggered control of a single marine vehicle, this paper considers reducing communication frequency between vehicles. Thus, an event-triggered mechanism is proposed, which can save computation resources compared with traditional ones while excluding the Zeno behavior. Subsequently, it is proved that all signals in the closed-loop system are ultimately uniformly bounded (UUB), meanwhile, all tracking errors converge to a small compact set under the proposed control strategy. Finally, numerical simulations illustrate the effectiveness of the proposed formation controller.

Event-triggered control of systems with sector-bounded nonlinearities and intermittent packet transmissions

The problem of event-triggered sampled-data control of nonlinear systems with sector-bounded nonlinearities is considered. We assume that sensors transmit their measurements to the controller over a communication channel, where the success of transmissions is defined by an i.i.d. Bernoulli process. For the analysis of the closed-loop system stability, we use the Lyapunov–Krasovskii technique. As a result, we obtain stability conditions in terms of linear matrix inequalities (LMIs), which can be used to design the appropriate triggering parameters. A global strictly positive minimum inter-event time is guaranteed to exist by design with the proposed triggering condition. A numerical example demonstrates the efficiency of the event-triggered approach in reducing the number of transmissions compared to periodic sampling, where the period is the enforced minimum time in the event-triggering condition.

A Zeno-Free Event-Triggered Control Strategy for Asymptotic Stabilization of Switched Affine Systems

This article investigates the event-triggered control problem for switched affine systems (SASs). The presence of affine terms brings many difficulties on the exclusion of triggering Zeno behavior when ensuring asymptotic stability. We propose an event-triggered control strategy dynamically updated with triggering to solve this problem, in which the triggering condition is associated with the affine terms and given with a time-varying term that is updated at triggering instants. Based on the triggering strategy, the controllers for subsystems and a switching rule are designed to achieve asymptotic stability of the resulting closed-loop system. Moreover, due to the special feature of event-triggered SASs, a new method for proving the exclusion of Zeno behavior is given. Finally, the developed results are illustrated by an electric circuit example.

Distributed Event-Triggered Control for Multiagent Systems Under Denial-of-Service Attacked Topology: Secure Mode Strategy

In this article, the secure event-triggered control problem is investigated for multiagent systems (MASs) compromised by Denial-of-Service (DoS) attacks with multiple modes. With the rapid development of information technology, DoS attacks against communication topologies are more and more common in MASs with cyber-physical features. To actively reduce the influences caused by DoS attacks, a secure mode strategy is proposed to make agents switch into the secure mode when attacks occur. In this strategy, each agent accesses or terminates the secure mode with bounded time delays after DoS attacks begin or end. Based on the switched system theory, the secure mode strategy against DoS attacks is modeled as the asynchronous switching between agent models and topologies. Finally, we obtain the sufficient conditions on the frequency and duration of DoS attacks, under which the designed controller can guarantee the consensus of MASs. By practical examples, the MASs with the secure mode strategy are illustrated to have better attack-resistant effectiveness than the ones without the secure mode strategy.

Event-Triggered Adaptive Neural Network Tracking Control with Dynamic Gain and Prespecified Tracking Accuracy for a Class of Pure-Feedback Systems

This paper studies the event-triggered adaptive tracking control problem of a class of pure-feedback systems. Via the backstepping method and the neural network approximation with the central symmetric distribution, an event-triggered adaptive neural network controller is designed. In particular, a dynamic gain driven by the tracking error is introduced into the event-triggering mechanism. Then, by using the Lyapunov stability theory, the boundedness of all the closed-loop signals is proved, and the tracking error falls into a prespecified ϵ-neighbourhood of zero. Meanwhile, the Zeno behaviour is avoided. Finally, two simulations verify the effectiveness of the proposed control scheme.

Model-based hybrid dynamic event-triggered control for systems subject to DoS attacks: A hybrid system approach

This article addresses the event-triggered control problem for networked control systems with uncertainties and denial-of-service (DoS) attacks. A resilient model-based hybrid dynamic event-triggered mechanism (HDETM) is proposed to defend against DoS attacks and reduce communication in sensor-controller-actuator networks. Owing to the introduction of regularization variables, Zeno behavior is naturally excluded, even if there exist disturbances. By using model-based computing, the novel HDETM outperforms the existing event-triggered mechanisms in terms of network utilization and robustness. To model and analyze the proposed HDETM, we propose a novel framework based on hybrid systems, which is different from the traditional discrete-time system framework. Meanwhile, the exponential stability and the L2-gain performance of the closed-loop system are guaranteed by utilizing the stability theorems for hybrid systems. In addition to the centralized model-based HDETM, a decentralized HDETM is also provided for large-scale systems which are composed of multiple interconnected subsystems. Finally, two examples are given that verify the improvement of the proposed model-based HDETM.

Event-triggered control with waiting time based on state observer for switched linear systems

This paper concentrates on the state observer–based event-triggered control problem for a class of switched linear systems with external disturbance and transmission delay. It is assumed that the controller can only access the transmitted information of the state observer at each delayed event-triggered instant with a waiting time. First, by adopting the multiple Lyapunov–Krasovskii functional method, some sufficient conditions are derived for the establishment of the state observer, the input-to-state stability (ISS) and the globally uniformly exponential stability (GUES) of the switched linear systems under adjacent mode-dependent average dwell time (AMDADT) scheme. Then, we propose a state observer-based event-triggered sampling mechanism with waiting time and design an observer-based state feedback controller for the considered switched systems. Under the proposed event-triggered mechanism, the Zeno behavior can be easily excluded in all sampling processes. Finally, a numerical example is included to validate the proposed theory.

Observer-Based Switching-Like Event-Triggered Control of Nonlinear Networked Systems Against DoS Attacks

This article investigates the problem of observer-based switching-like event-triggered control (ETC) for non- linear networked systems subject to aperiodic denial-of-service (DoS) attacks. First, a full-order state observer is developed to estimate the unavailable system states and used to establish the switching-like event-triggered condition, which includes two different threshold para- meters. Second, in order to improve the bandwidth re- source utilization and compensate for the influence of DoS attacks, a switching-like event-triggered mechanism (SETM) is designed, which can adaptively switch two different threshold parameters based on the presence or absence of DoS attacks. By combining the proposed SETM, an output feedback controller is constructed and a new observer-based switching-like ETC strategy is presented for nonlinear networked systems. Meanwhile, the relationship between the inactive/active period of the DoS attacks, the parameters of the SETM, the unmeasurable states, and the sampling period in the model are quanti- tatively discussed on the basis of the new strategy. Then, in terms of the proposed control strategy, the global asymptotical stability of the nonlinear networked systems can be obtained. Finally, two examples are used to verify the feasibility and effectiveness of the designed strategy.

Event-Triggered Model-Free Adaptive Iterative Learning Control for a Class of Nonlinear Systems Over Fading Channels.

This article investigates the problem of event-triggered model-free adaptive iterative learning control (MFAILC) for a class of nonlinear systems over fading channels. The fading phenomenon existing in output channels is modeled as an independent Gaussian distribution with mathematical expectation and variance. An event-triggered condition along both iteration domain and time domain is constructed in order to save the communication resources in the iteration. The considered nonlinear system is converted into an equivalent linearization model and then the event-triggered MFAILC independent of the system model is constructed with the faded outputs. Rigorous analysis and convergence proof are developed to verify the ultimately boundedness of the tracking error by using the Lyapunov function. Finally, the effectiveness of the presented algorithm is demonstrated with a numerical example and a velocity tracking control example of wheeled mobile robots (WMRs).

Event-Triggered Impulsive Control for Stochastic Networked Control Systems Under Cyber Attacks

The event-triggered impulsive control (ETIC) problem is studied for stochastic networked control systems (NCSs) under random cyber attacks. The random cyber-attacks model is proposed to integrate denial-of-service (DoS) attacks and deception attacks into a unified framework by means of two independent Bernoulli random sequences. In ETIC systems, the impulsive control time sequence is generated by the event-triggered mechanism (ETM). Both continuous ETM and periodic ETM are developed by continuous measuring and periodic sampling, respectively. In order to exclude the Zeno behavior, an easy and effective method is provided to choose the waiting time of continuous ETM and the sampling period of periodic ETM. According to the proposed ETMs, sufficient conditions of the mean-square exponential stability are derived for stochastic NCSs. An example of Chua’s circuits is given to explain our ETIC schemes.

Event-Triggered Adaptive Asymptotic Tracking Control of Uncertain MIMO Nonlinear Systems With Actuator Faults.

In this article, an adaptive event-triggered fault-tolerant asymptotic tracking control problem guaranteeing prescribed performance is addressed for a class of block-triangular multi-input and multioutput uncertain nonlinear systems with unknown nonlinearities, unknown control directions, and actuator faults. Through a systematic co-design of the adaptive control law and the event-triggered mechanism, including fixed and relative threshold strategies, a control scheme with low structure and calculation complexity is designed to conserve system communication and computation resources. In this design, the output asymptotic tracking is achieved. The Nussbaum gain technique is incorporated to overcome unknown control directions with a new adaptive law, and a type of barrier Lyapunov function is adopted to handle the prescribed performance control problem, which contributes to a novel control law with strong robustness. The robust controller can address the uncertainties and couplings derived from the system structure, actuator faults, and event-triggered rules, without using approximating structures or compensators. Besides, the explosion of complexity is avoided. It is proved that all signals of the closed-loop system remain bounded, and system tracking errors asymptotically approach 0 with the prescribed performance, while the Zeno behavior is prevented. Finally, the effectiveness of the proposed control scheme is evaluated via an application example of the half-car active suspension system.