Triggering Instants Research Articles

Synchronization of Euler-Lagrangian networks: a periodic intermittent dynamic event-triggered control strategy

In this paper, the synchronization problem of Euler–Lagrange networks is studied by designing periodic intermittent dynamic event-triggered control strategy. The synchronization of all agents is successfully realized by injecting negative comments into the discontinuous interval of the agents described by the Euler–Lagrange systems. Different from the traditional intermittent event-triggered control strategy, the control strategy proposed in this study introduces internal dynamic variables to expand the sampling interval of the event-triggered mechanism, thereby improving resource utilization efficiency. In addition, the event trigger instants of each agent are asynchronous. By using graph theory and Lyapunov method, the synchronization criteria of Euler–Lagrange networks are derived. The effectiveness of the proposed control scheme is verified by simulations for the Euler-Lagrangian network composed of six two-link rotating manipulators.

New Event-Triggered Synchronization Criteria for Fractional-Order Complex-Valued Neural Networks with Additive Time-Varying Delays

This paper explores the synchronization control issue for a class of fractional-order Complex-valued Neural Networks (FOCVNNs) with additive time-varying delays (TVDs) utilizing a sampled-data-based event-triggered mechanism (SDBETM). First, an innovative free-matrix-based fractional-order integral inequality (FMBFOII) and an improved fractional-order complex-valued integral inequality (FOCVII) are proposed, which are less conservative than the existing classical fractional-order integral inequality (FOII). Secondly, an SDBETM is inducted to conserve network resources. In addition, a novel Lyapunov–Krasovskii functional (LKF) enriched with additional information regarding the fractional-order derivative, additive TVDs, and triggering instants is constructed. Then, through the integration of the innovative FOCVII, LKF, SDBETM, and other analytical methodologies, we deduce two criteria in the form of linear matrix inequalities (LMIs) to ensure the synchronization of the master–slave FOCVNNs. Finally, numerical simulations are illustrated to confirm the validity of the proposed results.

Adaptive Transmission Interval-Based Self-Triggered Model Predictive Control for Autonomous Underwater Vehicles with Additional Disturbances

Most existing model predictive control (MPC) methods overlook the network resource limitations of autonomous underwater vehicles (AUVs), limiting their applicability in real systems. This article addresses this gap by introducing an adaptive transmission, interval-based, and self-triggered model predictive control for AUVs operating under ocean disturbances. This approach enhances system stability while reducing resource consumption by optimizing MPC update frequencies and communication resource usage. Firstly, the method evaluates the discrepancy between system states at sampling instants and their optimal predictions. This significantly reduces the conservatism in the state-tracking errors caused by ocean disturbances compared to traditional approaches. Secondly, a self-triggering mechanism was employed, limiting information exchange to specified triggering instants to conserve communication resources more effectively. Lastly, by designing a robust terminal region and optimizing parameters, the recursive feasibility of the optimization problem is ensured, thereby maintaining the stability of the closed-loop system. The simulation results illustrate the efficacy of the controller.

Secure pinning synchronization on aperiodic intermittent event-triggered control in discrete-time complex networks against multi-pattern link attacks

This paper investigates the problem of secure synchronization in aperiodic intermittent event-triggered pinning control for discrete-time complex networks (DCNs) against multi-pattern link attacks. Firstly, in order to reduce communication burden and control cost, a novel aperiodic intermittent event-triggered control (AIEC) with discontinuous characteristics is designed based on periodic sampling, where triggering instants are determined by the intermittent control (IC). Secondly, multiple pattern attack are modeled, as they can interrupt different edges and change the network topology. In addition, multi-pattern attacks for each link are independent and their impact on the coupling topology is analyzed. Thirdly, under destroyed network topology, this paper designs aperiodic intermittent event-triggered pinning control (AIEPC) by combining pinning control (PC) with the AIEC. Meanwhile, based on PC, the isolated node and pinned nodes form a like-directed spanning tree with an asymmetrical coupling matrix, where rooted at the isolated node and only directed connections between the isolated node and pinned nodes. Fourthly, using the segmentation analysis method and the inequality iteration technique, a sufficient condition for exponential synchronization of error system is obtained by considering the instants neighboring different intermittent control and attack intervals. Finally, a simulation example on Chua’s circuit network is provided to verify the validity of the theoretical results achieved in this paper.

Event-Triggered Adaptive Neural Control for MIMO Nonlinear Systems With Rate-Dependent Hysteresis and Full-State Constraints via Command Filter.

This article presents an event-triggered adaptive acrlong NN command-filtered control for a class of multi-input and multi-output (MIMO) nonlinear systems with unknown rate-dependent hysteresis in the actuator and the constraints on full states. The acrlong ETM is used to reduce the communication frequency between controller and actuator. The command filter technique is first employed to solve the dilemma between the nondifferentiable control signal at triggering instants and rate-dependent hysteresis input premise while avoiding the "explosion of complexity" problem. During the backstepping design, the barrier Lyapunov functions are utilized to guarantee that system states will stay in certain regions and the unknown nonlinear items are approximated by adaptive neural networks. The compensating signals are constructed to eliminate filtering errors. The estimates of unknown hysteresis parameters are updated by adaptive laws. The stability analysis is given and the effectiveness of the proposed method is verified by simulation.

Synchronization of Kuramoto-oscillator networks under event-triggered impulsive control with noise perturbation

This paper studies the stochastic average synchronization of Kuramoto-oscillator networks under event-triggered impulsive control (ETIC) strategies, in which the event-triggered mechanism (ETM) determines the impulsive control time sequence. The continuous ETM is designed to avoid the Zeno behavior by continuous measuring, and the periodic ETM is proposed by periodic sampling. Based on the proposed ETIC methods, several sufficient conditions for the stochastic average synchronization of Kuramoto-oscillator networks are established. Unlike time-triggered impulsive control, where the triggered instants are pre-designed, ETIC is activated only upon the occurrence of an event, so synchronization conditions are heavily dependent on the ETM. Furthermore, there is no control input between two successive triggering instants, and the control input is required only at the trigger instants. Finally, numerical simulations are shown to illustrate the effectiveness of the theoretical results. Besides, it is found that the presence of noise may favor the synchronization of Kuramoto-oscillator networks.

Observer-based bipartite consensus tracking of nonlinear fractional-order multi-agent systems with pull-based dynamic event-triggered mechanism

This paper investigates the observer-based bipartite consensus tracking of nonlinear fractional-order multi-agent systems (FOMASs) by employing a pull-based dynamic event-triggered mechanism (DETM). First, considering that the relevant state information of each agent is not always measurable, a class of distributed observers is considered for each agent to estimate its state information. Then, a pull-based DETM for FOMASs is proposed to avoid continuous controller updates, in which the dynamic threshold is modulated according to the preset conditions. The pull-based DETM constructed in this paper enables each agent to update the controller only based on its own trigger instants. Furthermore, an observer-based dynamic event-triggered control protocol is designed to guarantee the bipartite consensus tracking of FOMASs. Correspondingly, sufficient conditions are obtained by using graph theory and choosing suitable Lyapunov candidate functions. Moreover, the Zeno behavior is precluded. Finally, two simulation examples are presented to illustrate the theoretical results efficiently.

Design of distributed event‐triggered states and unknown disturbances observers for time‐varying delay interconnected systems

SummaryThis article considers the problem of designing distributed event‐triggered states and unknown disturbances observers for a class of nonlinear interconnected systems where the local state vectors are affected by unknown delays and the nonlinear function satisfying the Lipschitz condition. Distributed observers are designed based on the local input vector and both the local and remote output vectors. Different from previously distributed observers for interconnected systems where the local and remote output vectors are updated continuously, the one in this article uses only information on the local and remote output vectors updating at triggering instants of proposed event‐triggered mechanisms. This indicates that the proposed method in this article is better than the existing ones in saving communication resources while still keeping an acceptable estimation performance. Sufficient conditions for the existence of the proposed distributed observers are established and are formed in a convex optimization problem which can be easily solved by using the MATLAB LMI Control Toolbox. Finally, a numerical example is given to confirm the effectiveness and advantages of the proposed method.

Fixed‐time Synchronization of Stochastic Kuramoto‐Oscillator Networks With Switching Topology Under Dynamic Event‐triggered Scheme

AbstractThis paper proposes a dynamic event‐triggered fixed‐time control scheme for the phase synchronization of Kuramoto networks with switching topology and stochastic coupling noise. To deal with the problems of switching topology and stochastic coupling noise, a multilayered control structure with a specially designed noise reduction layer is developed. The effectiveness is proved based on stochastic differential theory. To save communication resources and reduce control frequency, a dynamic event‐triggered mechanism is proposed. By introducing a dynamic variable into the triggering condition, the triggered instants are further reduced compared to the traditional static event‐triggered method. The synchronizing criteria and parameter conditions are established with stochastic Lyapunov stability theory. The analysis of Zeno behavior is also given. Finally, numerical simulation experiments are conducted to demonstrate the effectiveness of the proposed dynamic event‐triggered control scheme.

Leader-following mean square consensus of stochastic switched multi-agent systems with event-triggered control

ABSTRACT In this paper, a novel distributed event-triggered mechanism (ETM) is used to solve the problem of the leader-following mean square consensus of stochastic switched multi-agent systems (SSMASs) with switching dynamics of agents, disturbed by the multiplicative noise. Moreover, the distributed ETM utilises only the state information at the triggering instants of neighbouring agents, which eliminates continuous communication among agents while reducing the frequency of controller updates. A general agent-dependent switching law is developed to achieve leader-following mean square consensus of SSMASs. Subsequently, it is proved that under the distributed ETM, linear SSMASs can achieve leader-following mean square consensus and no Zeno behaviour occurs with the help of stochastic analysis and the average dwell time approach. Finally, the effectiveness of the study is illustrated by a numerical example.

Cooperative Control of Multiagent Systems: A Quantization Feedback-Based Event-Triggered Approach.

This article addresses the synchronization tracking problem for high-order uncertain nonlinear multiagent systems via intermittent feedback under a directed graph. By resorting to a novel storer-based triggering transmission strategy in the state channels, we propose an event-triggered neuroadaptive control method with quantitative state feedback that exhibits several salient features: 1) avoiding continuous control updates by making the parameter estimations updated intermittently at the trigger instants; 2) resulting in lower-frequency triggering transmissions by using one event detector to monitor the triggering condition such that each agent only needs to broadcast information at its own trigger times; and 3) saving communication and computation resources by designing the intermittent updating of neural network weights using a dual-phase technique during the triggering period. Besides, it is shown that the proposed scheme is capable of steering the tracking/disagreement errors into an adjustable neighborhood close to the origin, and the existence of a strictly positive dwell time is proved to circumvent Zeno behavior. Both theoretical analysis and numerical simulation authenticate and validate the efficiency of the proposed protocols.

Hybrid protocols for leader–follower consensus of multi-agent systems with distributed delays

The primary focus of this paper is to investigate the leader–follower consensus problem of multi-agent systems (MASs) with discrete and distributed delays in complex domains. We propose a new hybrid consensus protocol that incorporates a continuous-time protocol based on the communication topology of follower agents, along with an event-triggered pinning impulsive control (ETPIC) protocol. Using the Lyapunov functional method in complex domains, we establish delay-dependent sufficient conditions for leader–follower consensus of delayed complex-valued MASs. Our results demonstrate that the proposed hybrid protocol can ensure leader–follower consensus even when the size of discrete and distributed delays exceeds the length of intervals between two consecutive triggering instants. Furthermore, we prove that the Zeno phenomenon can be excluded under the proposed control protocol. In particular, as a special case, we derive the leader–follower consensus result for delay-free complex-valued MASs based on a reduced hybrid control protocol. Two numerical examples are presented to validate the effectiveness of the proposed control scheme.

Enhanced Coordination in the PV–HESS Microgrids Cluster: Introducing a New Distributed Event Consensus Algorithm

To ensure reliable power delivery to customers under potential disturbances, the coordination of a microgrid cluster (MGC) is essential. Various control strategies—centralized, decentralized, distributed, and hierarchical—have been explored in the literature to achieve this goal. The hierarchical control method, with three distinct levels, has proven effective in fostering coordination among microgrids (MGs) within the cluster. The third control level, utilizing a time-triggering consensus protocol, relies on a continuous and reliable communication network for data exchange among MGs, leading to resource-intensive operations and potential data congestion. Moreover, uncertainties introduced by renewable energy sources (RESs) can adversely impact cluster performance. In response to these challenges, this paper introduces a new distributed event-triggered consensus algorithm (DETC) to enhance the efficiency in handling the aforementioned issues. The proposed algorithm significantly reduces communication burdens, addressing resource usage concerns. The performance of this approach is evaluated through simulations of a cluster comprising four DC MGs, in each of which were PV and a hybrid Battery-Super capacitor in the MATLAB environment. The key findings indicate that the proposed DETC algorithm achieves commendable results in terms of voltage regulation, precise power sharing among sources, and a reduction in triggering instants. Based on these results, this method can be deemed as a good development in MGC management, providing a more efficient and reliable means of coordination, particularly in scenarios with dynamic loads and renewable energy integration. It is also a viable option for current microgrid systems, due to its ability to decrease communication loads while retaining excellent performance.

A Concurrent Event-Triggered Approach for Fuzzy Adaptive Control of Nonlinear Strict-Feedback Systems.

If a control input signal constructed by backstepping is used to generate an event-triggered control signal, then not only the real control input is discontinuous, but all the virtual control signals that make up the control signal are also discontinuous and have the same triggering instants with the control input. This fact makes the control design and stability analysis more difficult and complex via backstepping. This article focuses on this problem and works at coming up a new backstepping design procedure of event-triggered fuzzy adaptive control for nonlinear strict feedback systems. A concurrent event-triggered mechanism is proposed to ensure that the real control input and the virtual control signals have the same triggering instants. Then, a systemic backstepping design procedure is developed to construct event-triggered fuzzy adaptive controller. The Lyapunov technique for nonlinear impulsive system is employed to provide the closed-loop stability analysis. It is shown that the derived event-triggered fuzzy adaptive controller ensures that the closed-loop system output well follows the desired tracking trajectory and the other closed-loop signals remain bounded. Eventually, two examples are provided to further verify the applicability and reliability of the presented control scheme.

Event-Triggered Adaptive Tracking With Guaranteed Transient Performance for Switched Nonlinear Systems Under Asynchronous Switching.

This article presents an event-triggered neural-network (NN) tracking control scheme, capable of ensuring transient performance for switched nonlinear systems. A mode-dependent event-triggered communication mechanism (MDETCM) is designed, and this significantly saves communication resources without limiting the number of switches between two consecutive triggering instants. Meanwhile, to solve the impact of asynchronous switching on system performance, the information of the switching signal is considered into the event-triggered mechanism (ETM). Also, by introducing a normalized function transformation and a tan-type barrier function, the transient performance is regarded as a tracking error constraint without considering the initial conditions of system output and reference signal required in traditional prescribed performance bound (PPB) control. At the same time, the improved admissible edge-dependent average dwell time (AED-ADT) method is cleverly connected with adaptive backstepping control, and a state-feedback tracking algorithm is proposed, under which all closed-loop signals are bounded and the transient performance of the controlled plant is ensured. Finally, the superiority of the proposed scheme is demonstrated through numerical studies, and the control scheme is available for a single-link robot.

Distributed dynamic event-triggered algorithm for optimization problem with time delay.

This paper focuses on studying the optimization problem of multi-agent systems (MAS) under undirected graph. To reduce the communication frequency among agents, a zero-gradient-sum (ZGS) algorithm based on dynamic event-triggered (DET) mechanism is investigated. The event-triggered condition of each agent only uses its own state information and the neighbor's state information at the previous triggering instants, without requiring continuous state information from the neighbor. In addition, the designed algorithm allows for the sampling period to be arbitrarily large. The Lyapunov method is utilized to derive the sufficient conditions that incorporate time delay and parameters. As the event is only checked at the periodic moment, zeno behavior can be directly excluded. Finally, numerical simulations demonstrate the effectiveness of the theoretical results.

Periodic event-based sliding mode tracking control of Euler–Lagrange systems with dynamic triggering

In this article, we propose the design of a robust tracking controller of perturbed Euler–Lagrange systems (ELSs) based on dynamic event-triggered (DET) sliding mode control (SMC) with periodic evaluation of triggering rule. To ensure robustness, we employ the SMC technique and introduce a dynamic periodic event-triggering strategy to reduce communication frequency significantly. This strategy involves the incorporation of an auxiliary dynamic variable to formulate the event-triggering condition, leading to the generation of sparser triggering instants. An upper bound of the sampling period is also obtained in this design to facilitate the periodic assessment of the event-triggered strategy, alleviating the need for continuous verification of the event condition. This technique is more economical with respect to communication resources and practical than its continuous counterpart due to the relaxation of continuous measurements. The stability of the closed loop system is established using Lyapunov analysis within the dynamically triggered event-based SMC framework. The necessary switching gain for maintaining the stable motion of the sliding variable is derived with the help of Lyapunov analysis. The tracking error is shown to be ultimately bounded, and Zeno-behaviour is excluded to ensure finite sampling. A comparative analysis based on simulation results is included to highlight the effectiveness of the proposed scheme, especially in reducing the network usage in the transient phase of the response while achieving comparable steady-state behaviour. Ultimately, we validate the effectiveness of the proposed algorithm by simulating a two-link manipulator and experimentally implementing it with a one-link manipulator.

Rolling self-triggered distributed MPC for dynamically coupled nonlinear systems

The mutual influences caused by dynamic couplings in large-scale systems increase the difficulty in the design and analysis of distributed model predictive control (DMPC), and require information exchange among subsystems which calls for a scheduling strategy to save communication resources in communication-limited environments. To circumvent the two problems, we design a rolling self-triggered DMPC strategy for large-scale dynamically coupled systems with state and control input constraints. First, the optimal control problem where the cost is subject to the coupled dynamic and the constraints are subject to the uncoupled counterpart is proposed, forming the dual-model DMPC that is simple in design and analysis but yields good control performance. Second, the information exchange only occurs at some specified triggering instants determined by a rolling self-triggered mechanism, saving communication resources more significantly. The effectiveness of the designed strategy is verified by numerical simulations.

Self-triggered formation control for multi-spacecraft attitude coordination with communication delays

This article addresses the event-triggered formation control problem for multi-spacecraft systems subject to time-varying delays. Firstly, a formation attitude dynamics model considering communication delays is proposed, and two auxiliary trigger instants are designed to transform the event-based control problem subject to delays into the conventional event-triggered control problem. Next, a nonlinear observer based on the triggering information of neighbors is developed to estimate the lumped nonlinear term. To avoid continuous communication, a dynamic event-based formation control strategy is proposed based on the nonlinear observer. To avoid continuous computation of the trigger mechanism, a self-triggered function is developed based on the current trigger information. Moreover, the system is Zeno-free under the proposed event-based control algorithms. Finally, simulation results show that compared with the dynamic triggering function, the self-triggered function avoids continuous computation and improves the control accuracy by nearly one order of magnitude while increasing communication frequency by 67.8 %.

Model-free frequency regulation in islanded microgrids: An event-triggered adaptive dynamic programming approach

This paper is concerned with frequency regulation in islanded microgrids via an event-triggered adaptive dynamic programming method. Comparatively to the existing works, we relax the typical limitations on the system, namely, exactly known models, constant load impedances, and single operation mode. The adopted frequency regulation scheme can reach frequency synchronization within the acceptable bounds in the presence of the model uncertainties, operation mode switching, and time-varying loads with no need for any prior information on the system parameters. By employing an event-triggered scheme, the secondary controller is updated only at the aperiodic triggering instants which contributes to less transmission cost. Besides, the use of measurements can help the adaptive weights to be adjusted online in the approximation process, which allows the proposed controller to adapt to the disturbances in real time. Finally, tests including the islanding process and load variation are performed in MATLAB/SimPowerSystem to show the effectiveness of the proposed method.