Event-triggered Function Research Articles

Distributed Disturbance Observer-Based Containment Control of Multi-Agent Systems with Event-Triggered Communications

This article investigates a class of multi-agent systems (MASs) with known dynamics external disturbances, where the communication graph is directed, and the followers have undirected connections. To eliminate the impacts of external disturbance, the technologies of disturbance observer-based control are introduced into the containment control problems. Additionally, to save communication costs and energy consumption, a distributed disturbance observer-based event-triggered controller is employed to achieve containment control and reject disturbance. Furthermore, designing the event-triggered function using an exponential function is beneficial for a time-dependent term while ensuring the exclusion of Zeno behavior. Finally, a numerical simulation is provided to validate the effectiveness of the theoretical analysis.

Fixed-Time Distributed Event-Triggered Cooperative Guidance Methods for Multiple Vehicles with Limited Communications to Achieve Simultaneous Arrival

Aiming at the salvo-attack problem of multiple missiles, a distributed cooperative guidance law based on the event-triggered mechanism is proposed, which enables missiles with large differences in spatial location and velocity to achieve simultaneous attacks with only a few dozen information exchanges. It effectively reduces the generation of control commands and communication frequency, thereby reducing channel load and improving communication efficiency and reliability. Compared to traditional periodic sampling communication, the number of communications has been reduced by over 90%. The guidance process is divided into two stages. The first stage is the cooperative guidance stage, where missiles achieve consensus of the time-to-go estimates through information exchange. In this stage, each missile is designed with an event-triggered function based on its own state error, and the missile only updates and transmits its information in the communication network when the error meets the set threshold, effectively reducing the occupancy rate of missile-borne resources during the cooperation process. The second stage is the independent guidance stage, where missiles can hit the target simultaneously while keeping the communication network silent. This is achieved by ensuring that the time-to-go estimates of missiles can represent the real time-to-go after achieving consensus. By the design of the two-stage guidance law and the replacement of the event-triggered function, the cooperative guidance system can be ensured to remain stable in scenarios where the leader missile is present and destroyed, and this excludes Zeno behavior. The stability of the cooperative guidance law is rigorously proved by algebraic graph theory, matrix theory, and the Lyapunov method. Finally, the numerical simulation results demonstrate the validity of the algorithm and the correctness of the stability analysis.

Matrix Measure-Based Event-Triggered Impulsive Quasi-Synchronization on Coupled Neural Networks.

In this article, the quasi-synchronization for a kind of coupled neural networks with time-varying delays is investigated via a novel event-triggered impulsive control approach. In view of the randomly occurring uncertainties (ROUs) in the communication channels, the global quasi-synchronization for the coupled neural networks within a given error bound is considered instead of discussing the complete synchronization. A kind of distributed event-triggered impulsive controllers is presented with considering the Bernoulli stochastic variables based on ROUs, which works at each event-triggered impulsive instant. According to the matrix measure method and the Lyapunov stability theorem, several sufficient conditions for the realization of the quasi-synchronization are successfully derived. Combining with the mathematical methodology with the formula of variation of parameters and the comparison principle for the impulsive systems with time-varying delays, the convergence rate and the synchronization error bound are precisely estimated. Meanwhile, the Zeno behaviors could be eliminated in the coupled neural network with the proposed event-triggered function. Finally, a numerical example is presented to prove the results of theoretical analysis.

Finite-Time Multiparty Synchronization of T–S Fuzzy Coupled Memristive Neural Networks With Optimal Event-Triggered Control

This paper considers multiparty synchronization (MS) for coupled memristive neural networks (CMNNs) with a time delay. Some T-S type If-Then fuzzy rules are also introduced into the CMNNs. An event-triggered controller (ETC) is designed to achieve the MS in finite time, which avoids continuous control signals. Along with Lyapunov theory, differential inclusion theory, and inequalities, some criteria can be obtained to achieve the finite-time MS (FTMS), and the setting time (ST) of the FTMS can be calculated. By jointly considering ST, control inputs, error networks, and synchronization conditions, an optimization model is provided to get an optimal ETC (OETC). Further, the particle swarm optimization (PSO) algorithm is utilized to solve the optimization model. Thus, it gives a method to choose control gains and parameters of an event-triggered function (ETF). Finally, two examples are given to verify the theoretical results. Especially, two comparative experiments are proposed to demonstrate that the OETC can save more control energy and reduce the number of triggered times.

Average Impulsive Weight Based Event-Triggered Impulsive Synchronization on Coupled Neural Networks

This article explores the stochastic synchronization for a class of coupled neural networks through a novel event-triggered impulsive control strategy. In view of hybrid impulses in the controller, the desynchronizing and synchronizing impulses are both discussed in consideration of the average impulsive weight. The triggering conditions are presented according to the latest impulsive weight and the overall impulsive weight, respectively and an exponential threshold function is correspondingly proposed to explain the triggering mechanism. Sufficient conditions for the synchronization are successfully obtained with jointly utilizing the mathematical induction methodology and the variation of parameter formula. In addition, the convergence velocity of the coupled neural networks is precisely estimated considering the different delayed impulsive comparison systems. In addition, the Zeno behaviors could be successfully eliminated with the proposed event-triggered function. Finally, one numerical example is presented to validate the results.

Model-Based Event-Triggered Dynamic Pursuing and Surrounding Control for a Multi-Robotic Fish System

This paper investigates the event-triggered-based pursuing and surrounding control of a multi-robotic fish system. A distributed surrounding control framework is put forward to deploy the whole system and enclose the dynamic evader into a convex hull. In particular, distributed kinematics-based motion predictions are hold for common agents in the multi-robotic fish system in addition to the evader. Based on the optimal state estimations, an innovative model-based event-triggered mechanism is tailored rather than frequent interactions to evaluate the importance of the messages. Afterwards, a two-stage position-based surrounding control method is provided. By arbitrating the trade-off between the control performance and interaction frequency, the event-triggered function is regulated to delicately execute the surrounding control task while sharply slashing the interactions. Finally, adequate simulations and experiments are conducted to ensure the effectiveness and robustness of the proposed method. Therefore, whether for communication energy conservation or attack defense, the proposed method shows its significance for future marine assignments.

Edge-event-triggered encryption-decryption observer-based control of multiagent systems for privacy protection under multiple cyber attacks

This study investigates the secure and privacy-preserving consensus problem for a class of Lipschitz nonlinear multiagent systems (MASs) under undirected topology and multiple cyber attacks. An observer-based dynamic cryptography-based encryption-decryption (CED) pairing algorithm is proposed to achieve privacy preservation and defend against replay attacks simultaneously. To reduce the computation and communication resources and facilitate paired password design, a Zeno-free edge-event-triggered mechanism (EETM) based on edge (rather than neighbor) information is developed in a completely distributed manner, using only local observation information without any knowledge about the global topology. The designed EETM can accommodate multiple event-triggered functions, which simplifies the EETM design procedure. Interestingly, the CED pairing algorithm makes the effect of replay attacks equivalent to that of denial-of-service (DoS) attacks. Thus, DoS and replay attacks can be handled as the same types of attacks. In addition, a resilient EETM-based control strategy against DoS and replay attacks is proposed to make the MAS reach consensus faster, within the attack sleep time. Furthermore, sufficient conditions for the frequency and duration of replay and DoS attacks are established to achieve secure consensus of the MAS. Finally, a numerical example is provided to demonstrate the validity and superiority of the proposed method.

A Novel Event-Triggered Secondary Control Strategy for Distributed Generalized Droop Control in Microgrid Considering Time Delay

With the wide use of new energy and power electronic devices, the problem of low inertia of microgrid (MG) is becoming more and more prominent. In order to solve the problem, this paper proposes an event-triggered secondary control strategy for distributed generalized droop control (GDC) considering time delay. Firstly, a distributed event-triggered active power and frequency controllers are established based on GDC, and a distributed voltage controller is designed based on droop control. Secondly, due to the different frequency parameters of each distributed generator (DG), the tracking controller of frequency and frequency reference model is established by using heterogeneous multi-agent theory. Thirdly, the event-triggered function of communication between DGs is constructed, and the stability of the proposed controller is proved. The complicated Lyapunov equation is avoided in the proof process. Finally, the effectiveness of the controller is verified by simulation. The simulation results show that the controller effectively realizes the secondary adjustment of frequency and voltage, reduces the number of communications, and increases the inertia of MG.

A dynamic event-triggered network control algorithm combined with gradient-sharing asynchronous advantage actor-critic strategy

In the existing memory event-triggered control (METC) algorithms, the threshold parameters and memory weights are fixed, reducing the system’s adaptability. In this paper, a new intelligent dynamic METC algorithm is proposed to reduce the amount of transmission data and decrease the communication burden in networked control systems. The proposed dynamic METC mechanism applies the gradient-sharing asynchronous advantage actor-critic (A3C-GS) learning algorithm to optimized memory event-triggered function of memory weights and threshold parameters. A time-varying delay system model for dynamic METC is developed by incorporating the A3C-GS for the networked control system with communication delays. Then, by solving two linear matrix inequalities (LMIs), the controller gain parameters of the networked control systems are derived. Finally, the performance of the proposed new METC algorithm is compared with the current three event-triggered control methods. Simulation results show that the proposed intelligent event-triggered algorithm reduces the number of triggers by about 40% compared with the traditional event-triggered algorithm under the pregiven simulation time. Thus, the effectiveness of the main results is verified.

A High-Reliability Event-Triggered Secondary Control Strategy for Microgrid Considering Time-Varying Delay

A decentralized hierarchical control strategy with communication time-varying delay is designed for microgrid (MG) to enhance the voltage and frequency regulation. Recently, event-triggered consensus algorithm is used to reduce energy consumption. To improve the communication reliability, data loss due to communication interruption is considered in this article. First, each distributed generator (DG) of MG is regarded as an agent. Based on multiagent consistency theory, the distributed secondary controller is established. Second, the event trigger function of the secondary controller is constructed, and the stability of the secondary controller is proved by Lyapunov theorem. Third, a data predictive controller is established to train and learn the historical voltage, frequency, and active power of MG by using the improved extreme learning machine (ELM) algorithm. When communication is interrupted, the ELM controller is triggered and the lost data is compensated in time. Finally, the effectiveness of the control strategy is verified by simulation. Simulation results show that the proposed control strategy effectively adjusts the frequency and voltage, realizes accurate active power sharing, reduces the communication burden, and improves the reliability of MG.

An Enhanced Distributed Event-Triggered Mechanism of Cyber-Switched Communications for Control of Islanded AC Microgrids

This article presents an innovative secondary control approach for islanded microgrids established from a distributed event-triggered mechanism (DETM) under switching communication topologies. An enhanced DETM based on combined triggering conditions, including state- and time-dependent threshold terms, are developed to improve convergence speed and simultaneously reduce the number of triggering events. The parameters of the event-triggered function are derived through a comprehensive analytical Lyapunov stability theory. In addition, it is proved that no Zeno behavior via intermittent communication between neighbors occurs under cyberswitched networks and the proposed combined triggering conditions. Extensive simulations in MATLAB/Simulink are performed to confirm the performance of the proposed DETM. It is shown that the proposed strategy reduces the average communication burden by 78% compared with the former methods. Finally, hardware-in-the-loop experimental tests through real-time simulation feature of MATLAB by utilizing Raspberry Pi as an embedded hardware controller are conducted to validate the effectiveness of the proposed DETM.

Energy-Efficient Optimization Method of Urban Rail Train Based on Following Consistency

Because of the short distance between stations in urban rail transit, frequent braking of urban rail trains during operation will generate a large amount of regenerative braking energy. Urban rail trains can reduce their actual traction energy consumption using regenerative braking energy. Therefore, an energy-efficient optimization method for urban rail trains is proposed. By taking the punctuality of trains as the premise, the weighted acceleration of trains is taken as the synergetic variable, the synergetic coefficient is introduced to construct the following consistency model, and its convergence is proved. By analyzing the influencing factors of the following consistency coordination time, an adaptive parameter adjustment strategy is designed to solve the latest secondary traction time and the corresponding maximum speed of the primary traction. In order to save communication resources, the event trigger function is used to construct trigger conditions, and the consistency algorithm is used to update the cooperative controller. The simulation results show that the weighted acceleration of the follower train achieves the following consistency on the premise of ensuring punctuality, and the actual traction energy consumption of the follower train is reduced by 5.73%. The proposed method provides a new strategy for the energy-efficient operation of urban rail trains.

Mean-square consensus of a semi-Markov jump multi-agent system based on event-triggered stochastic sampling.

This paper focuses on achieving leader-follower mean square consensus in semi-Markov jump multi-agent systems. To effectively reduce communication costs and control updates, we propose an event-triggered protocol based on stochastic sampling. The stochastic sampling interval randomly switches between finite given values, while the event-triggered function depends on the stochastic sampled data from neighboring agents. Using the event-triggered strategy, we present sufficient conditions to ensure mean square consensus. Finally, we provide a numerical example demonstrating the effectiveness of the theoretical results.

Pinning synchronization of dynamical neural networks with hybrid delays via event-triggered impulsive control

<abstract><p>In this study, a new event-triggered impulsive control strategy is used to solve the problem of pinning synchronization in coupled impulsive dynamical neural networks with hybrid delays. In view of discontinuous coupling terms and system dynamics, the inner delay and the impulsive delay are both investigated. Compared with the traditional pinning impulsive control, event-triggered pinning impulsive control (EPIC) generates impulse instants only when an event occurs, and is therefore more in line with practical applications. In order to deal with the complexities of mixed delays, some generalized inequalities related to hybrid delays based on Lyapunov functions are proposed, which are subject to the designed event-triggered rule. Then, in order to ensure network synchronization, linear matrix inequalities (LMIs) can provide some sufficient conditions with less conservatism while a proposed event-triggered function could successfully eliminate Zeno behavior. In addition, numerical examples are presented to prove the feasibility of the presented EPIC method.</p></abstract>

An event-triggered iteratively reweighted convex optimization approach to multi-period portfolio selection

This paper addresses multi-period portfolio selection driven by events. We define an event-triggering function to mimic fund managers to activate sequential portfolio rebalancing and maximize Sharpe and Sortino ratios in the Markowitz’s return–risk framework. At first, the multi-period portfolio selection problem is formulated with a variable weight as a series of biconvex optimization problems with a surrogated objective function to maximize the Sharpe ratio or Sortino ratio. In each period, the portfolio optimization problem is further reformulated as an iteratively reweighted convex quadratic optimization problem. The multi-period portfolio selection problem is then solved sequentially based on a defined event-trigger function and a quadratic optimizer. The experiments are done on eight world stock markets datasets to show the capabilities of the proposed approach in calculating market indices and equal-weighted portfolios in terms of Sharpe and Sortino ratios.

Discrete-time event-based coordinated formation control of multiple AUVs with time-varying delay and alterable topology

This article considers the issue of event-based coordinated formation control for multiple autonomous underwater vehicles subject to time-varying communication delay and alterable topology under discretized time. First, to derive the dynamics model in the discrete-time domain, the state feedback technique and the forward difference approach are employed for the continuous-time nonlinear model of autonomous underwater vehicle. For each follower, the event-triggering function and the coordinated controller are designed, using only discrete-time state information of the leader or other followers. Under this control strategy, the controller will not be updated at each discrete-time instant. Then, the coordinated control problem is turned into the asymptotic stability problem of the multi-autonomous underwater vehicle system. According to the stability analysis, sufficient conditions are presented for successfully completing the formation assignment without and with time-varying delay, respectively. Finally, by performing some numerical simulation experiments, the efficacity of our proposed event-based controller and the correctness of the main theoretical results are demonstrated. The impact of different communication conditions on the control system is revealed by the comparison of several scenarios.

Synchronization of hybrid switching diffusions delayed networks via stochastic event-triggered control

In this paper, the synchronization problem of stochastic complex networks with time delays and hybrid switching diffusions (SCNTH) is concerned based on event-triggered control. Therein, a new class of event-triggered function is proposed for the control design. Particularly, different from the existing work, the triggered instant generated by event-triggered control in this paper is a stochastic sequence instead of a number sequence to be more realistic for stochastic systems, which is a breakthrough. Furthermore, some sufficient conditions are derived to guarantee asymptotical synchronization in mean square, exponential synchronization in mean square and almost surely exponential synchronization of SCNTH based on sampled-data control, event-driven control theory and stability analysis. Meanwhile, the Zeno phenomenon can be avoided. Then, the synchronization of single-link robot arms is investigated in detail as a practical application of the obtained results. Ultimately, a numerical example is given for demonstration.

Distributed time-varying out formation-containment tracking of multi-UAV systems based on finite-time event-triggered control

Considering the limited communication resources and slow convergence speed of multi-unmanned aerial vehicle (UAV) systems, this paper presents a finite-time even-triggered control framework for multi-UAV systems to achieve formation-containment tracking control. First, a virtual leader with time-varying output is introduced so that the trajectory of the whole system can be manipulated in real time. Second, the finite-time control enables that the systematic error converge to a small neighborhood of origin in finite time. Third, in order to save communication resources, an event-triggering function is developed to generate the control event sequences, which avoids continuous update of the controller. Rigorous proof shows the finite-time stability of the proposed control algorithm, and Zeno behavior is strictly excluded for each UAV. Finally, some numerical simulations are given to verify the effectiveness of the proposed controllers.

Event-triggered consensus for delayed second-order leader-following heterogeneous multi-agent systems under input saturated condition

The event-triggered consensus problem for observer-based second-order leader-following heterogeneous multi-agent systems with nonlinear term delay under input saturation conditions is investigated in this study. For a class of second-order leader-following heterogeneous multi-agent system models, the situation of agents with nonlinear delay terms in the system is considered. The observer is designed to reconstruct the state of the system. The structural state replaces the real state of the system to achieve the required state feedback, and the difference between the output quantities is inputted into the system as a feedback quantity (deviation) to achieve a better simulation. Considering the phenomenon of saturation control in many control systems, multi-agent consensus is achieved by combining saturation control and event-triggered pinning control in the controller. On the premise that each agent is affected by input saturation, an event-triggered pinning control protocol is designed to achieve the purpose of control by pinning down some key agents. The sufficient conditions for the second-order multi-agent system to achieve consensus are obtained by using the Lyapunov stability theory, algebraic Riccati equation, matrix theory, and other analytical techniques. The proposed event-triggered function can avoid Zeno behavior. The feasibility of the results is verified by numerical simulation.

Event-triggered finite-time formation control for second-order leader-following multi-agent systems with nonlinear term time delay

ABSTRACT Event-triggered finite-time formation control is considered for second-order leader-following multi-agent systems with nonlinear term time delay in this study. Collision avoidance radius is designed for a class of second-order nonlinear multiagent systems to avoid collisions between agents. Collision avoidance control is realised by detecting the flight radius. Control cost is economised, and communication volume is reduced by controlling key nodes and designing an event-triggered control strategy. The system can realise formation control in finite time by designing an FTC function. Some sufficient conditions for the formation of the second-order multi-agent system in finite time are obtained by using Lyapunov stability theory and analysis. The integral sliding mode control algorithm and finite-time stability theory are used to enhance the robustness of the system, and the upper bound of finite time is given. At the same time, the ability of the designed event-triggered function to avoid Zeno behaviour is proven. Finally, the feasibility of the results is verified through a numerical simulation.