Event-triggered Instants Research Articles

Distributed formation containment control for multi-agent systems via dynamic event-triggering communication mechanism

This paper focuses on resolving the distributed formation containment control issue in general multi-agent systems (MASs) possessing multiple leader agents subject to limited communication resources. The unnecessary data transmissions among agents in MASs are reduced by utilizing a unique dynamic event-triggering communication mechanism (DETCM), which can build communication time sequences for each agent automatically. Based on the sampled states of agents at event-triggering instants, a novel distributed formation containment control protocol is proposed. By mathematical analysis, the formation containment control problem is turned into the problem of stability in a reduced-order system. The global formation containment of the MASs is finally achieved through the application of Lyapunov-Krasovskii functionals and general inequalities. Moreover, a valid example is also given to support the validity and effectiveness of the findings.

Event-Triggered Control of Switched Nonlinear Time-Delay Systems With Asynchronous Switching.

This article investigates the event-triggered switching control (ETSC) of switched nonlinear time-delay systems (SNTDSs) with asynchronous switching. First, we study the input-to-state stability (ISS) and integral ISS (iISS) for SNTDSs with asynchronous switching, where switching instants are generated based on the designed event-triggered mechanism. Among existing works on the ETSC, systems behavior at event-triggered instants is neglected. In fact, whenever an event is triggered, the systems mode will jump suddenly such that a switch is imposed to the systems, leading to the change of subsystems. Moreover, asynchronous switching behavior may occur between the actual subsystem and its corresponding controller. These facts bring great challenges for the event-triggered mechanism design and ISS analysis. To tackle these problems, a new Lyapunov-based event-triggered mechanism with adjustable parameters is designed to establish the relationship between systems switches and event triggers, and exclude the Zeno phenomenon. The analysis of the asynchronous switching behavior can be implemented and some ISS and iISS criteria of SNTDSs are derived utilizing the merging switching technique. Finally, two numerical examples, including a practical stirred tank reactor system, are presented to show the validity of the proposed methods.

Event-triggered H∞ control for switched systems based on interval observer

The paper studies the design of interval observer–based event-triggered [Formula: see text] controller for switched systems with frequent asynchronism. We first propose an interval observer–based event-triggered mechanism, which is used to transmit the observer states and the activated mode information for controller updating. Then, we design an interval observer–based event-triggered [Formula: see text] controller for the considered systems. By using the controller mode–dependent Lyapunov function method, sufficient conditions for the globally exponential stability of the closed-loop switched systems are obtained under average dwell time switching law. Moreover, we prove that the interevent interval length is a positive constant, which can exclude the Zeno behavior. Compared with the literature, the paper removes the strict requirement of at most one switch between two event-triggered instants, that is, frequent switches within an interevent interval are allowed. Finally, a numerical example is given to verify the effectiveness of the proposed method.

Fixed-time containment control for nonlinear multi-agent systems via dynamic event-triggered mechanism over directed graphs

This paper focus on a dynamic event-triggered mechanism to solve fixed-time containment control problems for nonlinear multi-agent systems (MASs) with uncertain disturbances over directed graphs. An event-triggered algorithm based on dynamic variables is proposed to achieve the fixed-time containment control of MASs, which can effectively reduce the number of event-triggered instants. By modifying the auxiliary variables and reconstructing the dynamic variables, the effect of input time-delays in MASs is successfully eliminated. It is noteworthy that only the auxiliary variables are modified while the structure of the dynamic variables is not changed, which further indicates that the designed dynamic event-triggered algorithm is also suitable for solving multi-agent systems with input time-delays. In addition, the setting time associated with the time-delays is also computed and the Zeno behavior is successfully avoided by computing the minimum time interval between event triggering as non-negative. Finally, simulation results are given to verify the effectiveness of proposed control protocol.

Event-Triggered Positive Filter Design for Positive Polynomial Fuzzy Systems via Premise Integration and Membership-Function-Dependent Methods

This paper focuses on the design of the positive fuzzy filter with event-triggered mechanism for positive polynomial fuzzy-model-based (PPFMB) system. The main objective is to design a positive and stable fuzzy filter which makes the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula> performance index of the estimated output signal as good as possible with limited networked bandwidth resources. Since the positive constraints exist in the positive systems, while the disturbance signal of the output signal and the transmission delay in the event-triggered mechanism are taken into account in this research, the augmented system is rebuilt by introducing the weight coefficient of disturbance signal, and a novel linear copositive Lyapunov function (LCLF) is proposed. In order to adapt to the analysis framework based on linear Lyapunov function, a novel linear event-triggered condition is proposed. Furthermore, to handle the mismatched premise variables caused by the event-triggered mechanism, the premise variable associated with event-triggered instants are integrated into the interval of continuous premise variable with the help of the novel event-triggered condition, which means that the original multi-dimensional type-1 membership functions (MFs) are transformed into single-dimensional interval type-2 MFs. Then, an interval type-2 membership-function-dependent (IT2MFD) method is employed to introduce MFs information into the resultant conditions, so that more optimized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula> performance index is obtained. Finally, an example with simulation results is given to verify the effectiveness of all the fuzzy filter design strategies proposed in this paper for optimizing performance index.

Optimal tracking control for unknown nonlinear systems with uncertain input saturation: A dynamic event-triggered ADP algorithm

This paper is devoted to proposing a novel dynamic event-triggered adaptive dynamic programming (ADP) algorithm to tackle the tracking control problem of unknown nonlinear systems with uncertain input saturation. Initially, an augmented system is established to address the investigated optimal tracking control issue with a discounted cost function. An online identifier based on neural networks (NNs) is designed to recover the unknown system dynamics. Furthermore, the controller design consists of two parts, including the optimal control policy for the nominal system and the NN-based feedforward compensator. In particular, the latter leverages adaptive NN techniques to cope with uncertain input constraints which can be deemed as uncertain saturation nonlinearities. A critic NN is constructed to obtain the approximate optimal control policy for the nominal system. Moreover, rather than traditional time-triggered and static event-triggered control schemes, an adaptive dynamic event-triggering condition is designed to determine the system sampling as well as the controller execution to further reduce transmission and computation burden. The introduction of an internal dynamic variable in possession of a positive constant lower bound can realize the dynamic adjustment of triggering threshold and effectively exclude Zeno behavior. Notice that the weights of identifier NN and critic NN are updated simultaneously, only at the event-triggering instants. Subsequently, the Lyapunov-based theoretical analysis is conducted to confirm the uniform ultimate boundedness of the tracking error and all the NN weight estimation errors. Eventually, the feasibility and effectiveness of the developed algorithm are validated by means of two simulation examples.

Model-Based Distributed Asynchronous Sampling for Multiagent Consensus With Event-Detecting Delays and Network Delays

In this paper, the practical average consensus problem of linear multi-agent systems with model-based distributed asynchronous sampling is investigated. Both internal event-detecting delays and external network delays are allowed in systems. Data-sampling instants are generated asynchronously by local event-triggering conditions. Particularly, data-sampling instants and event-triggering instants of each agent are also asynchronous due to the existence of event-detecting delays. Prediction models are utilized in detecting events and updating control inputs. Artificial interpolation instants are introduced in each sampling interval to address theoretical challenges brought by internal and external delays. To deal with this kind of complex asynchronous setup with multiple time delays, based on Barbalat's Lemma, a new procedure for deriving conditions for average consensus and a theoretical analysis approach are presented.

Model-based event-triggered control of switched discrete-time systems

In this paper, we aim to study model-based event-triggered control for a class of uncertain switched discrete-time systems composed of stabilizable and unstabilizable subsystems. A nominal model is introduced at the controller side to form a dynamic controller so that it can provide a kind of approximate estimate of the system state for system input even the overall switched discrete-time system is running in open-loop during any two consecutive event-triggered instants. By using multi-Lyapunov function method and the average dwell time switching strategy, stability conditions given in linear matrix inequality form for the closed-loop switched discrete-time system are derived. The design of control gains is also given. Finally, a numerical example and a physical example are provided to verify the effectiveness and usefulness of the proposed method.

Distributed Fixed-Time Secondary Control for MTDC Systems Using Event-Triggered Communication Scheme

Multi-terminal DC transmission (MTDC) systems have attracted much attention due to their significant advantages in long-distance and high-capacity transmission. To improve their reliability and operation performance, a distributed fixed-time secondary control of frequency restoration and active power sharing is proposed under event-triggered communication, which only depends on the states of each AC grid and its neighbors. By utilizing Lyapunov theory, we prove that the MTDC system with the fixed-time secondary control can be stable in a settling time, and the conditions of the settling time are established for fixed-time algorithms. In addition, we simulate a five-terminal MTDC system in Matlab/Simulink. Several cases of MTDC systems are exhibited to showcase how well the suggested controller works when dealing with load changes and attacks. The comparison of the number of event-triggered instants shows that the proposed control method can effectively reduce communication resources.

Distributed Adaptive Human-in-the-Loop Event-Triggered Formation Control for QUAVs With Quantized Communication

To improve the safety and reliability of quadrotor unmanned aerial vehicles (QUAVs) with limited communication, system uncertainties, and unknown external disturbances in a highly uncertain and safety-critical environment, a distributed adaptive human-in-the-loop (HiTL) event triggered (ET) formation controller is proposed. The non-autonomous leader are controlled by receiving control commands decided by the gesture recognition system, and the followers are controlled indirectly via the connected communication network. Thus, the safety and flexibility of the closed-loop system are improved. The designed controller is quantized and then sent to actuator only at the ET instants to further reduce the network burden. The radial basis function neural network (RBFNN) is used to approximate the system uncertainties. The unknown approximation error and the unknown external disturbance are viewed as a compound disturbance compensated by the high order disturbance observer (HODO). In addition, the uniformly ultimately bounded (UUB) stability of the closed-loop system is achieved through the Lyapunov method. Finally, comparative experiments are implemented on the QUAVs to demonstrate the validity of the presented control scheme.

Learning-Based Event-Triggered Tracking Control for Nonlinear Networked Control Systems With Unmatched Disturbance

This article concentrates on optimal tracking control for a class of nonlinear networked systems subjecting to limited network bandwidth and unmatched disturbance. Given the models of the control and reference systems, the considered optimal tracking control issue is initially formulated as a minimax optimization problem. Then, with the introduction of an event-triggered mechanism used for saving bandwidth, the formulated problem is transformed into solving an event-based Hamilton-Jacobi-Isaacs (HJI) equation by recurring to the Bellman optimality theory. Based on the HJI equation, we demonstrate that the stability of the concerned system in the sense of uniformly ultimately bounded (UUB) can be guaranteed with the envisioned optimal control and worst disturbance policies. Here, the disturbance policy can be varied periodically while the control policy can only be updated at event-triggering instants, which differs from the existed researches. Furthermore, we propose a reinforcement learning (RL)-based algorithm to handle the constructed HJI equation and thus settle the studied tracking control problem. The effectiveness of the algorithm is finally validated by both theoretical analysis and simulations.

Event-triggered adaptive dynamic programming for decentralized tracking control of input constrained unknown nonlinear interconnected systems

This paper addresses decentralized tracking control (DTC) problems for input constrained unknown nonlinear interconnected systems via event-triggered adaptive dynamic programming. To reconstruct the system dynamics, a neural-network-based local observer is established by using local input–output data and the desired trajectories of all other subsystems. By employing a nonquadratic value function, the DTC problem of the input constrained nonlinear interconnected system is transformed into an optimal control problem. By using the observer-critic architecture, the DTC policy is obtained by solving the local Hamilton–Jacobi–Bellman equation through the local critic neural network, whose weights are tuned by the experience replay technique to relax the persistence of excitation condition. Under the event-triggering mechanism, the DTC policy is updated at the event-triggering instants only. Then, the computational resource and the communication bandwidth are saved. The stability of the closed-loop system is guaranteed by implementing event-triggered DTC policy via Lyapunov’s direct method. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed scheme.

Finite-time impulsive control for stochastic T-S fuzzy systems: A waiting-time-based event-triggered method

The finite-time impulsive control problem is studied for stochastic T-S fuzzy systems with parameter uncertainties. In order to reduce numbers of impulsive control and information transmission, we proposed event-triggered impulsive control (ETIC) scheme involving the co-design of event-triggered mechanisms and impulsive gains to ensure stochastic finite-time stability (SFTS) of considered systems. For ETIC scheme, impulsive inputs are adopted to systems only at event-triggering instants. The waiting-time is introduced into ETIC scheme to avoid Zeno behavior and save communication resources further. Compared with the time-triggered impulsive control, a theoretical analysis indicates that ETIC not only removes the restriction of upper bound for impulsive intervals, but also significantly reduce the number of impulsive control while ensuring the same control performance. Two examples illustrated the advantage and validity of ETIC scheme.

Adaptive dynamic event-triggered cluster synchronization in an array of coupled neural networks subject to cyber-attacks

This paper is concerned with cluster synchronization in an array of coupled neural networks subject to cyber-attacks, where a random variable is employed to reflect the success ration of the launched cyber-attacks. To save the energy consumption and alleviate the transmission load of the network, a novel adaptive distributed dynamic event-triggered communication scheme is presented based on the local stochastic the state sampling information, compared with some existing results, the different event-triggered matrices and auxiliary variables are introduced for each node to adjust its threshold dynamically, which can further reduce the sampled-data transmission, the proposed event-triggered scheme includes some existing event-triggered schemes as special cases. The cluster synchronization controllers are designed based on the states of neighboring nodes at event-triggered instants, a new stochastic sampled-data dependent error model is constructed, some mean-square cluster synchronization criteria can be derived by the Lyapunov stability theory and algebraic graph theory, and the feedback matrices and event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the theoretical results.

Event-Triggered Optimal Attitude Consensus of Multiple Rigid Body Networks With Unknown Dynamics

In this paper, an event-triggered Reinforcement Learning (RL) method is proposed for the optimal attitude consensus of multiple rigid body networks with unknown dynamics. Firstly, the consensus error is constructed through the attitude dynamics. According to the Bellman optimality principle, the implicit form of the optimal controller and the corresponding Hamilton-Jacobi-Bellman (HJB) equations are obtained. Because of the augmented system, the optimal controller can be obtained directly without relying on the system dynamics. Secondly, the self-triggered mechanism is applied to reduce the computing and communication burden when updating the controller. In order to address the problem that the HJB equations are difficult to solve analytically, an RL method which only requires measurement data at the event-triggered instants is proposed. For each agent, only one neural network is designed to approximate the optimal value function. Each neural network is updated only at the event-triggered instants. Meanwhile, the Uniformly Ultimately Bounded (UUB) of the closed-loop system is obtained, and Zeno behavior is also avoided. Finally, the simulation results on a multiple rigid body network demonstrate the validity of the proposed method.

Adaptive event-triggered group consensus of multi-agent systems with non-identical nonlinear dynamics

The paper is concerned with mean-square group consensus for second-order multi-agent systems with non-identical dynamics, where the agents in the same group have the identical dynamics, the agents in the different groups have non-identical nonlinear dynamics. To reduce the update frequency of event-triggered controller, a novel adaptive dynamic event-triggered communication scheme is presented based on the local stochastic sampled information. The proposed event-triggered conditions of the position state and velocity state have be given separately owe to their state ranges may be different, which lead to the position state and velocity state with different event-triggered instants and release intervals. The event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered conditions, the given event-triggered conditions are detected only at discrete sampled times, which means Zeno behavior can be excluded. A novel distributed protocol is designed based on the neighboring agents information of the position state and velocity state at event-triggered instants. The group consensus issue can be transformed into the convergence problem of the augmented error system. Then some mean-square group consensus criteria can be derived with the help of tools from graph theory and matrix analysis, and the event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the proposed transmission scheme.

Adaptive event-triggered group consensus of multi-agent systems under stochastic sampling

This paper investigates group consensus for linear multi-agent systems with nonidentical dynamics. A novel adaptive event-triggered communication scheme is presented by using the stochastic sampling information, the event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered condition, where event-triggered parameters can be adjusted with the system dynamics evolving. The group consensus protocol is designed based on the neighboring agents information at event-triggered instants, then a new stochastic sampled-data dependent error model is constructed, some group consensus criteria in mean-square can be derived and the feedback matrices can also be obtained. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

A Fixed-Time Distributed Optimization Algorithm Based on Event-Triggered Strategy

This paper considers the fixed-time distributed optimization problem with consensus constraint and strongly convex local cost functions, and a distributed optimization algorithm involving two stages is designed. The first stage is to make each agent converge to its own locally optimal state (the minimizer of local cost function) from any initial value in fixed time by designing distributed local optimization controllers. The second one is to realize the goal that all agents achieve the globally optimal state (the minimizer of global cost function) in fixed time under the distributed global optimization protocol. During the second stage of the proposed algorithm, each agent only communicates with its neighbors at event-triggered instants. Hence, comparing to the continuous communication optimization algorithm, our method has the advantage in the terms of saving the communication resources. Furthermore, Zeno behavior is avoided under such control strategy. The proposed algorithm in this paper can ensure that all agents achieve the globally optimal state in fixed time, which is independent of agents’ initial values and decided by some tunable parameters. Finally, the effectiveness of the presented optimization algorithm is demonstrated by a simulation example.

Asynchronous Event-Based Set Stabilization of Logical Control Networks and its Applications in Finite-Field Networks

In this article, the asynchronous event-triggered control mechanism (AETCM) is introduced to the set stabilization problem of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -valued logical control networks (KVLCNs). Under the proposed AETCM, each node of the system updates its event-triggered instants independently. In this case, how to coordinate the behaviors of various nodes is a challenge for us. As for this article, we first transform the set stabilization problem of KVLCNs into the shortest path problem in graph theory and then construct a weighted directed hypergraph. Next, an improved heap-optimized Dijkstra algorithm is designed for the optimal asynchronous event-triggered controller. Furthermore, we study set stabilization of KVLCNs with time delays. In terms of applications, how to flexibly adapt the AETCM to specific models is a difficult problem. In this article, as applications, the consensus of finite-field networks with arbitrary communication delays and synchronization of KVLCNs is investigated. Finally, two numerical examples are shown to illustrate the effectiveness of the proposed algorithms.

H-infinity bipartite consensus of multi-agent systems with external disturbance and probabilistic actuator faults in signed networks

&lt;abstract&gt;&lt;p&gt;The H-infinity bipartite consensus problem is addressed for a class of linear multi-agent systems with external disturbance, where the positive and negative links are allowed in communication topology. A novel event-triggered communication scheme is presented to save limited network resources, which dependents on information from neighboring agents at event-triggered instants, the given event-triggered condition is detected only at discrete sampling times, thus Zeno behavior can be excluded, two types of event-triggered matrices have been introduced in our event-triggered communication scheme, which can further reduce the sampled-data transmission compared with some existed results. Considering the probabilistic actuator faults, the reliable controller is designed based on sampled-data, then a new distribution-based fault model is constructed by using coordinate transform. Some H-infinity bipartite consensus criteria can be derived by the Lyapunov stability theory and algebraic graph theory, at the same time, the feedback matrices and event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, a numerical example is employed to show the validity and advantage of the proposed transmission scheme.&lt;/p&gt;&lt;/abstract&gt;