Positive Minimum Inter-event Time Research Articles

Exponential synchronization of fractional-order T–S fuzzy complex multi-links networks with intermittent dynamic event-triggered control

In this paper, the exponential synchronization problem for fractional-order T–S fuzzy complex multi-links networks under an intermittent dynamic event-triggered control (IDE-TC) strategy is discussed. To this end, a new triggering rule with a dynamical variable is first introduced, including some available static triggering rules as its particular form. Then, it is proved that the applied dynamical variable is positive by using some properties of the Mittag-Leffler function. Hence, the inter-event time between any two successive triggering moments can be enlarged than static event-triggered results. Additionally, there is a guaranteed positive minimum inter-event time for each sample path solution of systems. Based on the Lyapunov method and the graph theory, exponential synchronization criteria of the proposed networks under the IDE-TC strategy is deduced. Finally, the validity and feasibility of the derived theoretical results are investigated by an application with simulations.

Consensus algorithms for double-integrator dynamics with different velocity and actuator saturation constraints

This paper considers consensus strategy design for double-integrator multi-agent systems with matched disturbances under a directed graph. Specifically, we consider the case where both the control inputs and velocities of the agents are subject to different and asymmetric constraints. A novel distributed algorithm exploiting saturation functions is proposed to achieve asymptotic consensus without violating the predefined velocity and actuator saturation constraints. Subsequently, we extend the obtained results to event-triggered communication, where agent position broadcasting occurs only when specific triggering conditions are met. We rigorously prove that there exists a positive minimum inter-event time to rule out Zeno behavior. Finally, the simulation results confirm the theoretical findings and illustrate the achievable performance.

Strong Non-Zeno Mixed Adaptive Dynamic Event-Triggered Control for Distributed Consensus.

This article studies the distributed adaptive event-triggered consensus control problem of linear multiagent systems. A strong non-Zeno mixed adaptive dynamic event-triggering scheme is proposed, which guarantees a strictly positive minimum interevent time (MIET) between any two consecutive events. A model-based event-triggered fully distributed adaptive control law is presented without using prior global information about the communication topology. Moreover, a hybrid system model is constructed to facilitate the stability analysis of the closed-loop system. It is shown that the proposed control strategy can achieve asymptotic consensus of all agents via intermittent communication in a fully distributed way, while guaranteeing the strictly positive MIET property. Finally, the effectiveness of the designed control method is illustrated by a simulation example.

Fully distributed adaptive cooperative output regulation of heterogeneous multi-agent systems with hybrid event-triggering mechanism

This study focuses on the event-triggered cooperative output regulation problem (CORP) of multi-agent systems with heterogeneous dynamics. Two design criteria are required be achieved: event-triggered communication between agents has strictly positive minimum inter-event time (MIET), and global information with respect to communication topology is not needed to implement the event-triggered control strategy. These two criteria are significant, but cannot be simultaneously satisfied using the relevant existing results. In this work, two event-triggered observers with hybrid triggering conditions are developed to estimate the matrix and state of the exosystem, the MIET is enforced to be positive by incorporating an auxiliary function with decreasing dynamics into the event-triggering mechanism (ETM). This is more stringent than simply removing Zeno behavior and is more useful in engineering applications. Additionally, distributed controllers are developed based on the estimated state and regulator equation. The proposed method, which is better and more useful than the up-to-date results in literature, and can satisfy the two design criteria as mentioned before. Finally, numerical examples are provided to demonstrate the effectiveness.

Decentralized event-triggered estimation of nonlinear systems

We investigate the scenario where a perturbed nonlinear system transmits its output measurements to a remote observer via a packet-based communication network. The sensors are grouped into N nodes and each of these nodes decides when its measured data is transmitted over the network independently. The objective is to design both the observer and the local transmission policies in order to obtain accurate state estimates, while only sporadically using the communication network. In particular, given a general nonlinear observer designed in continuous-time satisfying an input-to-state stability property, we explain how to systematically design a dynamic event-triggering rule for each sensor node that avoids the use of a copy of the observer, thereby keeping local calculation simple. We prove the practical convergence property of the estimation error to the origin and we show that there exists a uniform strictly positive minimum inter-event time for each local triggering rule under mild conditions on the plant. The efficiency of the proposed techniques is illustrated on a numerical case study of a flexible robotic arm.

Distributed event-triggered fuzzy control for nonlinear interconnected systems

This paper deals with the asynchronous distributed event-triggered control of continuous-time nonlinear interconnected systems. The nonlinear dynamics of the subsystems are represented by Takagi–Sugeno fuzzy models via the sector nonlinearity approach. Moreover, the nonlinear interconnections among the subsystems are assumed to be known and sector-bounded. In the event-triggered control setup, where the state information is asynchronously available to the local controllers only in specific time instants, it is necessary to deal with the asynchronous premise variables because they introduce extra difficulties to derive suitable co-design conditions. To deal with this issue, we propose a new triggering strategy such that the local event-triggering mechanisms (ETMs) counteract the effects of asynchronous premise variables. With this new distributed ETM, a co-design condition is proposed, and the existence of a strictly positive minimum inter-event time is proved to exclude Zeno behaviour. Moreover, a multi-objective optimization procedure is introduced to enlarge the estimate of the domain of attraction of the closed-loop equilibrium and minimize the number of transmissions provided by the ETMs. Finally, the approach is validated through the synchronization of interconnected oscillators.

Adaptive Event-Triggered Average Tracking Control With Activable Event-Triggering Mechanisms

The fully distributed adaptive event-triggered average tracking protocol for general linear multiagent systems (MASs) with a positive minimum interevent time (PMIET) is established in an asynchronous way. First, a fully distributed event-triggered detector and controller for each agent that includes internal variables and adaptive gains are designed to track the average of multiple time-varying references signals asymptotically via intermittent communication without the requirement of global information. Then, activable dynamic event-triggering mechanisms are designed for the detector and the controller, respectively, which can only be activated after certain specific instants; that is, the triggering condition needs to be monitored only after the event-triggering mechanism has been activated. The time interval between the event-triggered instant and a specific activation instant ensures that the event-triggering mechanisms for the detectors and the agents have PMIETs. Finally, the application of spacecraft formation tracking in low Earth orbit illustrates the availability of the theoretical results.

Dynamic asynchronous edge-based event-triggered consensus of multi-agent systems

This paper studies the asynchronous edge-based dynamic event-triggered consensus problems for multi-agent systems (MASs) with general linear dynamics. First, the static-gain edge-based protocol is proposed to assure that the agents achieve consensus asymptotically and that a uniformly positive minimum inter-event time (MIET) exists under the corresponding dynamic triggering mechanism. Then, to remove the requirement for the global information associated with the graph, an asynchronous edge-based event-triggered consensus control law that involves a dynamic gain is developed. A novel triggering mechanism that includes two dynamic parameters and a class of positive L1 functions under no Zeno behavior is further proposed to determine triggering instants of each edge in the graph. In addition, the continuous communication link is avoided. Finally, the application in a group of fixed-wing aircraft illustrates the validity of the theoretical results.

Event-triggered impulsive control for stability of stochastic delayed complex networks under deception attacks

In this paper, we consider the stability of stochastic complex networks with time-varying delays (SCNTD) under deception attacks, adopting the event-triggered impulsive control (ETIC). A new event-triggered mechanism (ETM) which was used to determine the impulsive instance is given using the topology of networks and the Lyapunov functions of subsystems. For stochastic complex networks, to avoid the Zeno behavior, a positive minimum inter-event time (MIET) is guaranteed. Combining the graph theory and the Lyapunov–Razumikhin method, several criteria for achieving pth moment exponential stability (pMES) of SCNTD under deception attacks which are related to the topology of networks, the event-triggered parameters and the signal sent by the enemy are obtained. Finally, the theoretical results apply to the stochastic oscillator systems, single-link robot arms systems, and Chua’s circuit systems. The stability of these systems under deception attacks is considered separately, and to show the validity of our theories, numerical simulations are provided.

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.

Dynamic event-triggered trajectory tracking control for underactuated marine surface vessels with positive minimum inter-event time guarantees

This paper proposes a dynamic event-triggered trajectory tracking control scheme for underactuated marine surface vessels (MSVs) with positive minimum inter-event time (MIET) guarantees. Under the presented scheme, control inputs only need to transmit to actuators at the designed event triggering time. Additionally, the maximum signal transmission frequency can be prior known by designers. To facilitate the design of the above control architecture, an unified second-ordered tracking error dynamic system is firstly derived. Then, based on the transformed error dynamic system, an event-based adaptive control law is developed. To counteract external disturbances and unmodeled dynamics, the minimum-learning-parameter (MLP) based neural approximator is constructed to enhance system robustness. Finally, by introducing internal dynamic variables, a dynamic event-triggered mechanism (DETM) is established to manage communications between the control module and actuators. Compared with existing event-triggered methods, the proposed event-driven method is dynamic and more flexible to satisfy network bandwidth requirements. Besides, MIETs of the presented DETM are also proved to be strictly positive and computable from control parameters. Theoretical analysis and simulation results verify the validity and effectiveness of the proposed DETM based control scheme.

Dynamic Event-Triggered Distributed Secondary Control of DC Microgrids

Emerging distributed control paradigms rely on communication among converters of a microgrid. We investigate the secondary control of dc microgrids with a distributed dynamic event-triggering mechanism. The physical and cyber layers are represented by different graph topologies. To reduce the communication burden, a distributed dynamic event-triggering mechanism is designed. Therein, the Zeno behavior is excluded and in addition, a positive minimum interevent time (MIET) is determined. Asymptotic stability of the closed-loop system dynamics is proven, and the adjustment of the positive MIET is discussed. Compared to the existing static event-triggering mechanisms, the proposed dynamic one guarantees the existence of a positive MIET, whose value can be tuned by the design parameters. Controller/hardware-in-the-loop implementation results validate the efficacy of the proposed method.

Distributed optimized dynamic event-triggered control for unknown heterogeneous nonlinear MASs with input-constrained

The distributed optimized dynamic event-triggered controller is investigated for completely unknown heterogeneous nonlinear multi-agent systems (MASs) on a directed graph subject to input-constrained. First, the distributed observer is designed to estimate the information of the leader for each follower, and a network of the augmented system is constructed by employing the dynamics of the followers and the observers. An identifier with a compensator is designed to approximate the unknown augmented system (agent) with an arbitrarily small identifier error. Then, consider that the input-constrained optimal controller, along with Hamilton–Jacobi–Bellman (HJB) equation, is under pressure to execute in certain systems associated with bottlenecks such as communication and computing burdens. A critic–actor-based optimized dynamic event-triggered controller, which tunes the parameters of critic–actor neural networks (NNs) by the dynamic triggering mechanism, is leveraged to determine the rule of aperiodic sampling and maintain the desired synchronization service. In addition, the existence of a positive minimum inter-event time (MIET) between consecutive events is also proved. Finally, the applications in non-identical nonlinear MAS and 2-DOF robots illustrate the availability of the proposed theoretical results.

Dynamic Event-Triggered Impulsive Control for Stochastic Nonlinear Systems With Extension in Complex Networks

This study proposes a novel dynamic event-triggered impulsive control (ETIC) scheme to study the exponential stabilization of general stochastic nonlinear systems, where the impulsive sequence is determined by a dynamic event-triggered mechanism. The dynamic ETIC can effectively reduce controller updates and significantly save energy under the same decay rate compared to traditional static event-triggered impulsive generators. Additionally, there is a guaranteed positive minimum inter-event time for each sample path solution of systems. Furthermore, the proposed dynamic ETIC scheme is employed to stabilize stochastic complex networks based on the graph theory and the Lyapunov method. Finally, we provide two illustrative examples to verify the effectiveness and correctness of the proposed dynamic ETIC scheme.

Fully Distributed Event-Triggered Cooperative Output Regulation of Multi-Agent Systems under Jointly Connected Digraphs

This paper addresses the cooperative output regulation problem of heterogeneous linear multi-agent systems (MASs) with <i>jointly connected digraphs</i> under the assumption that the exosystem matrix is only known by the neighbors of the exosystem. First, a novel event-based adaptive distributed observer with time-dependent power functions as the event-triggering threshold is proposed to estimate the exosystem matrix and the exogenous signal simultaneously. A new analytical method based on the weighted mean-value theorem for integrals and Bellman-Gronwall lemma is developed to prove the estimation errors converge to zero asymptotically. Second, a distributed dynamic control law is proposed based on the event-based adaptive observer, and it is shown that the tracking errors of the resulting closed-loop system converge to zero asymptotically. Two distinctive advantages of this work are (i) the event-triggered control (ETC) protocol is fully distributed, and (ii) a positive minimum inter-event time (MIET) is explicitly given so that Zeno behavior is strictly excluded. Finally, the effectiveness of the proposed fully distributed ETC protocol is illustrated by a numerical example.

Design of distributed adaptive event-triggered consensus control strategies with positive minimum inter-event times

This paper studies the design of distributed adaptive event-triggered control strategies with positive minimum inter-event times for linear multi-agent systems. To present our design idea, this paper focuses on the consensus problem of linear multi-agent systems defined on a fixed communication graph. In order to solve the consensus problem, a distributed adaptive event-triggered control strategy is proposed that consists of a distributed event-triggered adaptive control law and a distributed asynchronous event-triggering mechanism. It is shown that under the proposed event-triggered control strategy, the states of all agents asymptotically reach consensus via intermittent communication without using any global information of the communication graph. Moreover, using the proposed event-triggering mechanism, not only the exclusion of the Zeno behavior but also the existence of a uniform strictly positive minimum inter-event time is guaranteed for each agent. A simulation example demonstrates the effectiveness of the proposed event-triggered control strategy.

Distributed edge-based event-triggered coordination control for multi-agent systems

This paper studies edge-based event-triggered strategies for the average consensus problem in multi-agent systems. To this end, a distributed event-triggered algorithm is presented based on edge information rather than neighbor information, where positive minimum inter-event times are guaranteed between all communication links in the network. Moreover, the triggering mechanism is constructed in a fully distributed way which uses only relative state differences based on local neighborhood information without any global graph topology information. This treatment greatly reduces the communication frequency compared with continuous-time average consensus algorithms. We show that the proposed algorithm makes all agents converge to the average of their initial states asymptotically, and the positive minimum inter-event time for each link is controllable by two corresponding agents through their triggering parameters.

Stabilization of networked switched affine systems with event-triggered strategy

Using an event-based switching law, we address the stability issue for continuous-time switched affine systems in the network environment. The state-dependent switching law in terms of the region function is firstly developed. We combine the region function with the event-triggering mechanism to construct the switching law. This can provide more candidates for the selection of the next activated subsystem at each switching instant. As a result, it is possible for us to activate the appropriate subsystem to avoid the sliding motion. The Zeno behavior for the switched affine system can be naturally ruled out by guaranteeing a positive minimum inter-event time between two consecutive executions of the event-triggering threshold. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

Distributed dynamic event-triggered algorithm with minimum inter-event time for multi-agent convex optimisation

In this paper, the distributed convex optimisation problem of the multi-agent system over an undirected network is investigated, in which the local objective function of each agent is only known by itself. To reduce the communication consumption between agents, a state-based dynamic event-triggered algorithm with positive minimum inter-event time (MIET) is provided, where the aperiodic information communication only occurs at some discrete triggering time instants. Moreover, the sampling control technology is combined into the previous event-triggered algorithm for verifying the event-triggered condition at every sampling time, instead of continuous access. Finally, several numerical simulations are presented for illustrating and verifying the proposed algorithms.

Distributed dynamic event-triggered algorithm with positive minimum inter-event time for convex optimisation problem

In this study, we investigate the distributed convex optimisation problem of the multi-agent system over an undirected network, in which the global objective function is the sum of all the local cost functions and the local cost function of each agent is only known by itself. In order to save the computation and communication resources, the above optimisation problem is addressed by designing two zero-gradient-sum algorithms with state-based dynamic event-triggered mechanism, where the information communication only occurs at some discrete triggering time instants. The Zeno behaviour of the above event-triggered control scheme is excluded by the existence of the positive minimum inter-event time (MIET). The convergence is proved based on the Lyapunov method. Finally, we illustrate and evaluate the effectiveness of the proposed event-triggered algorithms through numerical experiments on simulated.