Inter-event Time Research Articles

Consensus Protocol for Discrete-Time Linear Multiagent Systems With Channel Fadings: A Dynamic Event-Based Approach

This article investigates the consensus problem of discrete-time linear multiagent systems with channel fadings over wireless sensor networks. The phenomena of channel fadings are described as the stochastic Rice fading model with random time-varying channel coefficients. By utilizing the local state information and constructing a dynamic auxiliary system, a novel control protocol with the dynamic discrete-time event-triggered scheme has been proposed. Sufficient conditions are obtained to guarantee the asymptotic consensus of the multiagent systems under the proposed protocol. Compared with the existing works related to discrete-time event-triggered consensus, the interevent time between any two successive events can be prolonged, and thus, the transmission data packages can be decreased immensely. Finally, the effectiveness of the proposed consensus protocol with a dynamic discrete-time event-triggered scheme is testified by numerical simulations.

Dynamic Event-Triggered Bipartite Output Consensus for Heterogeneous Multi-Agent Systems Under Signed Digraphs

In this brief, the bipartite output consensus (BOC) problem is studied by dynamic event-triggered control for heterogeneous multi-agent systems under signed digraphs. A novel fully distributed control protocol, containing an observer-based adaptive controller and a Zeno-free dynamic event-triggered mechanism (ETM), is provided to guarantee the asymptotic convergence of BOC errors. Notably, an internal dynamic variable is introduced in the ETM to prolong interevent time intervals, which further reduces consumption on transmission. In addition, it is worth pointing out that the provided protocol remains valid even if global information about signed digraphs is unavailable. Finally, a numerical example is taken to demonstrate the effectiveness of protocol.

A Hybrid Systems Approach to Event-Triggered Consensus of Multiagent Systems With Packet Losses

This article addresses the event-triggered consensus problem of multiagent systems (MASs) with packet losses. The packet losses are not restricted to be identical, and a hybrid systems framework is proposed to handle the considered problem with or without leader in a unified framework. Distributed control law is constructed based on an estimator, whose dynamics are related to whether packet losses occur. A novel hybrid event-triggering mechanism (ETM) is proposed, and a lower bound of the interevent times is enforced to guarantee Zeno-freeness. For stability analysis, a unified hybrid model is constructed to describe the dynamics of MAS with or without leader. In accordance to this model, how to design the hybrid ETM and consensus analysis are formally developed, and the maximum allowable successive packet losses can be explicitly computed. Moreover, even if there exist nonlinearities and disturbances in system dynamics, and the leader has nonzero input, the proposed method can still be applied. Finally, examples are provided to illustrate the superiority of the proposed method.

The role of three-dimensional fault interactions in creating complex seismic sequences

A physics-based earthquake simulator should reproduce first-order empirical power-law behaviors of magnitudes and clustering. These laws have emerged spontaneously in either discrete or low-dimension continuum simulations without power-law or stochastic heterogeneity. We show that the same emergence can occur in 3-D continuum simulations with fault interactions and rate-and-state friction. Our model approximates a strike-slip fault system as three en echelon faults. Simulations show spatio-temporally clustered earthquake sequences exhibiting characteristic Gutenberg-Richter scaling as well as empirical inter-event time distribution. The Gutenberg-Richter scaling occurs only in partial ruptures that result from fault interactions. With fault interactions, partial ruptures emerge when seismogenic width W over characteristic nucleation length L∞ is larger than 16.24, but none occur without fault interaction. The mainshock recurrence times of individual faults remain quasi-periodic. The system mainshock recurrence time is a combination of short-term Omori-type decay and Brownian passage time. Higher W/L∞ increase short-term clustering probability to at most 30%. These results indicate that physics-based multi-cycle models adequately reflect observed statistical signatures and show practical potential for long-term hazard assessment and medium-term forecasting.

Periodic event-based robust output regulation for a class of uncertain linear systems with inter-event analysis

This paper investigates the robust output regulation problem of uncertain linear systems by using a periodic event-triggered controller. A new type of event triggers based on local sampled signals is proposed to monitor events. An event detector only uses local information, avoiding infinitesimal inter-event times as in some continuous event-triggered schemes. A periodic event-triggered system naturally excludes Zeno behavior as the system operates at discrete-time instants. Convergence of tracking error holds for a class of decreasing triggering positive functions. When exponential functions bound the triggering function, analytical characterization of the relationship among sampling, event triggering, and inter-event behavior is established.

Experimental evaluation of event-triggered sliding mode control for trajectory tracking of a quadcopter

This paper presents an experimental assessment of event-triggered sliding mode control (ET-SMC) on a Quadcopter for trajectory tracking. Sufficient triggering conditions using Lyapunov analysis and a lower bound of inter-event time to avoid Zeno behaviour are derived to ensure robust stability. Real-time flights are performed for tracking constant and time-varying trajectories. Results reveal that while using the proposed controller, there is a significant reduction in the number of updates implying a substantial saving in the computations.

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.

A Non-Extensive Statistical Physics View of the Temporal Properties of the Recent Aftershock Sequences of Strong Earthquakes in Greece

Greece is one of Europe’s most seismically active areas. Seismic activity in Greece has been characterized by a series of strong earthquakes with magnitudes up to Mw = 7.0 over the last five years. In this article we focus on these strong events, namely the Mw6.0 Arkalochori (27 September 2021), the Mw6.3 Elassona (3 March 2021), the Mw7.0 Samos (30 October 2020), the Mw5.1 Parnitha (19 July 2019), the Mw6.6 Zakynthos (25 October 2018), the Mw6.5 Kos (20 July 2017) and the Mw6.1 Mytilene (12 June 2017) earthquakes. Based on the probability distributions of interevent times between the successive aftershock events, we investigate the temporal evolution of their aftershock sequences. We use a statistical mechanics model developed in the framework of Non-Extensive Statistical Physics (NESP) to approach the observed distributions. NESP provides a strictly necessary generalization of Boltzmann–Gibbs statistical mechanics for complex systems with memory effects, (multi)fractal geometries, and long-range interactions. We show how the NESP applicable to the temporal evolution of recent aftershock sequences in Greece, as well as the existence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for longer interevent times. The observed behavior is further discussed in terms of superstatistics. In this way a stochastic mechanism with memory effects that can produce the observed scaling behavior is demonstrated. To conclude, seismic activity in Greece presents a series of significant earthquakes over the last five years. We focus on strong earthquakes, and we study the temporal evolution of aftershock sequences of them using a statistical mechanics model. The non-extensive parameter q related with the interevent times distribution varies between 1.62 and 1.71, which suggests a system with about one degree of freedom.

On the Structure of the Intermittency of Rainfall

Quantification of rainfall intermittency via. interevent time distribution, series of continuous wet spells (burst size) and variability in interevent times between rainfall events is essential for planning and management of water resources and hydrologic extremes. However, their structure, quantification and association with long-term climatology are less explored. In this paper, a complex system-based measure – burstiness – is used to quantify the variability of interevent times across six meteorologically homogenous zones of India. It is observed that burstiness is related to the burst size as well as long-term rainfall climatology. The existence of unimodal and bimodal structure in burstiness distribution reveals the uniqueness and differences in the rainfall patterns. The differences in sensitivity of rainfall to burstiness highlight the role of interplay between climate-landscape and reveals the importance of the intermittent structure of rainfall. The study provides an approach to model intermittency by preserving the temporal structure of the interevent time distribution.

Explaining the “Mystery” of Periodicity in Inter-Transmission Times in Two-Dimensional Event-Triggered Controlled Systems

Motivated by scenarioswhere the communication or the computation resources are limited, event-triggered control consists of transmitting data between the plant and the controller according to the actual system needs and not the elapsed time since the last transmission instant as in traditional sampled-data control, so that the desired control objective is achieved. A range of techniques are nowadays available to design event-triggered controllers. However, we generally have only very little information about the actual behavior of the transmission instants and thus about the amount of transmissions being actually generated, though this is a key feature of the design. In this article, we analyze the inter-event times, i.e., the times between two successive transmission instants, when the plant is modeled as a two-dimensional linear time-invariant system. The controller is a state-feedback law and the triggering rule is the relative threshold policy, which is allowed to be time-regularized. One of the main results in this article is the explanation of the oscillatory behavior of the inter-event times when the constant used to define the threshold is small relative to 1, a phenomenon commonly observed in simulations but never explained so far. More generally, the presented results help to understand the behavior of the inter-event times, instead of solely relying on numerical simulations, and thereby can be exploited to rigorously evaluate the performance of the considered triggering condition in terms of (average) inter-transmission times.

Event-Triggered Cooperative Output Regulation of Heterogeneous Multiagent Systems Under Switching Directed Topologies.

In this article, the cooperative output regulation problem of heterogeneous linear multiagent systems under jointly connected digraphs is addressed. The event-triggered control protocols based on state feedback and output feedback are proposed, respectively. It is shown that the output tracking errors of the resulting closed-loop control systems converge to 0 exponentially via the proposed protocols. One of the key advantages of the proposed event-triggering mechanism is that the information transmissions induced by event triggerings and topology switchings are independent, and data transmissions among agents are thus reduced. Furthermore, an explicit minimum interevent time is provided for all the agents so that the Zeno-behavior is excluded strictly. Finally, three numerical examples are provided to verify the effectiveness of the proposed protocols.

KDE-Based Rainfall Event Separation and Characterization

Rainfall event separation is mainly based on the selection of the minimum inter-event time (MIET). The traditional approach to determining a suitable MIET for estimating the probability density functions is often using the frequency histograms. However, this approach cannot avoid arbitrariness and subjectivity in selecting the histogram parameters. To overcome the above limitations, this study proposes a kernel density estimation (KDE) approach for rainfall event separation and characterization at any specific site where the exponential distributions are suitable for characterizing the rainfall event statistics. Using the standardized procedure provided taking into account the Poisson and Kolmogorov–Smirnov (K-S) statistical tests, the optimal pair of the MIET and rainfall event volume threshold can be determined. Two climatically different cities, Hangzhou and Jinan of China, applying the proposed approach are selected for demonstration purposes. The results show that the optimal MIETs determined are 12 h for Hangzhou and 10 h for Jinan while the optimal event volume threshold values are 3 mm for both Hangzhou and Jinan. The KDE-based approach can facilitate the rainfall statistical representation of the analytical probabilistic models of urban drainage/stormwater control facilities.

Dynamic Event-Triggered Adaptive NN Control for Switched Uncertain Nonlinear Systems.

This article is concerned with the problem of dynamic event-triggered adaptive neural network (NN) control for a class of switched strict-feedback uncertainty nonlinear systems. A novel switched command filter-based dynamic event-triggered adaptive NN control approach is set up by exploiting the backstepping and command filter and the common Lyapunov function method. Since adaptive controllers of subsystems are event triggered, then if the switching happens between any two consecutive triggering instants, asynchronous switching will arise between candidate controllers of subsystems and subsystems. Unlike the existing literature, where maximum asynchronous time is restricted, without any strict limitations on maximum asynchronous time being needed in this article, the asynchronous switching problem is directly handled by proposing a novel switching dynamic event-triggered mechanism (DETM) and event-triggered adaptive controllers of subsystems. Moreover, a piecewise constant variable is introduced into the switching DETM, which overcomes the difficulty of switched measurement error being discontinuous. Also, a strictly positive lower bound of interevent times is obtained. Finally, a continuous stirred tank reactor system and a numerical example are presented to demonstrate the effectiveness of the developed approach.

Event-Triggered Model Predictive Control for Aero-Engine Transient-State Tracking Problems

Transient-state control is one of the most important parts in aero-engine design. It determines the performance of an aero-engine or even the maneuverability of an aircraft. An optimized transient-state process can stimulate the potential performance of an aero-engine. Thus, model predictive control (MPC) is widely applied in transient-state tracking control with complex control constraints. However, the enormous computation pressure restricts its implementation in aero-engine transient-state tracking control. This paper aims to improve the efficiency of MPC and investigates the event-triggered model predictive control (EMPC) for aero-engine transient-state tracking problems. A new event-triggered mechanism that can exclude the Zeno behavior without an artificial interevent time is designed based on linear parameter-varying (LPV) aero-engine models. The feasibility and stability of the designed EMPC are investigated, and a numerical simulation example is presented to show the effectiveness of the designed method. The simulation result shows that our proposed method can reduce the computation load and time consumption significantly compared with MPC.

Effect of minimum inter-event time for rainfall event separation on rainfall properties and rainfall erosivity in a humid area of southern China

An appropriate rainfall event definition helps to have more explanatory power in research on the effect of rainfall on runoff and soil erosion. The constant minimum inter-event time (MIT) criterion is a widely accepted method used to delineate independent rainfall events from continuous rainfall records. To explore the effects of the MIT selection on rainfall event properties, rainfall erosivity and its relationship with eroded sediment, 5-min interval rainfall data from 2016 to 2021 and runoff data from 2019 to 2021 were observed continuously for a bare plot site in a humid area of southern China. The results showed that increase in the MIT criteria had an important impact on the properties of erosive rainfall events, such as reducing rainfall frequency, increasing duration, and reducing the average rainfall intensity. Furthermore, the MIT increased continuously, changed the statistical relationship between rainfall and sediment erosion, and logarithmically increased the rainfall threshold for a certain cumulative eroded sediment probability. With continuous increase in the MIT, the total kinetic energy, maximum 30 min intensity, and rainfall erosivity of rainfall events increased as a power function (r2 greater than 0.97). On the rainfall event scale, the linear relationship between EI30 and eroded sediment is the closest when MIT = 4 h. Thus, more attention should be given to the use of the MIT criterion for rainfall event identification, as it relates to the properties of rainfall events and rainfall erosivity.

Near-optimal sliding mode control for multi-robot consensus under dynamic events

We propose a continuous-time design for finite-time consensus control for multi-robot system using event-based near-optimal sliding mode control. The system has a leader–follower framework prone to external bounded disturbance. The proposed design comprises of three parts: (i) formulation of control-affine dynamics, (ii) design a triggering condition for control updates that guarantee stability and consensus in the system, and (iii) design a near-optimal sliding mode control using neural-network based approximate dynamic programming. We derive a bound on inter-event time that guarantees admissibility of updated control input values. We finally validate the efficacy of proposed design through real-time experiments using three Pioneer P3-DX mobile robots (leader and two followers) and comparative analyses with other state-of-the-art approaches. The control updates of follower-1 and follower-2 robots are approximately and , respectively, that reduce the computational burden in multi-robot framework.

Accessing power-law statistics under experimental constraints

Power-law distributions appear in a large variety of situations and influence our understanding of various physical phenomena. Their identification and characterization are notoriously difficult because of the large fluctuations inherent to empirical data and also because of the unknown range over which the power-law behavior holds. Furthermore, the data on which one is trying to detect power laws are affected by technical constraints and experimental limitations. Here, we show how a power-law distribution is modified by two fundamental limitations: the spatiotemporal resolution and the time window. We consider a time series of events or states and investigate the interevent time probability density function (PDF) or the PDF of the duration of a state. We present in detail how each limitation affects the PDF and derive mathematical expressions that relate the observed distribution to the true one: the resolution globally affects the shape of PDF while preserving the asymptotic exponent and the time window introduces a nonexponential cutoff. We demonstrate that, instead of looking for a simple power law in experimental data, one should fit the data with the modified PDF that we derived for given experimental constraints. We apply our theory to data from an experimental study of the transport of mRNA-protein complexes along dendrites. The presented mathematical theory widens our understanding of the identification and characterization of power-law distributions in experimental data and can be used in a broad spectrum of science fields.

Dynamic event-triggered distributed observer for linear systems

This paper investigates a dynamic event-triggered distributed observer for linear systems including two groups of local observers: one can access the local outputs and another cannot. By the detectability decomposition, the proposed observer contains a detectable sub-state (DSS) observer and a distributed undetectable sub-state (USS) observer. The dynamic event-triggered mechanism (DETM) for the outputs only requires a copy of the DSS observer with low dimension. Besides, only the USS estimate is transmitted to the neighbors which can reduce the communication burden. Positive minimum inter-event times are prescribed previously in the DETMs, and piece-wise dynamics for internal dynamic variables are employed. By modeling the error systems as hybrid systems, the exponential stability of the proposed observer is assured with the utilization of time-triggering method and event-triggering method.

Incorporating Full Elastodynamic Effects and Dipping Fault Geometries in Community Code Verification Exercises for Simulations of Earthquake Sequences and Aseismic Slip (SEAS)

ABSTRACTNumerical modeling of earthquake dynamics and derived insight for seismic hazard relies on credible, reproducible model results. The sequences of earthquakes and aseismic slip (SEAS) initiative has set out to facilitate community code comparisons, and verify and advance the next generation of physics-based earthquake models that reproduce all phases of the seismic cycle. With the goal of advancing SEAS models to robustly incorporate physical and geometrical complexities, here we present code comparison results from two new benchmark problems: BP1-FD considers full elastodynamic effects, and BP3-QD considers dipping fault geometries. Seven and eight modeling groups participated in BP1-FD and BP3-QD, respectively, allowing us to explore these physical ingredients across multiple codes and better understand associated numerical considerations. With new comparison metrics, we find that numerical resolution and computational domain size are critical parameters to obtain matching results. Codes for BP1-FD implement different criteria for switching between quasi-static and dynamic solvers, which require tuning to obtain matching results. In BP3-QD, proper remote boundary conditions consistent with specified rigid body translation are required to obtain matching surface displacements. With these numerical and mathematical issues resolved, we obtain excellent quantitative agreements among codes in earthquake interevent times, event moments, and coseismic slip, with reasonable agreements made in peak slip rates and rupture arrival time. We find that including full inertial effects generates events with larger slip rates and rupture speeds compared to the quasi-dynamic counterpart. For BP3-QD, both dip angle and sense of motion (thrust versus normal faulting) alter ground motion on the hanging and foot walls, and influence event patterns, with some sequences exhibiting similar-size characteristic earthquakes, and others exhibiting different-size events. These findings underscore the importance of considering full elastodynamics and nonvertical dip angles in SEAS models, as both influence short- and long-term earthquake behavior and are relevant to seismic hazard.

Distributed adaptive event-triggered control for general linear singular multi-agent systems

<abstract><p>This paper investigates the leader-following consensus of general linear singular multi-agent systems. A fully distributed adaptive event-triggered control protocol is first proposed by using the relative state estimate information between neighboring agents. Moreover, the proposed protocol does not require continuous communication between neighbors, which greatly alleviate the negative impact of communication. In addition, a novel adaptive gain is proposed, which will avoid using the Laplace of communication graph. Zeno behavior is excluded by proving that the inter-event times are lower bounded by a positive constant. Finally, a numerical simulation is proposed to verify the effectiveness and reliability of the protocol.</p></abstract>