Discrete Time Instants Research Articles

Dynamic periodic event-triggered control for nonlinear systems with output dynamic quantization

This paper is concerned with the design of stabilizing event-triggered controllers for nonlinear systems subject to dynamic quantization. The plant state is assumed to be partially known, and the feedback signal is transmitted to the controller at discrete-time instants via a digital channel. To that end, an event-triggered controller is synthesized based solely on the available plant measurement. In addition, to better adapt it to practical implementation, the event-triggering law we construct is only verified at periodic time instants, i.e., periodic event-triggering mechanism. Since the network is digital, the transmitted output signal must be quantized to be encoded using a finite number of bits. Furthermore, the initial output value is assumed to be unknown, and the plant is affected by external disturbance, which can result in quantizer saturation. To overcome these challenges, a dynamic quantization policy is developed for the output measurement such that the quantization regions are dynamically updated according to the value of the quantized signal. The combined approach of periodic event-triggering mechanism and dynamic quantization ensures the stability of the networked control system under mild conditions. The stability is studied using appropriate Lyapunov functions. Numerical simulations have been conducted to justify the proposed technique.

Aeroacoustics computation for propellers based on harmonic balance solution

In this paper, a novel open-source framework is presented for the evaluation of noise emissions produced by aerodynamic bodies exhibiting dominant motion at specific frequencies. This behavior is frequently encountered in propellers used for urban air mobility applications. The reduced order model called harmonic balance is employed to compute the unsteady flow solution, reducing the computational cost. The approach tackles K different frequencies by capturing the flow solution at N discrete time instances within a single period, where N is defined as 2K+1. The time history of the conservative variables on the solid surfaces is reconstructed through a Fourier interpolation. The Kirchhoff Ffowcs Williams Hawkings integral formulation, integrated into SU2, is used to compute the sound pressure level perceived by farfield observers. The integral formulation propagates the acoustic solution with a computational cost independent of observer distance. The noise emission of a pitching wing and a propeller is computed with the proposed framework. Regarding a small, isolated propeller operating at low Reynolds numbers in forward flight, we conducted a comparison of the aerodynamic and aeroacoustic results between a fully time-accurate solution and a steady-state Reynolds Averaged Navier-Stokes solution within a rotating reference frame. The harmonic balance results demonstrated improved agreement with the fully unsteady solution across the first three blade-pass frequencies and exhibited this consistency over a broader range of propagation angles.

Probabilistic Analysis of Random Check Intrusion Detection System

The ubiquitous adoption of network-based technologies has left organizations vulnerable to malicious attacks. It has become vital to have effective intrusion detection systems (IDS) that protect the network from attacks. In this paper, we study the intrusion detection problem through the lens of probability theory. We consider a situation where a network receives random malicious signals at discrete time instances, and an IDS attempts to capture these signals via a random check process. We aim to develop a probabilistic framework for intrusion detection under the given scenario. Concretely, we calculate the detection rate of a network attack by an IDS and determine the expected number of detections. We perform extensive theoretical and experimental analyses of the problem. The results presented in this paper would be helpful tools for designing and analyzing intrusion detection systems. We propose a probabilistic framework that could be useful for IDS experts; for a network-based IDS that monitors in real-time, analyzing the entire traffic flow can be computationally expensive. By probabilistically sampling only a fraction of the network traffic, the IDS can still perform its task effectively while reducing the computational cost. However, checking only a fraction of the traffic increases the possibility of missing an attack. This research can help IDS designers achieve appropriate detection rates while maintaining a low false alarm rate. The groundwork laid out in this paper could be used for future research on understanding the probabilities related to intrusion detection.

Distributed Nash Equilibrium Seeking Dynamics With Discrete Communication.

In this brief, we aim to provide a distributed Nash equilibrium seeking algorithm in continuous time with discrete communications. A group of agents are considered playing a continuous-kernel noncooperative game over a network. The agents need to seek the Nash equilibrium when each player cannot get the overall action profiles in real time, rather are only able to get information from its networked neighbors. Meanwhile, a continuous-time dynamics is discussed for the players to update their variables, but the communications over the network are only assumed to allow at discrete-time instants, since continuous-time communications are prohibitive and cumbersome in practice. First, the periodic communication is considered at a fixed interval, and the solvability of Nash equilibrium seeking is shown with discrete communications. Then, an event-trigger communication scheme is proposed to further reduce the communication rounds. Nevertheless, the event-trigger communication scheme requires each player continuously monitoring its local states. To alleviate the monitoring burden, a periodic event detection mechanism is further developed. The exponential convergence of the dynamics with the three discrete communication schemes is proven. Finally, the comparative simulation studies are designed to illustrate the algorithm performance with different communication schemes and parameter settings.

Intermittent monitoring‐based adaptive fault‐tolerant control for uncertain nonlinear systems with actuator switching

AbstractIn this paper, an adaptive fault‐tolerant control (FTC) scheme is proposed for a class of uncertain nonlinear systems with actuator failure, in which a healthy actuator is available as a backup. Instead of monitoring the failure in real‐time, an intermittent monitoring mechanism (IMM) is proposed by designing a set of monitoring functions operating only at discrete time instants, which makes the proposed scheme more applicable for networked control systems for which the actuator status has to be monitored via network. An adaptive backstepping controller is designed with the errors being modified to include shifting functions. Once actuator failure is detected by the monitoring functions, the actuator is switched to its backup and the controller is reconfigured by updating the shifting functions so that the tracking error can be driven into the prescribed performance in a given time.

On a Positional Control Problem for a Nonlinear Equation with Distributed Parameters

We consider a guaranteed control problem for a nonlinear distributed equation of diffusion type. The problem is essentially to construct a feedback control algorithm ensuring that the solution of a given equation tracks the solution of a similar equation subjected to an unknown disturbance. The case in which a discontinuous unbounded function can be a feasible disturbance is studied. We solve the problem under conditions of inaccurate measurement of solutions of each of the equations at discrete instants of time and indicate a solution algorithm robust under information noise and calculation errors.

A novel hybrid time-variant reliability analysis method through approximating bound-most-probable point trajectory

In the engineering field, time-variant reliability analysis (TRA) is used to measure the safety level of structures under time-variant uncertainties. Lacking in information or data, some uncertainties cannot be directly quantified as stochastic models, which results in the simultaneous existence of aleatory and epistemic uncertainties in most of problems. In general, stochastic and interval models are respectively used to describe aleatory and epistemic uncertainties. For the hybrid TRA (HTRA) problem considering the two kinds of uncertainties, the existing method needs to excessively evaluate the original time-variant limit-state function, which is too expensive for engineering problems. To address this issue, we propose the concept of bound-most-probable point trajectory (BMPPT) which can be used to construct the approximation of the limit-state hyper-surface. Moreover, we develop a HTRA method based on approximating BMPPT which can further improve the computational efficiency. First, based on time discretization, we transform the HTRA problem into a time-independent series-system reliability problem which can be solved by searching the bound-most-probable point (BMPP) at all discrete time instants. Then, with the BMPPT, the lower and upper bounds of the time-variant limit-state function are linearized into two Gaussian processes. Finally, the expansion optimal linear estimation and Monte Carlo simulation are performed to estimate the time-variant reliability. To avoid excessive BMPP searches, the active learning Kriging is used to approximate the BMPPT. Two numerical examples including a cantilever beam, and a 10-bar truss, and two engineering applications of the solid rocket engine shell and the rocket inter-stage structure are investigated, and the results reveal that the proposed method can solve the HTRA problems with high accuracy and efficiency.

Asynchronous Platoon Control for Connected Vehicles With Intermittent and Delayed Information Transmission

This technical note investigates the asynchronous platoon control problem for connected vehicles with intermittent and delayed information transmission under dynamically changing communication topologies. An asynchronous consensus based protocol is proposed for each vehicle based on the state information of its neighbors at discrete times with communication delays, in which the asynchrony means that each agent updates its dynamics at discrete time instants determined by its own clock. The update intervals and the communication delays are allowed to be arbitrary bounded. We employ nonnegative matrix theory and graph theory to prove that the vehicle platoon asymptotically reaches a desired inter-vehicle spacing and a common velocity, if the effective communication topology jointly contains a directed spanning tree. Furthermore, we show that the string stability of the platoon control system is attained under the predecessor-following topology. Finally, we present numerical examples to validate the theoretical results.

Reliability analysis of geosynthetic-reinforced slopes under rainfall infiltration

The rainfall-induced instability of geosynthetic-reinforced is a time-dependent phenomenon owing to the infiltration process, and is influenced by rainfall patterns. Catering to the inherent uncertainty in soil properties, this study conducted a reliability analysis of three-dimensional (3D) vertical geosynthetic-reinforced slopes, in order to explore how the probabilistic stability of slope evolves over time under different rainfall patterns. A 3D horn-like mechanism incorporating the Conte-Troncone (CT) model is adopted as a framework for deterministic analysis. Through a Fourier transform-based theoretical reasoning, the CT model assesses the time-variable pore-water pressure of soils in response to any continuously varying rainfall intensity over time. Subsequently, the pore water pressure-driven changes in soil unsaturated strength and the corresponding extend power are integrated into the three-dimensional mechanism, enabling a rapid determination of the instantaneous safety factor at discrete time instants. To avoid the tedious computation generated by Monte Carlo simulation, a simplified Hasofer-Lind-Rackwitz-Fiessler (HLRF) algorithm is used to calculate the time-varying reliability indices. Using the implantation of the proposed method, the effects of rainfall pattern, slope width, and reinforcement tensile strength are investigated by parametric analysis.

Output-Based Dynamic Periodic Event-Triggered Control with Application to the Tunnel Diode System

The integration of communication channels with the feedback loop in a networked control system (NCS) is attractive for many applications. A major challenge in the NCS is to reduce transmissions over the network between the sensors, the controller, and the actuators to avoid network congestion. An efficient approach to achieving this goal is the event-triggered implementation where the control actions are only updated when necessary from stability/performance perspectives. In particular, periodic event-triggered control (PETC) has garnered recent attention because of its practical implementation advantages. This paper focuses on the design of stabilizing PETC for linear time-invariant systems. It is assumed that the plant state is partially known; the feedback signal is sent to the controller at discrete-time instants via a digital channel; and an event-triggered controller is synthesized, solely based on the available plant measurement. The constructed event-triggering law is novel and only verified at periodic time instants; it is more adapted to practical implementations. The proposed approach ensures a global asymptotic stability property for the closed-loop system under mild conditions. The overall model is developed as a hybrid dynamical system to truly describe the mixed continuous-time and discrete-time dynamics. The stability is studied using appropriate Lyapunov functions. The efficiency of the technique is illustrated in the dynamic model of the tunnel diode system.

Unified Filter Order Estimate for Minimax-Designed Linear-Phase FIR Wideband and Lowpass Digital Differentiators

Digital differentiators enable the computation of the derivative of a continuous-time signal at discrete time instances, and they are used in many signal processing applications. This paper derives a unified filter order estimate for digital differentiators that are realized with linear-phase finite-length impulse response filters and designed in the minimax sense. The estimate is useful at the high-level system design when assessing the implementation complexity and it enables fewer designs when finding the minimal filter order required to satisfy a prescribed tolerable approximation error. The proposed unified estimate covers both wideband and lowpass differentiators of integer degrees up to ten. Furthermore, degree-individual filter order estimates are derived which improve and extend previous results. The performance of both the unified and degree-individual order estimates is evaluated through simulation examples and compared with previous estimates.

Signal area estimation based on deep learning

In many practical application scenarios, radio communication signals are commonly represented as a spectrogram, which represents the signal strength measured at multiple discrete time instants and frequency points within a specific time interval and frequency band, respectively. In the context of spectrum occupancy measurements, the notion of Signal Area (SA) is defined as the rectangular region in the time–frequency domain where a signal is assumed to be present. Signal Area Estimation (SAE) is an important functionality in spectrum-aware wireless systems where spectrum usage monitoring is required. However, the conventional approaches to SAE have a limited estimation accuracy, in particular at low SNR. In this work, a novel technique for SAE is proposed using Deep Learning based on Artificial Neural Network (DL-ANN) for enhanced extraction of SA information from radio spectrograms. The performance of the proposed DL-ANN method is evaluated both with software simulations and hardware experiments, and the results are compared with several conventional methods from the literature, showing significant performance improvements. A key feature of the proposed method is the improvement in the SAE accuracy compared to other existing methods (in particular in the low SNR regime) and the capability to extract the location of the detected SAs automatically. Overall, the proposed technique is a promising solution for the automatic processing of radio spectrograms in spectrum-aware wireless systems.

Ergodic estimators of double exponential Ornstein–Uhlenbeck processes

The goal of this paper is to construct ergodic estimators for double exponential Ornstein–Uhlenbeck process, where the process is observed at discrete time instants with time step size h. We show the existence and uniqueness of the function equations to determine the estimators for fixed time step size h. Also, we show the strong consistency and the asymptotic normality of the estimators. Furthermore, we propose a simulation method of the double exponential Ornstein–Uhlenbeck process and perform some numerical simulations to demonstrate the effectiveness of the proposed estimators.

Analytic approach to the Landau–Zener problem in bounded parameter space

Three analytic solutions to the Schrödinger equation for the time-dependent Landau–Zener (LZ) Hamiltonian are presented. They correspond to specific finite-time driving paths in a bounded parameter space of a two-level system. Two of these paths go through the avoided crossing of levels, either with a constant speed or with variable speed that decreases in the region of reduced energy gap, the third path bypasses the crossing such that the energy gap remains constant. The solutions yield exact time dependencies of the excitation probability for the system evolving from the ground state of the initial Hamiltonian. The LZ formula emerges as an approximation valid within a certain interval of driving times for the constant-speed driving through the avoided crossing. For long driving times, all solutions converge to the prediction of the adiabatic perturbation theory. The excitation probability vanishes at some discrete time instants.

Preemptive multi-skill resource-constrained project scheduling of marine power equipment maintenance tasks1

The shipbuilding industry, characterized by its high complexity and remarkable comprehensiveness, deals with large-scale equipment construction, conversion, and maintenance. It contributes significantly to the development and national security of countries. The maintenance of large vessels is a complex management engineering project that presents a challenge in lowering maintenance time and enhancing maintenance efficiency during task scheduling. This paper investigates a preemptive multi-skill resource-constrained project scheduling problem and a task-oriented scheduling model for marine power equipment maintenance to address this challenge. Each task has a minimum capability level restriction during the scheduling process and can be preempted at discrete time instants. Each resource is multi-skilled, and only those who meet the required skill level can be assigned tasks. Based on the structural properties of the studied problem, we propose an improved Moth-flame optimization algorithm that integrates the opposition-based learning strategy and the mixed mutation operators. The Taguchi design of experiments (DOE) approach is used to calibrate the algorithm parameters. A series of computational experiments are carried out to validate the performance of the proposed algorithm. The experimental results demonstrate the effectiveness and validity of the proposed algorithm.

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.

Tabu search for proactive project scheduling problem with flexible resources

In this paper, we address a proactive resource-constrained project scheduling problem where resources have several skills and can switch the selected skill at discrete time instants. The objective of this paper is to simultaneously determine the starting times of activities and select the skills of resources to maximize the schedule robustness, while satisfying constraints of precedence, renewable resources and a project deadline. After defining the problem, an integer linear programming model is constructed and the studied problem is proven to be NP-hard. Considering the NP-hardness of the problem, we develop a tabu search embedded with two special algorithms to solve the problem. Based on the characteristics of the problem, a resource allocation algorithm for determining the skill for resources is proposed. The two special algorithms are regarded as two improvement measures to combine with the basic tabu search, leading to three versions of the tabu search, i.e., TS, TS-IM1, and TS-IM12. A commercial mathematical programming solver, which can optimally solve the model, is used as a benchmark for comparing the developed algorithm. Through a computational experiment performed on a randomly generated dataset, the effectiveness of the designed algorithms and the two improvement measures is verified, and the results for single-skilled resources as well as the skill switching of flexible resources are discussed. In addition, the effects of the key parameters on the objective function are also analysed. From the computational results, we can draw several conclusions. First, among the three developed algorithms, TS-IM12, which is the tabu search embedded with two improvement measures, performs best, and compared with the commercial software, TS-IM12 shows a higher efficiency in solving the studied problem. Second, the increase in the resource flexibility should be moderate. Third, the robustness of the baseline schedule increases with an increase of the resource flexibility, the resource availability and the project deadline. Finally, the improvement of the schedule robustness brought by the increase of the resource flexibility or the resource availability will be further magnified as the project deadline extends, while the improvement of the schedule robustness caused by the increase of the resource flexibility will be reduced as the resource availability augments.

Machine learning classification of non-Markovian noise disturbing quantum dynamics

In this paper machine learning and artificial neural network models are proposed for the classification of external noise sources affecting a given quantum dynamics. For this purpose, we train and then validate support vector machine, multi-layer perceptron and recurrent neural network models with different complexity and accuracy, to solve supervised binary classification problems. As a result, we demonstrate the high efficacy of such tools in classifying noisy quantum dynamics using simulated data sets from different realizations of the quantum system dynamics. In addition, we show that for a successful classification one just needs to measure, in a sequence of discrete time instants, the probabilities that the analysed quantum system is in one of the allowed positions or energy configurations. Albeit the training of machine learning models is here performed on synthetic data, our approach is expected to find application in experimental schemes, as e.g. for the noise benchmarking of noisy intermediate-scale quantum devices.

The generalized EPC method for the non-stationary probabilistic response of nonlinear dynamical system

It is well known that the non-stationary response probability density function (PDF) plays an important role in the reliability and failure analysis. With current approximate or numerical methods, the non-stationary approximate PDF is generally obtained in terms of the ones at the discrete time instants. Repeated computation must be conducted for the ones at other time instants since the response PDF at only one time instant can be obtained after performing the solution procedure. Thus, the computational efficiency suffers a major setback. In this paper, the exponential polynomial closure (EPC) method is further improved and enhanced to obtain the completely non-stationary PDF solution, which is distributed continuously in the time domain. It takes the temporal base function into the PDF approximation. The unknown coefficients in the EPC solution are generalized to be explicit functions of the time parameter. With the least squares method, the explicit time functions can be determined based on the few simulated response PDF values. This implementation makes the continues PDF distribution in the time domain available, which greatly improves the computational efficiency without the repeating computation. Two typical nonlinear systems under stationary and non-stationary random excitations are taken as examples to illustrate the efficiency of the proposed method. Numerical results show that the results obtained by the proposed method agree well with the simulated results. In addition, the relationship between the explicit time function and the modulate function is discussed.

Event-driven adaptive intermittent control applied to a rotational pendulum

Intermittent control combines open-loop trajectories with feedback at discrete time instances determined by events. Among other applications, it has recently been used to model quiet standing in humans where the system was assumed to be time-invariant. This article expands this work to the time-variant case by introducing an adaptive intermittent controller that exploits the well-known self-tuning architecture of adaptive control with a Kalman filter to perform online state and parameter estimation. Simulation and experimental results using a rotational inverted pendulum show advantages of the intermittent controllers compared to continuous feedback control since the former can provide persistent excitation due to their internal triggering mechanism, even when no external reference changes or disturbances are applied. Moreover, the results show that the event thresholds of intermittent control can be used to adjust the degree of responsiveness of the adaptation in the system, becoming a tool to balance the trade-off between steady-state performance and flexibility against parametric changes, addressing the stability–plasticity dilemma of adaptation and learning in control.