Time-varying Delays Research Articles

A new approach to state bounding for coupled differential-difference equations with bounded disturbances

In this paper, we present a new method to the state bounding problem for a class of coupled differential-difference equations (CDDEs) with bounded disturbances and time-varying delays. Instead of using the state transformation to reformulate the considered problem into the one for non-perturbed CDDEs, our novel idea is to construct suitable comparison systems, from which the state vector can be estimated directly and the information on the initial value is exploited more effectively in order to derive a sharper state bound. For computing and minimising the state bound, a numerical linear programming-based algorithm is also presented. The effectiveness of the presented method is verified via two numerical examples.

Probing Photoionization Dynamics in Acetylene with Angle-Resolved Attosecond Interferometry.

Photoionization of acetylene by extreme ultraviolet light results in a stand-alone contribution from the outermost valence orbital, followed by well-separated photoelectron bands from deeper molecular orbitals. This makes acetylene an ideal candidate for probing the photoionization dynamics in polyatomic molecules free from the spectral congestion often arising after interaction with an attosecond pulse train. Here, using an angle-resolved attosecond interferometric technique, we extract the photoionization time delays for the outermost valence orbital in acetylene relative to an atomic target, namely argon. Compared to argon, the photoemission from the acetylene molecule is found to be advanced by almost 28 attoseconds. The strong variation of the relative photoionization time delays as a function of the photoemission angle was interpreted using an analytical model based on semiclassical approximations to be the interplay between different short-range potentials along and perpendicular to the molecular axis. Our results highlight the importance of using attosecond time-resolved measurements to probe the nonspherical nature of the molecular potential, even in the case of relatively small, linear systems.

VB-Based Gaussian Sum Cubature Kalman Filter for Adaptive Estimation of Unknown Delay and Loss Probability

The traditional Kalman filter assumes that all measurements can be obtained in real time, which is invalid in practical engineering. Therefore, a variational Bayesian- (VB-) based Gaussian sum cubature Kalman filter is proposed to solve the nonlinear tracking problem of multistep random measurement delay and loss (MRMDL) with unknown probability. First, the measurement model with MRMDL is modified by Bernoulli random variables. Then, the expression of the likelihood function is reformulated as a mixture of multiple Gaussian distributions, and the cubature rule is used to improve the estimation accuracy under the framework of Gaussian sum filter in the process of time update. Finally, by constructing a hierarchical Gaussian model, the unknown and time-varying measurement delay and loss probability are estimated in real time with the state jointly using the VB method in the measurement update stage. The algorithm does not need to calculate the equivalent noise covariance matrix so as to avoid the possible division by zero operation, which improves the stability of the algorithm. Simulation results for a target tracking problem show that the proposed algorithm has a better performance in the presence of MRMDL and can estimate the unknown measurement delay and loss probability accurately.

Retracted: Global Exponential Stability of Both Continuous-Time and Discrete-Time Switched Positive Time-Varying Delay Systems with Interval Uncertainties and All Unstable Subsystems

Retracted: Global Exponential Stability of Both Continuous-Time and Discrete-Time Switched Positive Time-Varying Delay Systems with Interval Uncertainties and All Unstable Subsystems

Transient responses of double core-holes generation in all-attosecond pump-probe spectroscopy

Double core-holes (DCHs) show remarkable and sensitive effects for understanding electron correlations and coherence. With advanced modulation of x-ray free-electron laser (XFEL) facility, we propose the forthcoming all-attosecond XFEL pump-probe spectroscopy can decipher the hidden photon-initiated dynamics of DCHs. The benchmark case of neon is investigated, and norm-nonconserving Monte-Carlo wavefunction method simulates non-Hermitian dynamics among vast states, which shows superiority in efficiency and reliability. In our scheme, population transfer to DCHs is sequentially irradiated by pump and probe laser. By varying time delay, Stark shifts and quantum path interference of resonant lines sensitively emerge at specific interval of two pulses. These ubiquitous multi-channel effects are also observed in phase-fluctuating pulses, derived from extra phases of impulsive Raman processes by pump laser. Non-perturbation absorption/emission verifies the uniquely interchangeable role of two pules in higher intensity. Our results reveal sensitive and robust responses on pulse parameters, which show potential capacity for XFEL attosecond pulse diagnosis and further attosecond-timescale chemical analysis.

Observer-based HOFA predictive cooperative control for networked multi-agent systems under time-variant communication constraints

This research focuses on a cooperative control problem for networked multi-agent systems (NMASs) under time-variant communication constraints (containing time-variant communication delays and time-variant data losses) in the forward and feedback channels. From the perspective of high-order fully actuated (HOFA) system theory, a HOFA system model is adopted to describe the NMAS, which is called the networked HOFA multi-agent system (NHOFAMAS). Because of complicated working scenarios over the network, the states of NMASs are immeasurable and the communication constraints are always present, such that an observer-based HOFA predictive control (OB-HOFAPC) method is designed to implement the cooperative control when existing the immeasurable states and time-variant communication constraints. In this method, a HOFA observer is established to estimate the immeasurable states for constructing a consensus control protocol. Then, an incremental prediction model (IPM) in a HOFA form is developed via a Diophantine equation to take the place of a reduced-order prediction model. Through this IPM, multi-step output ahead predictions are derived to optimize the cooperative control performance and compensate for time-variant communication constraints in real-time. The depth discussion gives a sufficient and necessary criterion to analyze the simultaneous consensus and stability for closed-loop NHOFAMASs. The capability and advantage of OB-HOFAPC method are illustrated via numerical simulation and experimental verification on a cooperative flying-around task of three air-bearing spacecraft simulators.

Existence and Stability Results of Nonlinear Random Impulsive Integro-Differential Evolution Equations with Time-Varying Delays

This study examines the existence, uniqueness, and stability of nonlinear random impulsive integrodifferential equations with time-varying delays under sufficient conditions. Our study is based on the Leray-Schauder alternative fixed point theorem, Pachpatte’s inequality, and the Banach contraction principle. Besides, we generalize, extend, and develop some results for Kasinathan et al.

Practical Approaches Towards Transparent and Stable Bilateral Teleoperation Under Time-Varying Network Delay

AbstractIn real-life teleoperation scenarios, the presence of time-varying network delays, particularly in wireless networks, poses significant challenges in maintaining stability in a bilateral teleoperation system. Various approaches have been proposed in the past to address stability concerns; however, these often come at the expense of system transparency. Nevertheless, increasing transparency is crucial in a teleoperation system to enable precise and safe operations, as well as to provide real-time decision-making capabilities for the operator. This paper presents our comprehensive approaches to maximize teleoperation transparency by minimizing system impedance, enhance the wave variable method to handle time-varying network delays, and alleviate non-smooth effects caused by network jitters in bilateral teleoperation. The proposed methodologies take into account the real-world challenges and considerations to ensure the practical applicability and effectiveness of the teleoperation system. Throughout these implementations, passivity analysis is employed to ensure system stability, guaranteeing a reliable and safe teleoperation experience. The proposed approaches were successfully validated in Team Northeastern’s Avatar telepresence system, which achieved the 3rd place in ANA Avatar XPRIZE challenge.

How aging shapes our sense of agency

The sense of agency refers to the feeling of controlling one’s actions and their effects on the external environment. Here, we tested how the physiological process of aging affects the agency experience by taking advantage of a validated ecological experimental paradigm and exploring the different dimensions of agency. We tested 60 young and older adults during active and passive movements, causing, after a variable time delay, an external sensorial event. We collected overt agency judgments (i.e., explicit agency dimension), and we measured the perceived compression of the time interval between the active/passive movements and outcomes (to quantify the intentional binding phenomenon, an implicit index of agency). Our results indicate that the sense of agency significantly changes across the adult life span, with older participants exhibiting a reduced sense of agency, both at the explicit and implicit level. Crucially, the temporal dimension of the action outcome did not affect their agency experience. We suggest that elderly adults are more reliant on internal predictions, making them less sensitive to cognitive biases and external manipulations. We discuss these results in the domain of neurocognitive models of motor control, with reference to how aging affects the weighting process of predictive and sensory signals for efficient sensorimotor integration.

Exponential synchronization of quaternion-valued memristor-based Cohen-Grossberg neural networks with time-varying delays: norm method.

In this paper, the exponential synchronization of quaternion-valued memristor-based Cohen-Grossberg neural networks with time-varying delays is discussed. By using the differential inclusion theory and the set-valued map theory, the discontinuous quaternion-valued memristor-based Cohen-Grossberg neural networks are transformed into an uncertain system with interval parameters. A novel controller is designed to achieve the control goal. With some inequality techniques, several criteria of exponential synchronization for quaternion-valued memristor-based Cohen-Grossberg neural networks are given. Different from the existing results using decomposition techniques, a direct analytical approach is used to study the synchronization problem by introducing an improved one-norm method. Moreover, the activation function is less restricted and the Lyapunov analysis process is simpler. Finally, a numerical simulation is given to prove the validity of the main results.

Aperiodically synchronization of multi-links delayed complex networks with semi-Markov jump and their numerical simulations to single-link robot arms

This paper investigates the pth moment exponential synchronization problem of multi-links stochastic delayed complex networks with semi-Markov jump via aperiodically intermittent control. Combining random disturbances, time-varying delay and semi-Markov jump with multi-links systems, our work is more relevant than previous work. Based on Lyapunov method and graph theory, a novel inequality for disposing of the problem of pth exponential synchronization is established under the aperiodically intermittent control and some sufficient criteria are derived. The theoretical results supply a new perspective showing the synchronization criterion and the topological structure of multi-links systems related closely. Furthermore, the value of our results is exhibited by applying them to the single-link robot arms in engineering. Eventually, a numerical simulation is provided to demonstrate the validity of our results.

Almost sure finite-time synchronization of Markov jump complex dynamical networks with asynchronous switching

The almost sure finite-time synchronization for Markovian jump complex dynamical networks (CDNs) with time-varying delay is studied. The designed controller is supposed to be asynchronous with the CDNs states. The existing almost sure synchronization result of networks is explored within a finite time interval. The sampled-data control approach is employed to improve the control precision. Some sufficient criteria are obtained under the definition of almost sure finite-time synchronization for the CDNs with Markovian switching topology. To determine the asynchronous controller gain, the linear matrix inequality-based conditions are proposed. Then, two examples are given to illustrate the effectiveness.

Delay-variation-dependent summation inequality and its application to stability analysis of discrete-time systems with time-varying delay

This work tends to research the stability of the discrete-time systems with a time-varying delay based on the Lyapunov-Krasovskii functional (LKF) method. In order to acquire a less conservative stability criterion, some techniques in this work are refined and taken into use. Firstly, to reduce the conservatism generated when estimating the forward difference of the LKF, a newly delay-variation-dependent summation inequality is constructed, which includes the existing free-matrix-based and Bessel function-based summation inequalities, using delay-variation-product relaxed matrices to provide more freedom for the estimation results. Secondly, to further show the influence of the introduced variation information in the time-varying delay, we give another selection of the allowable delay set for the delayed discrete-time systems. Thirdly, by taking advantages of the above method and by constructing a delay-product-type LKF, using extended free-weighting-matrices zero equations, and considering different allowable delay sets, two improved linear matrix inequality (LMI)-based delay-variation-dependent criteria for delayed discrete-time systems are formulated. Some classical numerical instances are presented to explain the effectiveness of these proposed stability criteria.

Robust passivity-based nonlinear controller design for bilateral teleoperation system under variable time delay and variable load disturbance

Abstract This research focuses on implementing a robust passivity-based nonlinear control method for bilateral/teleoperation systems. The key challenge is addressing communication pathways between the master and slave, control delays, and load disturbances, which can lead to instability and reduced transparency. To tackle these issues, the proposed controller incorporates a second-order super-twisting sliding-mode observer to counteract communication and control delays. A sliding mode assist disturbance observer compensates for load torque variations. The approach aims to ensure stability and transparency by handling time-varying delays. The system model comprises two interconnected direct-drive motors, simulating robotic configurations without a physical robot. The nonlinear controller framework simplifies the complex bilateral control problem, significantly improving stability and transparency performance. Computer simulations with step and sinusoidal inputs demonstrate the effectiveness of the approach, providing a satisfactory level of accuracy and transparency between estimated and actual slave positions, even with varying delays and load variations. The research contributes to control engineering by offering a robust method to enhance bilateral system performance, ensuring stable and transparent communication between the master and slave, particularly suitable for real-time internet-based bilateral control systems.

Design of nonsingular second-order terminal sliding mode controller for cyber-physical systems with time-delays and cyber-attack on actuators

This paper introduces an innovative adaptive nonsingular Second-Order Terminal Sliding Mode (SOTSM) control strategy specifically designed to stabilise disturbed nonlinear Cyber-Physical Systems (CPSs) within a finite timeframe. Unlike the conventional methods, our approach incorporates a novel nonlinear sliding surface that eliminates the need for a reaching step, significantly enhancing the system's robustness. Novel real-time adaptive control laws are developed to cope with external perturbations, time-varying delays, and cyber-attack on actuators without requiring the identification of their upper bounds. The proposed method ensures robust performance for time-varying delayed and disturbed nonlinear CPSs, even in the face of strong cyber-attacks targeting the actuators. Moreover, the proposed method has distinct advantages: it delivers rapid response times, enhanced flexibility, exceptional accuracy, smooth and robust control devoid of transient fluctuations or chattering, and ensures finite-time convergence. Simulation results comprehensively demonstrate the superior efficiency and success of our proposed technique compared to traditional methods such as integral Sliding Mode Control (SMC) and State-Feedback Control (SFC) schemes.

Robust cascade observer for a disturbance unmanned aerial vehicle carrying a load under multiple time-varying delays and uncertainties

In this article, a novel approach of a robust flight observer for a disturbance quadrotor transporting a payload in the presence of multiple time-varying delays is proposed. The developed algorithm is not only pertinent to a vehicle output signal with multiple small time-varying delays but also to long time-varying delays that are common for a quadrotor transporting a hanging load because a cascade structure is also employed to achieve outstanding performance, and the delay can be removed. The multiple time-varying delays and disturbances are compensated in the system with the proposed observer. The stability of the proposed methodology is proved using the Lyapunov–Krasovskii functional associated with an H ∞ criterion. Numerical simulations are shown to assess and validate the observer's performance and robustness under multiple time-varying delays and disturbances.

Event-triggered hybrid impulsive control for synchronization of fractional-order multilayer signed networks under cyber attacks

In this paper, we consider the exponential bipartite synchronization (EBS) problem of fractional-order multilayer signed networks with time-varying delays (FO-MSNT) under random cyber attacks. In contrast to the existing literature, the proposed hybrid event-triggered controller combines the advantages of feedback controller and impulsive controller, and the event-triggered condition is constructed by applying the network topology and the Lyapunov function of the subsystem, rather than the state function of the subsystem. Based on the Lyapunov–Razumikhin method and the graph theory, some sufficient conditions for achieving EBS of FO-MSNT under cyber attacks which are related to the topology of networks, the event-triggered parameters, the order of fractional derivative and the signal sent by the enemy are obtained. Furthermore, fractional-order coupled Chua’s circuits model and fractional-order power systems built on MSNT are established and the EBS issues under cyber attacks are analyzed. Numerical examples and simulations are provided to show the validity of our theories.

Observer-based aperiodically intermittent pinning synchronization of complex-valued dynamical networks with time-varying delay

This paper addresses the impact of time delay and unavailability of system states on synchronization in complex networks. Specifically, it focuses on observer-based synchronization of complex-valued dynamical networks (CDNs) with time-varying delays, encompassing both complex-valued node dynamics and outer coupling forms. Two aperiodically intermittent control schemes, with and without pins, are proposed to reduce control costs by minimizing control frequency and the number of controllers. The proposed schemes establish sufficient criteria for guaranteeing synchronization in CDNs with time-varying delays, utilizing a combination of Lyapunov function and inequality technology in the complex field. Numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

New results on stability analysis for a class of generalized delayed neural networks

This paper addresses the stability analysis of neural networks with a time-varying delay, where the delay is periodically varying bounded function with constrained derivatives. In order to obtain less conservative stability criteria, two novel Lyapunov-Krasovskii functionals (LKFs) with delay-derivative-variation-dependent matrices are constructed. In one LKF, two delay-product terms are double utilized and more free matrices are incorporated. Additionally, a new type of the LKF with delay-derivative-variation-dependent matrices, namely, the neuronal-activation-function-based looped functional, is developed by accounting for the periodic nature of the delay function and the coupling information of the system state and the neural activation function. Then, several stability conditions of delayed neural networks are developed by combining some integral inequalities. Finally, the superiority and validity of developed stability conditions are validated on two benchmark examples.

Robust $${H}_{\infty }$$ filtering and time-varying delay compensation for car suspension systems: a comprehensive approach to reduced disturbance and enhanced estimation

Robust $${H}_{\infty }$$ filtering and time-varying delay compensation for car suspension systems: a comprehensive approach to reduced disturbance and enhanced estimation