Delay Systems Research Articles

Tackling artefacts in the timing of relativistic pulsar binaries: Towards the SKA

Common signal-processing approximations produce artefacts when timing pulsars in relativistic binary systems, especially edge-on systems with tight orbits, such as the Double Pulsar. In this paper, we use extensive simulations to explore various patterns that arise from the inaccuracies of approximations made when correcting dispersion and Shapiro delay. In a relativistic binary, the velocity of the pulsar projected onto the line of sight varies significantly on short timescales, causing rapid changes in the apparent pulsar spin frequency, which is used to convert dispersive delays to pulsar rotational phase shifts. A well-known example of the consequences of this effect is the artificial variation of dispersion measure (DM) with binary phase, first observed in the Double Pulsar 20 years ago. We show that ignoring the Doppler shift of the spin frequency when computing the dispersive phase shift exactly reproduces the shape and magnitude of the reported DM variations. We also simulate and study two additional effects of much smaller magnitude, which are caused by the assumption that the spin frequency used to correct dispersion is constant over the duration of the sub-integration and over the observed bandwidth. We show that failure to account for these two effects leads to orbital phase-dependent dispersive smearing that leads to apparent orbital DM variations. The functional form of the variation depends on the orbital eccentricity. In addition, we find that a polynomial approximation of the timing model is unable to accurately describe the Shapiro delay of edge-on systems with orbits of less than four hours, which poses problems for the measurements of timing parameters, most notably the Shapiro delay. This will be a potential issue for sensitive facilities such as the Five-hundred-meter Aperture Spherical Telescope (FAST) and the forthcoming Square Kilometre Array (SKA); therefore, a more accurate phase predictor is indispensable.

The Interference of Identical Nominal Factors in the Positions of Stopping and Starting

this study explores the interference caused by identical nominal factors in the dynamic transitions between starting and stopping positions within systems or processes. Identical nominal factors, defined as elements with the same characteristics or nominal values, often lead to overlaps or ambiguities in system behaviors, causing inefficiencies, delays, or errors in operations. By analyzing case studies and theoretical models across various disciplines—such as manufacturing systems, transportation logistics, and automated control systems—this paper identifies key patterns of interference. The findings highlight the conditions under which such factors impede smooth transitions and propose strategies to mitigate their effects. This research aims to improve the reliability and performance of systems by refining design principles and operational protocols that account for these interferences.

Event-Triggered Sampling Problem for Exponential Stability of Stochastic Nonlinear Delay Systems Driven by Lévy Processes

Event-Triggered Sampling Problem for Exponential Stability of Stochastic Nonlinear Delay Systems Driven by Lévy Processes

Quasi-Sure Exponential Stability of Stochastic Differential Delay Systems Driven by G-Brownian Motion

Quasi-Sure Exponential Stability of Stochastic Differential Delay Systems Driven by G-Brownian Motion

Spectral submanifolds in time delay systems

Abstract The concept of spectral submanifolds, a powerful method of model order reduction of nonlinear systems, is extended to time delay systems that have infinite dimensional phase space representation. The proposed sun-star calculus based algorithm results in system reduction to manifolds which are constructed corresponding to either a real eigenvalue or to a pair of complex conjugate eigenvalues of the linearized system. Furthermore, it allows an improved approximation of self-excited oscillations exactly at the parameter point of interest, which could be further away from the corresponding Hopf bifurcation point. The paper includes case studies that demonstrate the capabilities of the algorithm.

Enhanced disturbance mitigation in nonlinear time delay systems with applications to double boost converters in microgrid environments

This study proposes an enhanced Smith Predictor (ESP) based Modified repetitive control (MRC) technique to develop a precise tracking performance of the input delayed double boost converter model, which is highly influenced by disturbances and saturation nonlinearity. A group of inequalities is derived on the basis of Lyapunov stability concept, which are in the form of linear-matrix-inequalities (LMIs) to guarantee the asymptotic stability and tracking performance of the considered delayed double boost converter. To be more specific, the proposed Lyapunov method not only provides the asymptotic stability of the system but also design the controller parameters when the feasibility of the derived LMIs are analyzed. The validation of the suggested ESP based MRC technique is confirmed through the simulation analysis and the corresponding outcomes from the considered double boost converter model. Moreover, the recommended control procedure yields better accuracy in tracking performance and disturbance elimination when comparing with the existing active disturbance methods such as improved equivalent-input-disturbance (IEID), parallel EID (PEID), higher-order EID (HEID) and EID based Smith predictor (SP) techniques.

Symptom appraisal and help-seeking before a cancer diagnosis during pregnancy: a qualitative study.

Background Estimated incidence of cancer diagnosis during or shortly after pregnancy is 1 in 1,000 women. Pregnancy can impact symptom appraisal and help-seeking for symptoms subsequently diagnosed as cancer. Little is known about the pathway to cancer diagnosis in pregnancy or delays that women can encounter. Aim To explore symptom appraisal, help-seeking decisions, and experience of receiving a cancer diagnosis during pregnancy. Design and setting Semi-structured interviews with women diagnosed with cancer during or shortly after pregnancy in the previous four years, recruited between January and May 2022 via the charity Mummy's Star. Method Reflexive Thematic Analysis of 20 interviews. Analysis was largely inductive, and the themes generated were mapped onto the intervals of the Model of Pathways to Treatment. Results Symptoms were often interpreted through the lens of pregnancy by both participants and most of the healthcare professionals from whom they sought help. Participants who found breast lumps were likely to suspect cancer and be referred promptly for tests in secondary care. While most participants sought timely help for their symptoms, some subsequently encountered health system delays, partly due to both the vague nature of their symptoms and the COVID-19 pandemic. Conclusion Health services need to better support women presenting with possible cancer symptoms during pregnancy to ensure timely diagnosis. Recommendations include prioritising symptoms over attributing them solely to pregnancy, ensuring timely referrals to rule out serious conditions, and emphasising clear communication alongside robust safety-netting practices. A full assessment is essential before dismissing symptoms as pregnancy related.

Design and performance evaluation of a novel fractional order filtered PI controller for fractional order time delay systems

This study introduces an innovative algorithm for designing a PI controller filtered with fractional-order derivatives or integrals. The algorithm is applied to two distinct models of fractional-order time delay systems. A new reference model is proposed, utilising a unity feedback structure and incorporating a fractional-order time-delayed Bode transfer function in the forward path. The parameters of this proposed reference model are determined based on the specified phase margin and gain margin requirements. Before solving the design problem, the stability analysis of the proposed reference model is analysed through a theorem. Next, the four nonlinear equations with four unknown parameters are formulated and a solution method is provided in this study. By employing the recently introduced reference model, a robust fractional-order controller is formulated. The effectiveness of this robust controller is validated through simulations that employ various phase and gain margin specifications and through the existing controllers in the literature.

Adaptive Fault‐Tolerant Control of High‐Order Nonlinear Delay Systems Under Unknown Dead‐Zone Fault and Unknown Control Coefficients and Its Application

Adaptive Fault‐Tolerant Control of High‐Order Nonlinear Delay Systems Under Unknown Dead‐Zone Fault and Unknown Control Coefficients and Its Application

A General Maximum Principle for Optimal Control of Stochastic Differential Delay Systems

A General Maximum Principle for Optimal Control of Stochastic Differential Delay Systems

Positive Periodic Solutions of Non-Autonomous Predator-Prey System with Stage-Structured Predator on Time Scales

In this note, we investigate the existence and asymptotic property of positive periodic solutions to non-autonomous predator-prey system with stage-structured predator on time scales. Via Schauder’s fixed theorem, easily verifiable sufficient existence conditions of positive periodic solutions for the considered system are obtained. We also study asymptotic property of positive periodic solutions on the basis of existence conditions. Due to the symmetry of periodic solutions, the results of this paper have a certain impact on the study of symmetry. It should be pointed out that the system we are studying is built on arbitrary time scale, so our results generalize the results of existing continuous or discrete systems. Furthermore, we develop Schauder’s fixed theorem for studying the delay system on time scales.

Lyapunov stability tests for integral delay systems

Lyapunov stability tests for integral delay systems

Tracking Control of Heterogeneous Multiagent Systems With Intrinsic Nonlinear Dynamics in Noisy and Time-Delayed Environments.

This article investigates the tracking control problem of heterogeneous multiagent systems (MASs) with intrinsic nonlinear dynamics in noisy and time-delayed environments. First, a stability criterion for nonlinear stochastic delay systems with multiplicative noise and time-varying delay is proposed by applying the appropriate Lyapunov-Krasovskii functional. Then, based on the proposed stability criterion, sufficient conditions are derived for mean square (m.s.) and almost sure (a.s.) tracking of heterogeneous MASs with intrinsic nonlinear dynamics. Afterward, the above sufficient conditions further degenerate to integrator heterogeneous MASs. In particular, when the time-delay vanishes, the explicit conditions are obtained for the integrator heterogeneous MASs in the form of scalar inequalities, which can intuitively reflect the relationship between noise intensity and control gains. Finally, simulation results validate the effectiveness of the proposed control protocol.

Application of Laplace Transform Method to Solve Neutral-Type Delay Differential Equation

This study investigates the use of the Laplace transform method to resolve a particular class of second-order linear initial-value neutral delay differential equations, which are prevalent in fields such as physics and engineering. By employing this analytical approach, we derive exact solutions that facilitate a deeper awareness of the dynamics of the system and its stability characteristics. A thorough illustrative example is provided to illustrate the Laplace transform method's efficacy, showcasing its practical utility in addressing real-world problems. This study not only highlights the advantages of the Laplace transform in providing clear insights into complex delay systems but also emphasizes its relevance in both theoretical and applied contexts.

Dynamic switching of transmission modes hydroacoustic communication MAC protocols

In recent years, the hydroacoustic communication MAC (Medium Access Control) protocol has attracted wide attention. Hydroacoustic communication networks suffer from issues such as long propagation delays and rapid dynamic changes in network load, which prevent the maximization of network performance through the use of a single transmission mode. In this paper, we propose a Dynamic Switching Transmission MAC protocol called the DSTM-MAC protocol. Firstly, the protocol realizes the design of dynamic switching transmission mode by adapting to changes in network load, introduces a more accurate model for total system delay, and computes parameters such as the switching threshold L and the optimal fixed contention window. Secondly, it carries out parameter design for different transmission modes and realizes dynamic concurrent transmission based on these modes, ultimately achieving the goal of maximizing network performance improvement. Finally, experiments demonstrate that the DSTM-MAC protocol surpasses the traditional DCF protocol in terms of end-to-end delay and system throughput.

Control Semiflows, Chain Controllability, and the Selgrade Decomposition for Linear Delay Systems

A continuous semiflow is introduced for linear control systems with delays in the states and controls and bounded control range. The state includes the control functions. It is proved that there exists a unique chain control set which corresponds to the chain recurrent set of the semiflow. The semiflow can be lifted to a linear semiflow on an infinite dimensional vector bundle with chain transitive base flow. A decomposition into exponentially separated subbundles is provided by a recent generalization of Selgrade’s theorem.

A new design of predictive plus PID control for second order plus time delay systems

AbstractThis paper proposes two novel predictive proportional‐integral‐derivative (PID) controllers for second‐order non‐self‐balance systems and self‐balance systems with time delays. For second‐order non‐self‐balance systems with time delays, traditional predictive PID controllers suffer from the drawback of failing to return to the setpoint after disturbances. Therefore, this paper introduces a novel double predictive PID controller, termed PPI‐PPD controller, which consists of an inner‐loop predictive PD controller and an outer‐loop predictive PI controller. In second‐order self‐balance systems encountered in practical chemical processes, time delays can lead to longer adjustment times, increased overshoot, and divergence issues. In order to solve these problems, an improved predictive PID (PPID) controller is proposed in this paper, which introduces a compensation link and an anti‐interference link in the traditional predictive PID controller. This enhancement improves the dynamic response and disturbance resistance of the control system. Simulation results demonstrate that both novel predictive PID controllers exhibit excellent control performance and robustness.

Finite‐Time Decentralized Adaptive Fuzzy Control for Non‐Triangular Form Large‐Scale Time‐Delay Systems With Full State Constraints

ABSTRACTThis paper is concerned with the problem of finite‐time decentralized adaptive fuzzy fault tolerant control for a class of non‐triangular form large‐scale time delay systems with full state constraints. By using the fuzzy logic systems and domination approach, the unknown nonlinear functions are approximated and the non‐triangular form structure is tackled, respectively. The time‐varying barrier Lyapunov function (TBLF) is used to ensure that the full state constraints are satisfied. Based on the proposed TBLF and backstepping technique, an adaptive fuzzy fault‐tolerant control protocol is presented. It can assure that the errors converge to a small neighborhood of the origin in a finite time, the signals of the whole closed‐loop systems are bounded and the full state constraints are satisfied. Simulation example is presented to further demonstrate the effectiveness of the proposed approach.

Synchronization of Time-Delay Coupled Neural Networks With Stabilizing Delayed Impulsive Control.

This brief studies the distributed synchronization of time-delay coupled neural networks (NNs) with impulsive pinning control involving stabilizing delays. A novel differential inequality is proposed, where the state's past information at impulsive time is effectively extracted and used to handle the synchronization of coupled NNs. Based on this inequality, the restriction that the size of impulsive delay is always limited by the system delay is removed, and the upper bound on the impulsive delay is relaxed, which is improved the existing related results. By using the methods of average impulsive interval (AII) and impulsive delay, some relaxed criteria for distributed synchronization of time-delay coupled NNs are obtained. The proposed synchronization conditions do not impose on the upper bound of two consecutive impulsive signals, and the lower bound is more flexible. Moreover, our results reveal that the impulsive delays may contribute to the synchronization of time-delay systems. Finally, typical networks are presented to illustrate the advantage of our delayed impulsive control method.

Synchronization of complex dynamical networks with saturated delayed impulsive control.

This paper considers the local exponential synchronization problem for a type of complex dynamical networks (CDNs) with both system delay and coupled delay using saturated delayed impulsive control. Based on the methods of average impulsive interval (AII), average impulsive delay (AID) and average impulsive estimation (AIE), a Razumikhin-type inequality with hybrid delayed impulses (which include delayed impulses and delay-free impulses) is derived. This inequality includes pure delayed impulsive inequalities. By utilizing the constructed inequality and the Lyapunov stability theory, the saturation nonlinearities are treated as the convex hulls, and sufficient synchronization criteria for local exponential synchronization of CDNs are presented in the framework of linear matrix inequalities (LMIs). Moreover, to enlarge the estimation of region of attraction (ROA) and the design of impulsive control gain, a convex optimization problem based on LMIs is formulated. Finally, a numerical example demonstrates the effectiveness of the obtained results.