Time-varying Time Delays Research Articles

Projective synchronisation of bipartite networks with nonlinear couplings via quantised event-triggered control

In this paper, the issue of projective synchronisation of bipartite networks (BNs) with multiple time-varying delays and nonlinear couplings has been studied. To reduce wasted communication resources, the novel quantised event-triggered controllers and the measurement error functions are introduced. In particular, the event-triggered schemes without Zeno behaviour are designed, which can determine whether controllers need to be updated or not. For the purpose of investigating the synchronisation with isolated nodes, comparing to the usual 1-norm and 2-norm, generalised { ξ , 1 } -norm has been utilised to derive sufficient conditions. Furthermore, in the proof of the theorem, constant time-delays and time-varying time delays are dealt with by utilising novel Lyapunov functions, and then some valid criteria are established to achieve different types of projective synchronisation. Lastly, numerical simulations are well provided to confirm the given theoretical results.

Tuning of fuzzy controller with arbitrary triangular input fuzzy sets based on proximal policy optimization for time-delays system

The analytical structure of fuzzy controller is important for better understanding and effective design of the fuzzy control system, especially for explaining why fuzzy control system work well. In this paper, we develop a three-dimensional fuzzy controller with arbitrary triangular input fuzzy sets. Then, the analytical structure of this fuzzy controller is derived rigorously, and some properties of this controller are given. To determine the parameters of the fuzzy controller, a novel proximal policy optimization algorithm with recall pool (RP-PPO) is proposed. A recall pool is designed in proximal policy optimization algorithm to store the best ten sets of parameters to enhance the optimization results. Finally, simulation studies are carried out on two time-delay systems and a nonlinear chemical process with time-varying time delay to validate the applicability and effectiveness of the proposed fuzzy controller.

Variational Bayesian Inference for Robust Identification of PWARX Systems With Time-Varying Time-Delays.

This article presents a robust variational Bayesian (VB) algorithm for identifying piecewise autoregressive exogenous (PWARX) systems with time-varying time-delays. To alleviate the adverse effects caused by outliers, the probability distribution of noise is taken to follow a t -distribution. Meanwhile, a solution strategy for more accurately classifying undecidable data points is proposed, and the hyperplanes used to split data are determined by a support vector machine (SVM). In addition, maximum-likelihood estimation (MLE) is adopted to re-estimate the unknown parameters through the classification results. The time-delay is regarded as a hidden variable and identified through the VB algorithm. The effectiveness of the proposed algorithm is illustrated by two simulation examples.

CZT Algorithm for the Doppler Scale Signal Model of Multireceiver SAS Based on Shear Theorem

In multireceiver synthetic aperture sonars (SASs), the traditional non-stop-hop-stop model normally ignores the intrapulse motion of sonar platform. However, such intrapulse motion brings the Doppler scale effect (DSE) to the echo signal, which will lead to the change in carrier frequency (CF) and frequency modulation (FM) rate of echo signal and may eventually result in image defocus. In this article, considering the intrapulse motion, the time-varying time delay and range history of multireceiver SAS were derived by introducing the range time into the range history, and then the Doppler scale signal model was established. After approximating the derived time-varying range history, the 2-D spectrum was derived by using the shear theorem. When compared with the traditional 2-D spectrum, an interesting phenomenon was found that the change in FM rate has no effect on the 2-D spectrum. Actually, only two additional terms, i.e., range cell migration (ARCM) and azimuth modulation (AAM), were introduced into the new 2-D spectrum due to the change in CF. Besides, the condition of neglecting the ARCM was given by further analyzing the 2-D spectrum, while the AAM is usually small and can be easily compensated together with the ARCM correction. Finally, a chirp-z transform (CZT) algorithm for the Doppler scale signal model was proposed to correct the ARCM, which can simultaneously correct the ARCM and compensate the AAM (although not required) in the 2-D frequency domain by phase multiplication. The effectiveness of the signal model and the proposed algorithm is verified by simulations and field data.

A Soft Sensor Model for Cement Specific Surface Area Based on TCN-ASRU Neural Network

One of the key indicators for evaluating finished cement products is the cement specific surface area. The soft sensor model for cement specific surface area serves as the foundation for scheduling cement production and is critical for increasing cement quality. To solve the issue of soft sensor models of cement specific surface area caused by the non-linearity, time lag and strong coupling of the cement industry’s big data, the soft sensor model of Time Convolution Network (TCN) and Attention Simple Recurrent Unit (ASRU) Network is proposed.TCN suppresses the issue of feature redundancy due to data coupling. Meanwhile, an improved network structure ASRU is established considering the long time series of process industrial data. ASRU can quickly screen out the higher value information from a vast amount of information to enhance the sensitivity to information. TCN-ASRU can capture the spatiotemporal features in the input data and the dynamic response relationship on the time sequence to solve the problems including time-varying time delay. The model was trained and validated on a cement specific surface area data-set collected. The results demonstrated that the model has the higher prediction accuracy and good generalization ability.

Effect of state-dependent time delay on dynamics of trimming of thin-walled structures

Trimming of cantilever thin-walled structures is commonly seen in aerospace industry, including trimming of blades. Trimming with helix angle tools can cause the vibration of the thin-walled workpiece along the tool-axis, which may disturb the time delay between cutting by the current and previous teeth. The time delay dependent on the vibration state makes the stability analysis of trimming process challenging. This paper is the first attempt to uncover the effect of state-dependent time delay of the trimming process caused by workpiece vibration on chatter stability. Modeling of the cutter-workpiece interactions, state-dependent time delay and the dynamic chip generation mechanism are presented. A time-domain numerical algorithm with an improved stability metrics is constructed to analyze the trimming stability behaviors. We found that the two dominant states can occur, namely, period-n instabilities with time-varying time delay and stability with constant time delay. A focused experimental study was carried out to calibrate this new finding. This study reveals the way the workpiece vibration affects the time delay and stability in the trimming process.

Multirate Sensor Fusion in the Presence of Irregular Measurements and Time-Varying Time Delays Using Synchronized, Neural, Extended Kalman Filters

Sensor fusion plays a critical role in improving estimation accuracy of process quality variables. In this article, the dual, neural, extended Kalman filter (DNEKF) and the state model compensation neural, extended Kalman filter (SNEKF) are synthesized to compensate for modeling errors in the extended Kalman filter (EKF)-based multirate sensor fusion. Specifically, fusion is performed in the presence of irregularly sampled, slow-rate measurements with time-varying time delays. The proposed algorithm estimates the state and neural network parameters simultaneously through state vector augmentation. The estimated parameters of the state model compensation neural network (SNN) are shared between the DNEKF and SNEKF. It is demonstrated through two numerical examples that the proposed algorithm effectively reduces the estimation error under different conditions. In addition, it successfully improves the critical industrial quality variable estimation accuracy from the fast-rate soft sensor for over 20%, in terms of the mean squared error, demonstrating its advantages.

Consensus Conditions for a Class of Fractional-Order Nonlinear Multiagent Systems with Constant and Time-Varying Time Delays

The consensus problem for a class of fractional-order nonlinear multiagent systems with a distributed protocol containing input time delay is investigated in this paper. Consider both cases of constant time delay and time-varying delay, the delay-independent consensus conditions are obtained to achieve the consensus of the systems, respectively, by adopting the linear matrix inequality (LMI) methods and stability theory of fractional-order systems. As illustrated by the numerical examples, the proposed theoretical results work well and accurately.

Asynchronous Impulsive Protocols With Asymmetric Feedback Saturation on Leader-Based Formation Control of Multiagent Systems.

Saturation phenomena often exist due to limited system resources, and impulsive protocols can lead to a reduction in communication cost. From these issues, this article investigates a leader-based formation control problem of multiagent systems via asynchronous impulsive protocols with saturated feedback. General linear system models with and without finite time-varying time delays under asymmetric saturated feedback control are concurrently considered. The asynchronous impulsive protocols only permit communication at impulsive instants and each agent has its own communication instants independently. Moreover, to improve system performance, an offset only containing desired formation information is introduced. Finally, because the feedbacks are saturated, admissible regions are proved to exist, which are also estimated by a mean of optimization. Numerical simulations are presented to demonstrate the validity of the proposed schemes.

Oscillating synchronization in delayed oscillators with time-varying time delay coupling: Experimental observation.

The time-varying time-delayed (TVTD) systems attract the attention of research communities due to their rich complex dynamics and wide application potentiality. Particularly, coupled TVTD systems show several intriguing behaviors that cannot be observed in systems with a constant delay or no delay. In this context, a new synchronization scenario, namely, oscillating synchronization, was reported by Senthilkumar and Lakshmanan [Chaos 17, 013112 (2007)], which is exclusive to the time-varying time delay systems only. However, like most of the dynamical behavior of TVTD systems, its existence has not been established in an experiment. In this paper, we report the first experimental observation of oscillating synchronization in coupled nonlinear time-delayed oscillators induced by a time-varying time delay in the coupling path. We implement a simple yet effective electronic circuit to realize the time-varying time delay in an experiment. We show that depending upon the instantaneous variation of the time delay, the system shows a synchronization scenario oscillating among lag, complete, and anticipatory synchronization. This study may open up the feasibility of applying oscillating synchronization in engineering systems.

Intrinsic stability: stability of dynamical networks and switched systems with any type of time-delays

In real-world networks, interactions between network elements are inherently time-delayed. These time-delays can both slow and destabilize the network, leading to poor performance. However, not all networks can be destabilized by time-delays. Previously, it has been shown that if a network is intrinsically stable, it maintains stability when constant time-delays are introduced. Here we show that intrinsically stable networks and a broad class of switched systems remain stable in the presence of any type of time-varying time-delays whether these delays are periodic, stochastic, or otherwise. We apply these results to a number of well-studied systems to demonstrate that intrinsic stability is both computationally inexpensive and improves on previous stability methods. Furthermore, we prove that the asymptotic state of an intrinsically stable switched system is independent of both the system’s initial conditions and the presence of time-varying time-delays. Thus, we justify ignoring the occurance of any type of time-delays when modeling intrinsically stable real-world systems for asymptotic analysis, and provide an efficient means of engineering delay-robust systems.

Fuzzy Sliding Mode Predictive Control of Air Flow Rate for a High-Speed High-Temperature Heat-Airflow Test System

To solve the problem of accurate control of air flow rate of a high-speed high-temperature heat-airflow test system, this paper introduces the working principle, establishes the mathematical model and analyzes the characteristics of the air supply subsystem. According to the characteristics of the air supply subsystem, such as time-varying parameters, time delay and disturbance, which are difficult to control accurately, a new fuzzy sliding mode predictive control algorithm is proposed based on fuzzy sliding mode control and Smith predictor. On this basis, the proposed control algorithm is simulated and studied. The results show that the proposed fuzzy sliding mode predictive control algorithm has good control performance. It can not only achieve high-performance tracking of step, slope, square wave and sinusoidal signals, but also can overcome the influence on the system caused by pure time delay, time-varying parameter and external disturbance.

Composite control for switched impulsive time-delay systems subject to actuator saturation and multiple disturbances

This paper focuses on the composite control problem for a class of uncertain switched impulsive systems with time-varying time delay, actuator saturation and multiple disturbances which are matched and mismatched with continuous control inputs. The system under consideration involves parameter uncertainties and nonlinear uncertainties, and the actuators of both continuous control inputs and impulsive control inputs are considered to be limited by saturation. Actuator saturation brings great difficulties and challenges to implement composite control based on disturbance compensation, especially when the system is with matched disturbances. A novel switching composite controller and a switching state feedback controller are constructed respectively such that the performance requirement of anti-disturbance control for the system is achieved, the former of which can realize rejection of the matched disturbances simultaneously. Based on the treatment of the saturation as polytopic differential inclusion, the design conditions of the controllers are developed to guarantee the locally robustly asymptotic stability and robust H∞ disturbance attenuation of the closed-loop system with an estimation of the domain of attraction. Finally, a simulation example is performed to validate the feasibility of our results.

Discrete-Time Systems With Constrained Time Delays and Delay-Dependent Lyapunov Functions

It is proved in this paper that the existence of a delay-dependent suitable Lyapunov function is a necessary and sufficient condition for a discrete-time fully nonlinear time-delay system, with given delays digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the delays digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions. The case of arbitrary time-varying time delays, with no constraints as long as bounded, is covered as a special case.

A Novel Stability Criteria of a Class Nonlinear Fractional-order HIV-1 System with Multiple Delay

This paper mainly deduces a new stability criteria of the fractional-order HIV-1 system with delay on the basis of Wirtinger inequality, fractional-order Lyapunov method and integral mean value theorem. The Wirtinger inequality is rarely applied to stability analysis of fractional-order system. Nevertheless, this paper extends the general form of the Lyapunov-krasovskii function to a novel fractional expression form by applying definition of Caputo fractional derivative. Via the the integral mean value theorem, fractional-order Lyapunov method and Wirtinger inequality, the novel stability criteria is deduced. It is the integral mean value theorem that reduces the conservatism of the stability criteria. The simulation results show that the proposed criteria can satisfy different fractional-order operators.In addition, it can not only solve the stability problem of fractional-order HIV-1 system with the constant time delay, but also of the fractional-order HIV-1 system with time-varying time delay. Thus, the new stability criteria has generality and universality. So as to verify our theoretical results, many numerical simulations are provided.

A robust controller design for networked hydraulic pressure control system based on CPR

The hydraulic CPR (Common Pressure Rail) system has some advantages (i.e. modularization and energy saving), which can be integrated with the characteristics of networked control system (NCS) to enhance the control performance. However, the strong nonlinearity and parameter uncertainty issues of the CPR system based on HT (hydraulic transformer) must be addressed. Moreover, the time-varying time delay and packet loss induced by NCS should be solved at the same time. In the paper, an adaptive fuzzy sliding mode controller based on Pi-sigma fuzzy neural network combining with Pade approximation is proposed to solve these problems. By constructing an appropriate Lyapunov function, the stability of the controller is proved. Finally, the simulation is proceeded to show the proposed controller can guarantee the robustness and compensate the input delay and packet loss in presence of external disturbance and parameter uncertainty.

Stability and Stabilization for Polytopic LPV Systems with Parameter-Varying Time Delays

In this paper, we deal with the problem of stability and stabilization for linear parameter-varying (LPV) systems with time-varying time delays. The uncertain parameters are assumed to reside in a polytope with bounded variation rates. Being main difference from the existing achievements, the representation of the time derivative of the time-varying parameter is under a polytopic structure. Based on the new representation, delay-dependent sufficient conditions of stability and stabilization are, respectively, formulated in terms of linear matrix inequalities (LMI). Simulation examples are then provided to confirm the effectiveness of the given approach.

Moving horizon estimation for multirate systems with time-varying time-delays

This paper presents a moving horizon estimation approach for the multirate sampled-data system with unknown time-delay sequence. To estimate the unknown variables of interest, two main challenging issues need to be addressed: (a) synthesizing the multirate input and output data for state estimation, (b) simultaneously estimating the continuous state and discrete time-delay sequence. In this work a moving horizon estimation based approach is developed to tackle these issues. The proposed approach can simultaneously estimate both the continuous states and discrete time-delay sequence for dynamic systems. The effects of different noise level on the estimation of continuous states and discrete time-delay sequence are analyzed. The effectiveness of this method is illustrated through a simulation study.

A novel optimized SVM algorithm based on PSO with saturation and mixed time-delays for classification of oil pipeline leak detection

ABSTRACTIn this paper, a novel particle swarm optimization (PSO) algorithm is proposed in order to improve the accuracy of the traditional support vector machine (SVM) approaches with applications in analyzing data of oil pipeline leak detection. In the proposed saturated and mix-delayed particle swarm optimization (SMDPSO) algorithm, the evolutionary state is determined by evaluating the evolutionary factor in each iteration, based on which the velocity updating model switches from one to another. With the purpose of reducing the possibility of getting trapped in the local optima and also expanding the search space, time-varying time-delays and distributed time-delays are introduced in the velocity updating model to respectively reflect the history of previous personal and global optimum particles. The introduction of saturation constraint ensures that the particles will convergence in case that the velocity of the particles is too large. Eight well-known benchmark functions are employed to evaluate the proposed SMDPSO algorithm which is shown via extensive comparisons to outperform some currently popular PSO algorithms. To further illustrate the application potential, the developed framework SMDPSO-based SVM algorithm is exploited in the problem of oil pipeline leak detection. Experiment results demonstrate that the SMDPSO-based SVM method is superior over other well-known classification algorithms.

P th moment consensus of multi‐agent systems with relative state‐dependent measurement noises and time delays

This study investigates the distributed consensus control problem of multi-agent systems impacted by the combined uncertainty of measurement noises and communication delays under directed fixed topology. Each agent can only obtain the state information of its own and neighbours, which is delayed and interfered by measurement noises. The intensity of the noise is considered as a function related to the relative state of the agent. Under general networks with directed fixed topology, a distributed consensus protocol is proposed to obtain the pth moment linear χ -consensus of the multi-agent system. The sufficient condition for the consensus of the multi-agent system is derived under the arbitrary upper bound of the time-delay, in which both relative state-dependent measurement noises and time-varying time delays are taken into account. The effectiveness of the proposed consensus protocol is shown by some simulations.