Time-delay Case Research Articles

Impact of coronavirus pandemic on stock index: A polynomial regression with time delay

MotivationUnder contemporary market conditions in China, the stock index has been volatile and highly reflect trends in the coronavirus pandemic, but rare scientific research has been conducted to model the possible nonlinear relations between the two indicators. Added, on the advent that covid-related news in one time period impacts the stock market in another period, time delay can be an equally good predictor of the stock index but rarely investigated. ObjectivesTo contribute to filling the gaps identified in existing research, this study models relationship between the stock market index and coronavirus pandemic by leveraging volatility in the stock market and covid data through time delay and best degree in a polynomial environment. The resultant optimal time delay and best degree model is used to derive a high-accuracy prediction of stock market index. NoveltyIn line with the possible relations, the novelty of this study is that it proposes, validates and implements polynomial regression with time delay to model nonlinear relationship between the stock index and covid. MethodsThis study utilizes high-frequency data from January 2020 to the first week of July 2022 to model the nonlinear relationship between the stock index, new covid cases and time delay under polynomial regression environment. FindingsThe empirical results show that time delay and new covid cases, when modelled in a polynomial environment with optimal degree and delay, do present better representation of the nonlinear relationship such predictors have with stock index for China. Relative to results from the polynomial regression without delay, the empirical evidence from the model with delay show that an optimal time delay of 17 weeks makes it possible to predict the stock index at high accuracy and record improvements of 16-fold or higher. The representative delay model is used to project for up to 17 weeks for future trends in the stock index. ImplicationThe implication of the findings herein is that the prowess of the time delay polynomial regression is heavily dependent on instability in covid-related time trends and that researchers and decision-makers should consider modeling to cover for the unsteadiness in coronavirus cases to achieve better results.

Modeling of first order plus time delay system dynamics with adaptive IIR filters based on gradient descent methods and performance analyses for different time delay cases

Modeling of first order plus time delay system dynamics with adaptive IIR filters based on gradient descent methods and performance analyses for different time delay cases

Handling of time delays in system identification with regularized FIR models

Abstract System identification with finite impulse response (FIR) models has been recently revised by introducing specific forms of regularization in the estimation. By utilizing prior knowledge of the dynamic process under investigation different kernels for regularization can be derived. However, the dynamical processes considered are mainly restricted to time-delay free systems. Therefore, in this paper we propose two novel methods to handle the time-delay case. Both methods incorporate the time-delay estimation in the hyperparameter optimization of the regularized FIR models. The first method is built on a single kernel (SK) and the second utilizes a multiple kernel (MK) approach. Simulations on different dynamical systems show the superior behavior of both methods in comparison to standard regularization methods, whereupon the MK outperforms the SK approach.

A Particle Swarm Optimization tuned nonlinear PID controller with improved performance and robustness for First Order Plus Time Delay systems

The Proportional, Integral, and Derivative (PID) controller is a ubiquitous controller within industry. The conventional PID controller can struggle to provide a satisfactory response for the nonlinear systems faced by industry. In addition, conventional PID controllers have a trade-off between performance and robustness, where they cannot compensate for both without compromising stability or speed. In this paper, a novel Nonlinear gains Proportional, Integral, and Derivative (NLPID) control algorithm is proposed as a practical control strategy that shows improvements in the simultaneous set-point tracking and disturbance rejection, to control nonlinear systems. The paper shows the performance and robustness of the proposed controller for the case of a First Order Plus Time Delay (FOPTD) system, which heavily exists in industry. The Particle Swarm Optimization (PSO) algorithm is used to tune the proposed NLPID controller. The performance of the proposed NLPID controller is simulated and compared against established controllers in literature such as conventional PID, two degree of freedom PID, and Smith Predictor PID controllers in MATLAB/Simulink for an FOPTD system, with various uncertainties and disturbances. This study shows that the proposed NLPID controller maintains faster settling and rise time, with no overshoot and excellent disturbance rejection, without compromising stability or speed, and is robust against parametric, additive, and multiplicative uncertainties.

Design of developed distributed observers for nonlinear time-delay systems

This paper considers a distributed observer design for a class of nonlinear systems with time delays in a network. Specifically, each distributed observer has access to partial output as it communicates with its neighboring observers through consensus protocols defined on the network. The network includes N local observers where adjacent observers transmit and receive information through a delayed telecommunication graph network. The design method is based on Lipschitz condition of nonlinear terms while having time-delay cases in view. Appropriate selection of Lyapunov functions is made and the Jensen inequality applied in delayed nonlinear systems in undirected, strongly connected, and directed networks containing spanning trees. Also, via the design algorithm, the necessary and sufficient conditions for the design of parameters are defined so as to stabilize the error dynamics. Finally, numerical simulations are provided to verify the effectiveness of the proposed method.

Stability and persistence analysis of a microorganism flocculation model with infinite delay.

In this paper, we study the global stability and persistence of a microorganism flocculation model with infinite delay. First, we make a complete theoretical analysis on the local stability of the boundary equilibrium (microorganism-free equilibrium) and the positive equilibrium (microorganism co-existent equilibrium), and give a sufficient condition for the global stability of the boundary equilibrium (applicable to the forward bifurcation and the backward bifurcation). Then, for the persistence of the model, we present an explicit estimate of the eventual lower bound of any positive solution for which only the parameter threshold $ R_0 > 1 $ is required. The obtained results extend some of the conclusions of the existing literatures on the case of discrete time delay.

OBSERVER-BASED SYNCHRONIZATION OF TIME-DELAY COMPLEX-VARIABLE CHAOTIC SYSTEMS WITH COMPLEX PARAMETERS

Time-delay and unavailability of system states bring extra difficulties to synchronization of chaotic systems. This paper investigates observer-based synchronization of time-delay complex-variable chaotic systems (CVCSs) with complex parameters. Differing from the existing works that considered time delay only in the linear term of some special CVCSs, the two cases of time delay in and out of nonlinear terms in general CVCSs are considered here, respectively. In addition, for the case that system states are not available for control, an observer-based output feedback control approach is developed to estimate the system states and guarantee the time-delay CVCSs to achieve synchronization. Moreover, by combining Lyapunov–Krasovskii function with linear matrix inequality in the complex field, two sufficient criteria are derived to ensure complete synchronization of time-delay CVCSs. Finally, a numerical example is presented to illustrate the theoretical results.

AOA based optimal control of combined AVR-LFC model in wind integrated power system

This manuscript analyses a case study of a wind-integrated power plant where an Arithmetic Optimization Algorithm-based Model Predictive Controller (AOA-MPC) has been employed for the combined control of voltage and frequency. The work in this manuscript considers stochastic variations in wind output caused by the small stochastic drifts and sudden deterministic shifts in the wind turbine output. The proposed controller’s performance has been judged after assessing the time response performance specifications/indices and comparing it with the existing recent methodologies available in the literature. Further improvement in frequency oscillations reduction has been obtained while considering the Redox Flow Battery (RFB) loop as an auxiliary Load Frequency Control loop. Moreover, the computational potential of the presented algorithm has been tested under different nonlinearities and time delay cases in the Area Control Error (ACE) of the load frequency control (LFC) loop.

Razumikhin and Krasovskii approaches for safe stabilization

This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel control barrier functions/functionals for the safety problem. The proposed control Lyapunov and barrier functions/functionals extend the existing ones from the delay-free case to the time-delay case, and allow for designing the stabilizing and safety controllers in closed-form. Since analytical solutions to time-delay optimal control problems are hard to be achieved, a sliding mode control based approach is developed to merge the proposed control Lyapunov and barrier functions/functionals. Based on the sliding surface functional, a feedback control law is established to investigate the stabilization and safety objectives simultaneously. In particular, the properties of the sliding surface functional are analyzed, and further how to construct the sliding surface functional is discussed. Finally, the proposed approaches are illustrated via two numerical examples from the connected cruise control problem of automotive systems and the synchronization problem of multi-agent systems.

Stability analysis of impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise

This note investigates the stabilities for impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise (ISDCGNNs-LN), including the input-to-state stability (ISS), integral input-to-state stability (iISS) and ϕθ(t)-weight input-to-state stability (ϕθ(t)-weight ISS, θ>0). Utilizing the multiple Lyapunov-Krasovskii (L-K) functions, principle of comparison, constant variation method and average impulsive interval (AII) method, adequate ISS-type stability conditions of the ISDCGNNs-LN under stable impulse and unstable impulse are obtained. This shows that the stochastic systems are ISS in regard to a lower bound of the AII, provided that the continuous stochastic systems is ISS but has destabilizing impulse. Furthermore, the impulse can effectively stabilize the stochastic systems for a upper bound of the AII, provided that the continuous stochastic systems is not ISS. In addition, our results can also deal with the case of variable time delay. In the end, two examples are presented to reflect the rationality and correctness for the theoretical conclusions.

Performance, robustness and noise amplification trade-offs in Disturbance Observer Control design

In this work, we propose a Disturbance Observer (DOB) with a low pass filter with a single tuning parameter. The DOB can be added to a standard PI controller that is assumed to be controlling the system. Our DOB design can be applied to delayed and non-minimum phase systems and is decoupled from the PI control design. We analyse the impact of the DOB filter time constant in disturbance rejection performance, closed loop robustness and measurement noise amplification. The case of First Order plus Time Delay has been studied leading to a set of figures that highlight the trade-offs between those factors and can guide the designer. For arbitrary systems we propose simple rules and instructions for tuning the single parameter of the DOB, taking into account the trade-off between performance, robustness and noise amplification. Finally, we test our proposal experimentally in a real two-tank system setup.

A new digital resonant current controller for AC power converters based on the advanced Z-transform

In this paper, we present a new digital resonant current controller that can be applied in single-phase and three-phase alternating current (AC) power converters, based on voltage source inverters (VSI) with pulse width modulation (PWM). Since power converters based on PWM introduce fractional time delays regarding the sampling period (Ts), because of the current sampling and PWM command updating techniques that are employed, there is a need to develop analytical tools for precise modelling of these types of delays. To achieve this, the advanced Z-transform is applied in order to model the AC controllers in VSIs with PWM for the general case of a fractional time delay, including power converters with current sampling within a PWM period at any chosen time instance. This new approach to power converter modelling and current sampling allowed us to develop a modified resonant AC current controller for a VSI with RL load, based on the pole-placement parameter tuning method. It includes fractional time delays, which are conventionally employed in the power converter design, in the controller parameter derivations, and introduces the minimal order resonant controller that enables strict placement of all closed-loop control system poles. Simulations and experimental tests are carried out to show the improvements introduced by novel solution in this paper compared with conventional resonant current controllers. In the analysis of dynamic performance and robustness, in this paper conventional indices are applied to compare the proposed controller with a conventional design.

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.

Leader-following consensus of delayed multi-agent systems with aperiodically intermittent communications

In this paper, the leader-following consensus of nonlinear multi-agent systems with time delay and aperiodically intermittent communications is investigated. Compared with the intermittent communications for multi-agent systems in previous literature, we relax the periodicity or quasi-periodicity of the intermittent communications and render the intermittent communications to be completely aperiodic. The concepts of average communication ratio and average communication period are adapted to characterize the distributions of communication time and non-communication time. Then the consensus problem for the studied systems with large time delay and small time delay is studied, respectively. Especially, for the case of small time delay, the upper bound of time delay is assumed to be less than the average communication length (average communication ratio × average communication period), but can be larger than some communication lengths, which is less conservative. Finally, numerical examples are provided to show the effectiveness of the main results.

The Temporal Dynamics of Functional Networks are Modulated by Acupuncture: an EEG Microstates Study

Information transition delay is an inherent factor in neuronal systems and has great influences on their dynamical behaviors. For theoretical studies about time delay in neuronal systems, researchers usually set all connections between neurons to be delayed. However, in real neural systems, communication between some connected neurons maybe instantaneous which make the connection be delay-free. Thus, we will discuss effects of partial time delay on detecting subthreshold signal of neuronal systems in this paper from the viewpoint of stochastic resonance. Partial time delay is introduced by assuming that time delay between two connected neurons to be τ (which is not zero) with a probability pdelay. With the obtained numerical results, we show that the ability of detecting subthreshold signal could be reduced or enhanced strongly depending on the values of pdelay and τ. Especially, the detecting ability could be enhanced by a wide range of time delay τ when pdelay is small. It means that partial time delay could have quite different influences on the ability of detecting subthreshold signal as comparing with the full time delay case (all connections are delayed). Meanwhile, we also exhibit that network topology, noise intensity and coupling strength could have great influences on the effects of partial time delay on detecting subthreshold signal of the neuronal systems.

Aperiodically intermittent stabilization for complex-valued hybrid stochastic delayed systems: An average technique

This paper focuses on the stabilization problem of complex-valued hybrid stochastic delayed systems via aperiodically intermittent control (AIC). As for AIC in existing literature, strict conditions on the lower bound of control intervals and upper bound of control periods or the maximum proportion of rest intervals are required. In this paper, we relax these constraints by proposing average control ratio and average control period to describe the distribution of control and rest intervals of AIC, i.e., the lower bound of certain control widths can be arbitrarily small, upper bound of certain control periods can be very large and the proportion of rest widths can be any value in (0,1). Thus, the conservativeness is reduced compared with the existing related results. Then based on the complex generalized Itô’s formula, several novel stabilization criteria are obtained for small time delays and large time delays, respectively, which avoid splitting the real and imaginary parts. Especially, for the case of small time delays, the upper bound of time delays can be larger than the lower bound of all control widths, which has wider applications than previous results. Finally, two examples along with their numerical simulations are given to show the effectiveness and less conservativeness of our results.

Eigenvalue optimisation-based centralised and decentralised stabilisation of time-delay systems

Both centralised and decentralised stabilisation of multi-input multi-output linear time-invariant (LTI) systems with discrete time-delays are considered. No restriction has been made on the number and type of the time-delays. The main objective is to design LTI finite-dimensional static/dynamic stabilising centralised/decentralised output feedback controllers. For this, the decentralised pole assignment algorithm developed for decentralised stabilisation of finite-dimensional systems is extended to the time-delay case. In this approach, decentralised controllers are designed sequentially, where a centralised design approach is used in each step. As the centralised design approach, the eigenvalue optimisation-based stabilisation method is utilised. Regarding the nonconvexity of the optimisation problem, an initialisation procedure, which determines the minimum possible dimension of the stabilising controller and the initial controller parameters, is developed. As a particular case of dynamic output feedback, the decentralised proportional-integral control is also considered. The proposed controller design methods are verified through numerical and practical examples.

Modulated Time Delays, Synchronized Josephson Junctions in High-Temperature Superconductors and Chaotic Terahertz Waves

We make the first report on chaos synchronization between Josephson junctions governed by a central junction, when the coupling time between the driving junction and driven junctions is modulated. The results are compared with the case of constant coupling time delays between the junctions. We establish that synchronization is quite robust to the modulation of the coupling time delays, including chaotically modulated delay times. Synchronized Josephson junctions can serve as a terahertz wave generators with enough power for practical applications in diverse scientific fields.

Group Leader-Following Consensus Control for Heterogeneous Multi-Agent Systems With Time Delays

In this paper, the problem of group leader-following consensus is discussed for high-order heterogeneous multi-agent systems(HMASs) with multiple leaders and time delays. The four situations are considered: autonomous leaders, active leaders with controllers, and accepting their own information with/without time delays. Different protocols are designed for different situations. Under the corresponding protocols, HMASs can achieve group leader-following consensus without the limitation of in-degree balance. And the networked predictive scheme(NPS) actively compensating for time delays is used to predict current information of agents. Besides, the results are extended to multiple groups case. Finally, the simulation results show that, based on the NPS, the state trajectory of each agent in the time-delay case is very close to that in no time-delay case.

Accessibility and System Reduction of Nonlinear Time-Delay Control Systems

This article addresses the problem of checking the accessibility property for nonlinear single-input-single-output retarded time-delay systems with constant commensurable delays, described by higher order input-output functional differential equations. Necessary and sufficient conditions are found to check the accessibility property, and sufficient conditions are found to decompose the system equations into accessible and non-accessible subsystems. The conditions are presented in terms of autonomous elements, i.e., functions that cannot be influenced by system input. The results are generalizations from the delay-free case. However, the proofs do not transfer to the time-delay case easily, since algebraic structures with different properties are used here.