Constant Delay Research Articles

Robust (Q, S, R)‐γ‐dissipative control of Takagi–Sugeno fuzzy systems with interval time‐varying delay and sampling

AbstractThe robust (Q, S, R)‐γ‐dissipative control of Takagi–Sugeno fuzzy time‐delay model is considered by the developed robust control with sampling in this article. The proposed Lyapunov–Krasovskii functional and inequality are investigated to improve the main results in this article. Full matrix formulation approach is present to show our proposed results by some linear matrix inequalities. Interval delay and sampling period are contemplated instead of constant delay and fixed sampling in some circulated literatures. The less conservatism of our proposed results is demonstrated by our proposed numerical examples. Finally, we illustrate a mass‐spring‐damper nonlinear system to show our developed results.

A Partial Inverse Problem for the Sturm–Liouville Operator with Constant Delays on a Star Graph

A Partial Inverse Problem for the Sturm–Liouville Operator with Constant Delays on a Star Graph

A kernel-based method for Volterra delay integro-differential equations

Volterra integro-differential equations with constant delay $\tau>0$ are presented in this paper. We used a numerical method based on reproducing kernels to investigate well-known equations. The convergence analysis of the utilized approach is taken into account, which also provides the theoretical structure of the method. In addition, we derive some effective error estimates for the proposed method when applied to Volterra delay integro differential equations. Numerical experiments are carried out to illustrate the efficiency and applicability of the proposed method.

L1 Method on Nonuniform Meshes for Linear Time-Fractional Diffusion Equations with Constant Time Delay

L1 Method on Nonuniform Meshes for Linear Time-Fractional Diffusion Equations with Constant Time Delay

Gain scheduling model predictive controller design for tankless gas water heaters with time-varying delay

• Thermal model with time-varying delay is developed for a tankless gas water heater. • Feedback, feedforward and model predictive controllers are designed. • Controllers are assessed for cold start and water flow rate sudden disturbances. • Impact of temperature overshoots and undershoots are diminished. • Gain scheduling MPC presents superior performance than classic controllers. One of the most significant drawbacks of tankless gas water heaters is the difficulty of controlling the outlet hot water temperature as changes in water demand cannot be predicted. These sudden changes in hot water flow rate, are associated with the system inhered delays, and are responsible for temperature overshoots and undershoots that severely affect the comfort perception of the user. In the present work, a linear model predictive controller (MPC) design is employed for the stabilization of a constrained nonlinear thermal process with time-varying delay, however, control performance degrades significantly when operating far from the linearization operating point. The idea is to design multiple linear MPC controllers, each with its linear state-space model and constant time delay, describing process dynamics at a specific level of operation. Gain scheduling MPC presents improved performance when compared with classic PID and combined feedforward-feedback controllers, reducing the settling time up to two thirds.

Application of the Generalized Backstepping Control Method for Lotka-Volterra Prey-Predator System with Constant Time Delay

A well-known method, namely the backstepping method, which is used for stabilizing systems of ordinary differential equations is applied in this paper to solve the system of Lotka-Volterra prey-predator with time delay. The followed approach is accomplished with the cooperation of the method of steps, which is a well-known approach followed in solving delay differential equations, to transform the system of nonlinear delay differential equations into an equivalent system of ordinary differential equations. The fundamental concept behind the backstepping method is to construct recursively Lyapunov functions in quadratic form to stabilize the system for each time step interval. Matlab computer software is used to carry out the numerical simulation in order to investigate the effectiveness of the followed approach.

Scalable Load Balancing in Networked Systems: A Survey of Recent Advances

In this survey we provide an overview of recent advances on scalable load balancing schemes which provide favorable delay performance and yet require minimal implementation overhead. The basic load balancing scenario involves a single dispatcher where tasks arrive that must immediately be forwarded to one of $N$ single-server queues. The join-the-shortest-queue (JSQ) policy yields vanishing delays as $N$ grows large, as in a centralized queuing arrangement, but involves a prohibitive communication burden. In contrast, JSQ($d$) schemes that assign an incoming task to a server with the shortest queue among $d$ servers selected uniformly at random require little communication, but lead to constant delays. In order to examine this fundamental trade-off between delay performance and implementation overhead, we discuss a body of recent research on JSQ($d(N)$) schemes in which the diversity parameter $d(N)$ depends on $N$ and investigate the growth rate of $d(N)$ required to match the optimal JSQ performance on fluid and diffusion scales. Stochastic coupling techniques and scaling limits play an instrumental role in establishing this asymptotic optimality. We demonstrate how this methodology carries over to infinite-server settings, finite buffers, multiple dispatchers, servers arranged on graph topologies, and token-based load balancing schemes such as join-the-idle-queue (JIQ), thus providing a broad overview of the main trends in the field.

Existence, exponential mixing and convergence of periodic measures of fractional stochastic delay reaction-diffusion equations on [formula omitted

This paper is concerned with periodic measures of fractional stochastic reaction-diffusion equations with variable time delay defined on unbounded domains. We first prove the existence of periodic measures of the Markov process associated with the equation by showing the weak compactness of distribution laws of a family of solutions based on the uniform estimates and the equicontinuity of solutions in probability. We then establish the regularity of periodic measures and prove the tightness of the set of all periodic measures of the equation for small noise intensity. As a result, any sequence of periodic measures possesses at least one limit point, and we further prove every such limit must be a periodic measure of the corresponding limiting system. Finally, under further assumptions on the nonlinear terms, we establish the uniqueness and the exponential mixing property of periodic measures in the sense of Wasserstein metric. All the results of the paper are also valid for invariant measures of the corresponding autonomous version of the stochastic equation with constant time delay. The idea of uniform tail estimates of solutions in probability is employed to overcome the difficulty introduced by the non-compactness of Sobolev embeddings on unbounded domains.

Energy transfer and coherence in coupled oscillators with delayed coupling: a classical picture of two-level systems

The Frimmer-Novotny model to simulate two-level systems by coupled oscillators is extended by incorporating a constant time delay in the coupling. The effects of the introduced delay on system dynamics and two-level modeling are then investigated and found substantial. Mathematically, introducing a delay converts the dynamical system from a finite one into an infinite-dimensional system. The resulted system of delay differential equations is solved using the Krylov method with Chebyshev interpolation and post-processing refinement. The calculations and analyses reveal the critical role that a delay can play. It has oscillatory effects as the main dynamical eigenmodes move around a circle with a radius proportional to the coupling strength and an angle linear with the delay. This alteration governs the energy transfer dynamics and coherence. Accordingly, both, the delay and the coupling strength dictate the stability of the system. The delay is the main related parameter as for certain intervals of it, the system remains stable regardless of the coupling. A significant effect occurs when one of the main modes crosses the imaginary axis, where it becomes pure imaginary and dampingless. Thus, the two states energies can live and be exchanged for an extremely long time. Furthermore, it is found that the delay alters both the splitting and the linewidth in a way further influencing the energy transfer and coherence. It is found also that the delay should not be large to have significant effect. For example, for an optical system with 500 nm wavelength, the critical delay can be in tens of attoseconds.

Adaptive control of time delay teleoperation system with uncertain dynamics.

A bilateral adaptive control method based on PEB control structure is designed for a class of time-delay force feedback teleoperation system without external interference and internal friction to study the uncertainty of dynamic parameters and time delay. The stability and tracking performances of the closed-loop constant time delay teleoperation system are analyzed by Lyapunov stability theory. Finally, the controller designed in this paper is successfully applied to the teleoperation system composed of a two-degree of freedom rotating manipulator as the master robot and the slave robot. The simulation is carried out in no operator and environment force or with operator and environment force. The adaptive bilateral control method's control performance is compared with that of the traditional time-delay teleoperation system. Finally, it is verified that the method has good control performance.

Convergence of a Class of Delayed Neural Networks with Real Memristor Devices

Neural networks with memristors are promising candidates to overcome the limitations of traditional von Neumann machines via the implementation of novel analog and parallel computation schemes based on the in-memory computing principle. Of special importance are neural networks with generic or extended memristor models that are suited to accurately describe real memristor devices. The manuscript considers a general class of delayed neural networks where the memristors obey the relevant and widely used generic memristor model, the voltage threshold adaptive memristor (VTEAM) model. Due to physical limitations, the memristor state variables evolve in a closed compact subset of the space; therefore, the network can be mathematically described by a special class of differential inclusions named differential variational inequalities (DVIs). By using the theory of DVI, and the Lyapunov approach, the paper proves some fundamental results on convergence of solutions toward equilibrium points, a dynamic property that is extremely useful in neural network applications to content addressable memories and signal-processing in real time. The conditions for convergence, which hold in the general nonsymmetric case and for any constant delay, are given in the form of a linear matrix inequality (LMI) and can be readily checked numerically. To the authors knowledge, the obtained results are the only ones available in the literature on the convergence of neural networks with real generic memristors.

Exponential Stability of Highly Nonlinear Hybrid Differently Structured Neutral Stochastic Differential Equations with Unbounded Delays

This paper mainly studies the exponential stability of the highly nonlinear hybrid neutral stochastic differential equations (NSDEs) with multiple unbounded time-dependent delays and different structures. We prove the existence and uniqueness of the exact global solution of the new stochastic system, and then give several criteria of the exponential stability, including the q1th moment and almost surely exponential stability. Additionally, some numerical examples are given to illustrate the main results. Such systems are widely applied in physics and other fields. For example, a specific case is pantograph dynamics, in which the delay term is a proportional function. These are widely used to determine the motion of a pantograph head on an electric locomotive collecting current from an overhead trolley wire. Compared with the existing works, our results extend the single constant delay of coefficients to multiple unbounded time-dependent delays, which is more general and applicable.

Leader-following successive lag consensus of nonlinear multi-agent systems via observer-based event-triggered control

This article investigates the leader-following successive lag consensus (SLC) for nonlinear multi-agent systems (NMASs) via the observer-based event-triggered control (OBETC), in which two scenarios including constant consensus delay and time-varying consensus delay are considered. Since the system states might not be directly available in actual scenes, the state estimation method is utilized for followers to track their full information. Based on the relative state, a class of distributed event-triggered control protocols is constructed, where the event-triggered strategy is introduced such that each follower can determine the broadcasting time to its neighbors. Obviously, these designed control protocols considerably lessen the expense over communication networks and the frequency of protocol updates. Furthermore, with the aid of the Lyapunov function method, a series of sufficient conditions for guaranteeing the leader-following SLC of NMASs is obtained. Meanwhile, it is proved that no Zeno behavior is exhibited. Finally, several numerical examples are given to illustrate the validity of our theoretical results.

State bounding and controller design for genetic regulatory networks with multiple delays and bounded disturbances

AbstractThis article addresses the problems of state bounding and state‐feedback controller design for genetic regulatory networks with multiple delays and bounded disturbances. Multiple time‐varying discrete delays and multiple constant distributed delays are involved. A delay‐dependent sufficient condition containing several simple inequalities is first given to guarantee that the state trajectories remain inside or converge exponentially into a Cartesian product of two polytopes. Furthermore, equivalent sufficient conditions directly represented by the system parameters are derived. Based on the state bounding results, one can obtain reachable set estimation and global exponential stability criteria. By designing state‐feedback controllers, the state trajectories of the close‐loop system are limited in a given Cartesian product of two polytopes. It is worthy to stress that the proposed method does not need to construct any Lyapunov–Krasovskii functional, and it can be easily realized. The effectiveness of the obtained theoretical results is illustrated by a numerical example.

Improve Stock Price Model-Based Stochastic Pantograph Differential Equation

Although the concept of symmetry is widely used in many fields, it is almost not discussed in finance. This concept appears to be relevant in relation, for example, to mathematical models that can predict stock prices to contribute to the decision-making process. This work considers the stock price of European options with a new class of the non-constant delay model. The stochastic pantograph differential equation (SPDE) with a variable delay is provided in order to overcome the weaknesses of using stochastic models with constant delay. The proposed model is constructed to improve the evaluation process and prediction accuracy for stock prices. The feasibility of the proposed model is introduced under relatively weak conditions imposed on its volatility function. Furthermore, the sensitivity of time lag is discussed. The robust stochastic theta Milstein (STM) method is combined with the Monte Carlo simulation to compute asset prices within the proposed model. In addition, we prove that the numerical solution can preserve the non-negativity of the solution of the model. Numerical experiments using real financial data indicate that there is an increasing possibility of prediction accuracy for the proposed model with a variable delay compared to non-linear models with constant delay and the classical Black and Scholes model.

A Delay Compensation Framework for Connected Testbeds

This work considers connected testbeds, i.e., engineering testbeds that are remotely accessible over a network, and focuses on the challenge of achieving a high-fidelity closed-loop integration despite the network delays. To address this challenge, a model-free framework is presented. In previous work, a model-free delay compensation framework with a single design parameter was developed. However, having only one design parameter could limit tuning flexibility and thus delay compensation performance. Furthermore, this framework has not yet been validated on an actual connected testbed. To address these two shortcomings, in this article, this delay compensation framework is first expanded into a two-parameter form, and its open-loop stability and performance are studied for constant delays. The predictor stability criterion is established in terms of the two design parameters and the constant network delay. To evaluate the transient delay compensation performance of this framework and understand its advantages and limitations, simulation case studies are conducted on a connected engine testbed representing a medium-duty diesel pickup truck. These studies include two testbed architectures, constant and variable delays, two drive cycles, two levels of driver aggressiveness, and a comparison against wave transformation as a state-of-the-art benchmark. Finally, the framework is tested experimentally on a physical realization of the same connected testbed. The results validate the robustness of the delay compensation performance of the framework under dynamic operations, and show up to 30% higher integration fidelity due to the additional design degree of freedom introduced through the two-parameter form.

Global finite-dimensional observer-based stabilization of a semilinear heat equation with large input delay

We study global finite-dimensional observer-based stabilization of a semilinear 1D heat equation with globally Lipschitz semilinearity in the state variable. We consider Neumann actuation and point measurement. Using dynamic extension and modal decomposition we derive nonlinear ODEs for the modes of the state. We propose a controller that is based on a nonlinear finite-dimensional Luenberger observer. Our Lyapunov H 1 -stability analysis leads to LMIs, which are shown to be feasible for a large enough observer dimension and small enough Lipschitz constant. Next, we consider the case of a constant input delay r > 0 . To compensate the delay, we introduce a chain of M sub-predictors that leads to a nonlinear closed-loop ODE system, coupled with nonlinear infinite-dimensional tail ODEs. We provide LMIs for H 1 -stability and prove that for any r > 0 , the LMIs are feasible provided M and the observer dimension N are large enough and the Lipschitz constant is small enough. Numerical examples demonstrate the efficiency of the proposed approach.

Retarded Sampled-Data Control Design for Interconnected Power System With DFIG-Based Wind Farm: LMI Approach.

In this article, we investigate the robust stabilization for an interconnected power system with a doubly fed induction generator (DFIG)-based wind farm via retarded sampled-data control (RSDC). Generally, the interconnected power system with DFIG-based wind farm considers a mechanical torque, and load deviation, which is taken into disturbance of the proposed model. The main concern of this article is to stabilize and mitigate the frequency fluctuation, and speed deviation of the DFIG-based wind farm. To do this, a more general sampled-data control strategy, involving the effect of constant time delay is considered and the sampling period is assumed to vary within an interval. In addition, the defined disturbances are attenuated by using the H∞ performance-based RSDC scheme. An appropriate Lyapunov Krasovskii functional (LKF) is constructed to obtain the delay-dependent sufficient conditions in the form of linear matrix inequalities (LMIs) by using the RSDC strategy. The obtained conditions ensure the proposed closed-loop system is asymptotically stable under the designed controller. Finally, simulation results and comparative results are given to illustrate the effectiveness of the designed control scheme.

Stability of Discrete-Time Delayed Systems Subject to External Interference and Generalized Overflow Nonlinearities

This article concerns the stability of delayed discrete-time systems (DTSs) through <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> performance under external interference and generalized overflow nonlinearities. The novel criteria that analyze the exponential stability of DTSs with constant state delays are presented. Moreover, an extension to attain the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> performance is developed to handle the external interference of systems with time-varying delays based on Wirtinger-based inequality and reciprocal convex inequality. For such systems, the presented approach ensures zero-input overflow stability as well as robustness against interferences with a guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> level. The presented methodology can also be applied to determine the minimum attenuation level to achieve the desirable performance specifications for the sake of hardware optimization. The presented criteria are less conservative than several existing criteria. The efficacy of the presented criteria is exemplified by examples.

Irreversible investment with random delay and partial prepayment

Classical irreversible investment problem admits an optimal strategy of threshold type. But there is no consensus on how the investor should adjust the threshold, if there is an implementation delay. By formulating a general problem with random delay and partial prepayment, we find that the effect of delay can be opposite for different prepayment rates. Besides, although the constant delay model is commonly used, we argue that it is a reasonable approximation only if the discount rate is small.