Time-delay Systems Research Articles

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.

Observer design for discrete T-S fuzzy time-delay singular systems

In this paper, we investigate the design of observers tailored for discrete T-S fuzzy time-delay singular systems, considering the presence of process disturbances and measurable premise variables. An observer with more design degrees of freedom than the commonly used Luenberger observer is designed. By constructing an asymmetric Lyapunov-Krasovskii functional, a criterion ensuring the existence of the fuzzy state observer is provided, which eliminates the limitations of the positive definiteness and symmetry of the previous functional matrix. In the process of solving the inequality, the relaxation matrix is incorporated to acquire additional flexibility and alleviate the conservatism of parameter design. Ultimately, two numerical instances are provided to thoroughly validate the rationale and efficacy of the approach.

Oscillation Solutions for Nonlinear Second-Order Neutral Differential Equations

This research investigates the oscillation criteria of nonlinear second-order neutral differential equations with multiple delays, focusing on their noncanonical forms. By leveraging an innovative iterative technique, new relationships are established to enhance the monotonic properties of positive solutions. These advancements lead to the derivation of novel oscillation criteria that significantly extend and refine the existing body of knowledge in this domain. The proposed criteria address gaps in the literature, providing a robust framework for analyzing such differential equations. To demonstrate their practical implications, three illustrative examples are presented, showcasing the applicability and effectiveness of the results in solving real-world problems involving delay differential equations.

Design of Event-Triggered Finite-Time Dissipative Control for Fractional-Order Time-Delay Interconnected Systems

Design of Event-Triggered Finite-Time Dissipative Control for Fractional-Order Time-Delay Interconnected Systems

Applying Stiff Integrators for Ordinary Differential Equations and Delay Differential Equations to Problems with Distributed Delays

Applying Stiff Integrators for Ordinary Differential Equations and Delay Differential Equations to Problems with Distributed Delays

Numerical Solution of Delay Differential Equations with Heronian Implicit Runge-Kutta Method

In recent years, there has been growing interest in the numerical solution of Delay Differential Equations (DDEs). This is due to the fact that DDEs provides a good means of modelling many phenomena in diverse application fields ranging from physical sciences, economy, medicine, education to electrodynamics. Hence, the increased attention in the numerical solutions to such problems becomes a necessity. The purpose of this study is to present a numerical method that uses a polynomial interpolating function when solving DDEs. In this paper, Heronian Implicit Runge-Kutta method is considered for the solution of DDEs while the delay term is being estimated with the aid of Hermite Interpolation of the third order. The Stability analysis of this method is considered, and its efficiency is represented and compared with some numerical examples. It is evident from the obtained results of the numerical examples that this numerical method alongside the polynomial interpolating function, which was used to approximate the delay term, is suitable for solving DDEs.

Learning-based adaptive optimal control of linear time-delay systems: A value iteration approach

This paper proposes a novel learning-based adaptive optimal controller design method for a class of continuous-time linear time-delay systems. A key strategy is to exploit the state-of-the-art reinforcement learning (RL) techniques and adaptive dynamic programming (ADP), and propose a data-driven method to learn the near-optimal controller without the precise knowledge of system dynamics. Specifically, a value iteration (VI) algorithm is proposed to solve the infinite-dimensional Riccati equation for the linear quadratic optimal control problem of time-delay systems using finite samples of input-state trajectory data. It is rigorously proved that the proposed VI algorithm converges to the near-optimal solution. Compared with the previous literature, the nice features of the proposed VI algorithm are that it is directly developed for continuous-time systems without discretization and an initial admissible controller is not required for implementing the algorithm. The efficacy of the proposed methodology is demonstrated by two practical examples of metal cutting and autonomous driving.

Matrix projective combination synchronization of time-delayed chaotic system and its application in image encryption

Matrix projective combination synchronization of time-delayed chaotic system and its application in image encryption

Zero-sum games subject to time-delayed uncertain stochastic systems

Zero-sum games subject to time-delayed uncertain stochastic systems

Solving a delay differential equation through the Fourier transform

Solving a delay differential equation through the Fourier transform

Numerical investigation of singularly perturbed time lag parabolic differential-difference equations.

This paper deals with the numerical investigation of a singularly perturbed parabolic differential-difference equation with a time lag. The proposed method comprises the θ method ( ) and the non-standard finite difference methods for temporal and spatial variable discretization, respectively. Besides, the Richardson extrapolation technique is employed to boost the accuracy and order of convergence of the scheme. The applicability of the proposed approach is confirmed through some numerical examples. Furthermore, we have improved the convergence from almost first to almost second order.

Existence of meromorphic solutions of a certain nonlinear differential-difference equation

Existence of meromorphic solutions of a certain nonlinear differential-difference equation

Distributed power economic dispatch algorithm based on hybrid time-delay system framework under DoS attacks

Distributed power economic dispatch algorithm based on hybrid time-delay system framework under DoS attacks

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.

Delay margin computation for single area load frequency control system with time delay

In this paper, the delay margin is computed for a load frequency control system with time delay of a single area using delay-independent stability analysis method. The delay-independent stability analysis method is used to consider some characteristics. The delay-independent stability of time-delayed systems may lose stability if their eigenvalue spectrum lies on the imaginary axis for delays. The stability is guaranteed for the delay margin, which must be known. A method for computing the delay margin for load frequency control system with delay is presented. In this method, the system's characteristic equation is converted into frequency-dependent equation. Then the spectral radius of the matrix pair is used to compute the crossing frequency at which eigenvalues cross the imaginary axis. The crossing frequencies and angles are computed using sweeping tests and binary recursive algorithm. At the end, the effectiveness of the proposed method is demonstrated using a case study of load frequency control system with delay of a single area.

Analysis of Stability in a Delay Differential Equation Model for Malaria InfectionWith Treatment

In this paper, we introduce a biological model employing delay differential equations to explore the evolution of malaria within a host undergoing drug treatment. Our analysis focuses on the stability of equilibrium points, leveraging the critical case theorem, an extension of the Lyapunov-Malkin theorem, which is particularly useful for scenarios involving zero roots in the characteristic equation. By determining equilibrium points and assessing their stability through the eigenvalues of the linearized system, we ensure the applicability of the theorem via translations to zero. The results highlight the significant influence of treatment-induced delays on the stability of malaria dynamics, offering valuable insights for optimizing control strategies and improving disease management.

An online fault-tolerant control approach based on policy iteration algorithm for nonlinear time-delay systems

This paper introduces an online fault-tolerant control method for nonlinear time-delay systems with actuator faults using a policy iteration algorithm. A new performance index function is proposed to account for time-delay states, from which control laws are derived. The approach combines policy iteration with a fault compensator, solving the Hamilton-Jacobi-Bellman equation associated with this innovative value function via a critic neural network. Actuator faults are reconstructed for online fault compensation without the need for fault detection and isolation. The Lyapunov functional analysis demonstrates the closed-loop system's asymptotic stability in the presence of actuator faults and time-delay states. Simulation results validate the effectiveness of the proposed fault compensation strategy. The key contribution of this paper is the incorporation of time-delay states into the value function of the policy iteration algorithm, addressing the problem of fault compensation in nonlinear time-delay systems.

Optimal Control Strategies for Constrained Linear Time-Delay Systems with Disturbances

Optimal Control Strategies for Constrained Linear Time-Delay Systems with Disturbances

Existence of Analytic Solutions to Linear Delay Differential Equations

Existence of Analytic Solutions to Linear Delay Differential Equations

Dynamics of Chronic Myeloid Leukemia Under Imatinib Treatment: A Study of Resistance Development

Chronic myeloid leukemia (CML) is a hematological disorder characterized by the abnormal proliferation of leukemic cells. This study aims to model the dynamics of leukemic and healthy cell populations in CML, considering the role of the immune system and the effects of treatment with Imatinib. The model also addresses the development of treatment resistance in cells, following the Goldie–Coldman hypothesis. We employ a system of delay differential equations to simulate the interactions between leukemic cells, healthy cells, and the immune system under treatment. The results provide insights into the dynamic balance between leukemic cells, healthy cells, and immune responses, and the impact of developing resistance on treatment outcomes.