Time-varying Delays Research Articles

Data-Driven Dynamic Event-Triggered Control for NCSs Under Denial-of-Service and Time-Varying Delays

Data-Driven Dynamic Event-Triggered Control for NCSs Under Denial-of-Service and Time-Varying Delays

Fixed-Time H∞ Consensus Control of Uncertain Vehicular Platooning Systems With Homogeneous Time-Varying Actuator Delay

Fixed-Time H_∞ Consensus Control of Uncertain Vehicular Platooning Systems With Homogeneous Time-Varying Actuator Delay

Output Feedback Consensus for High-order Stochastic Multi-agent Systems With Unknown Time-varying Delays

Output Feedback Consensus for High-order Stochastic Multi-agent Systems With Unknown Time-varying Delays

Delay-compensatory synchronization on uncertain chaotic neural networks via average delayed impulsive gains

This paper mainly studies the exponential synchronization issue of chaotic neural networks with parametric uncertainties and time-varying delays via hybrid impulsive control and delay compensatory strategy. Considering the hybrid impulses and flexible delays in the controller, the idea of average delayed impulsive gain (ADIG) is introduced to quantify the effects of hybrid impulses from a comprehensive viewpoint, i.e., not only the desynchronizing/synchronizing delay-free impulses but also the desynchronizing/synchronizing delayed impulses are discussed. Meanwhile, the impulsive delays are fetched and integrated to compensate the desynchronizing impulses dynamically, which removes certain strict restrictions on the impulsive gains and impulsive delays compared with existed works. Correspondingly, some relaxed sufficient criteria for exponential synchronization are derived by jointly utilizing the concept of average delayed impulsive gain, the delay compensatory scheme and the mathematical induction methodology. Ultimately, two examples with some comparisons are given to verify the applicability and superior performance of the obtained results.

Input delay compensation of nonlinear systems with uncertain time-varying parameters

A robust adaptive control law is designed for the class of nonlinear systems with uncertain time-varying parametric dynamics and input delays. The Constitution of control law design is based on filtered tracking errors, previous values of control input and estimate of uncertain parameters which is updated by the update law. An arbitrary large input delay compensation is guaranteed by deriving sufficient control gain conditions using Lyapunov-Krassovskii based stability analysis. The efficacy of the design is verified by Simulation results of two-link robot manipulator dynamical system.

Stabilization for a class of fractional-order nonlinear reaction–diffusion systems with time-varying delay: Event-triggered boundary control approach

Based on the hybrid event-triggered mechanism (HETM), the boundary stabilization issue for fractional-order nonlinear reaction–diffusion systems (FNRDSs) with time-varying delay is studied by using two kinds of measurements. First, when the system state is measurable, a event-triggered feedback controller (ETFC) is designed directly based on the average measured output. Secondly, for the case that the state is unmeasurable, an event-triggered feedback controller based on observer framework is constructed through the boundary point measurement information. Utilizing the Lyapunov method and Wirtinger’s inequality, sufficient conditions for the asymptotic stability of the system are given in the form of linear matrix inequalities (LMIs), respectively, in which the Razumikhin theorem is used to deal with time-varying delay. Meanwhile, it is proved that Zeno behavior can be excluded by the designed HETM. Finally, numerical simulations demonstrate the validity and feasibility of the proposed control scheme.

Relaxed stability criteria of delayed neural networks using delay-parameters-dependent slack matrices

This note aims to reduce the conservatism of stability criteria for neural networks with time-varying delay. To this goal, on the one hand, we construct an augmented Lyapunov–Krasovskii functional (LKF), incorporating some delay-product terms that capture more information about neural states. On the other hand, when dealing with the derivative of the LKF, we introduce several parameter-dependent slack matrices into an affine integral inequality, zero equations, and the S-procedure. As a result, more relaxed stability criteria are obtained by employing the so-called Lyapunov–Krasovskii Theorem. Two numerical examples show that the proposed stability criteria are of less conservatism compared with some existing methods.

Distributed control of virtual energy storage systems for voltage regulation in low voltage distribution networks subjects to varying time delays

Distributed communication-based strategies are popular for regulating nodal voltages in distribution networks with high penetration of Photovoltaic (PV) sources. Time delays inevitably pose challenges to efficient voltage regulation and power sharing. In response, this paper presents a distributed, event-triggered voltage regulation approach that enables power sharing across virtual energy storage systems (VESS) with different parameters while accommodating diverse time delays. The process begins by determining the delay margin for the primary Volt/Watt controller in a low-voltage distribution network (LVDN), laying the foundation for stable feedback control gain design. To accommodate any arbitrary large and time-varying delays, a distributed resilient event-triggered secondary controller for VESS is designed to share voltage regulation tasks according to their capacities and state of energy (SoE) values. A mathematical analysis, grounded in the Lyapunov–Krasovskii approach, evaluates the stability and convergence of the proposed controller amidst time delays thoroughly. To validate the proposed method, simulation studies are conducted, which demonstrate the effectiveness in mitigating voltage limit violations, even with variable communication delays, and highlight balanced power sharing and SoE among VESS.

Predefined-time synchronization of time-varying delay fractional-order Cohen–Grossberg neural network based on memristor

This paper delves into the synchronization dynamics of fractional-order memristor Cohen–Grossberg neural network systems with time-varying delays at predefined times (PTS-MFCGNNs). Firstly, leveraging the concept of predefined-time stability, we devise a fractional-order controller, establish sufficient conditions for predefined-time synchronization, and achieve synchronization within the Cohen–Grossberg drive–response system. Secondly, building upon these findings, we scrutinize the synchronization dynamics within the time domain of the PTS-MFCGNNs system. Finally, we validate our theoretical framework through numerical simulations and engage in a comprehensive discussion on predefined-time synchronization within the PTS-MFCGNNs system.

Non-fragile output-feedback control for delayed memristive bidirectional associative memory neural networks against actuator failure

This article investigates the stabilization property for the modeled memristive bidirectional associative memory neural networks with time-varying delay when the faulty signals received from the fluctuated controller. The non-fragile output-feedback controller is taken into account to counteract the impact of gain perturbations to end up with robust fault-tolerant setup. To tackle the weak signals in the actuator received from the fluctuated controller, control gain matrices encompass situations intended to memory non-fragile output-feedback controller. Based on the Lyapunov stability theory, differential inclusion theory, and congruence transformation, the sufficient condition for the global asymptotic stabilization property for the designed fault-tolerant memristive bidirectional associative memory neural network model is obtained in terms of linear matrix inequality by utilizing Wirtinger's inequality. Finally, numerical examples are approached with the state performance plots of the proposed memristive bidirectional associative memory neural network model with respect to the time-domain plane, to confirm the stabilization results and it illustrates the working mechanism of the designed controller.

Lagrange Stability of Competitive Neural Networks with Multiple Time-Varying Delays

In this paper, the Lagrange stability of competitive neural networks (CNNs) with leakage delays and mixed time-varying delays is investigated. By constructing delay-dependent Lyapunov functional, combining inequality analysis technique, the delay-dependent Lagrange stability criterion are obtained in the form of linear matrix inequalities. And the corresponding global exponentially attractive set (GEAS) is obtained. On this basis, by exploring the relationship between the leakage delays and the discrete delay, a better GEAS of the system is obtained from the six different sizes of the two types of delays. Finally, three examples of numerical simulation are given to illustrate the effectiveness of the obtained results.

Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability

Abstract Spacecraft models that mimic the Planck satellite’s behaviour have produced information on cosmic microwave background radiation, assisting physicists in their understanding of the composition and expansion of the universe. For achieving the intended formation, a framework for a discrete fractional difference spacecraft model is constructed by the use of a discrete nabla operator of variable order containing the Mittag–Leffler kernel. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as exterior disruptions, parameterized variations, time-varying feedback delays, and actuator defects. The implementation of the Banach fixed-point approach provides sufficient requirements for the presence of the solution as well as a distinctive feature for such mechanisms Furthermore, the consistent stability is examined. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of spacecraft systems to provide justification for structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the spacecraft system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional orders in the offered system. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the spacecraft chaotic model is an intriguing and crucial subject for research.

Quantification of the time-varying epidemic growth rate and of the delays between symptom onset and presenting to healthcare for the mpox epidemic in the UK in 2022

The mpox epidemic in the UK began in May 2022, with rates of new cases unexpectedly and rapidly declining during August 2022. Interpreting trends in infection requires disentangling the underlying growth rate of cases from the delay from symptom onset to presenting to healthcare. We developed a nowcasting Bayesian method which incorporates time-varying delays (EpiLine) to quantify the changes in the delay from symptom onset to healthcare presentation and the underlying mpox growth rate over the period May-August 2022 in the UK. We show that the mean delay between symptom onset and healthcare presentation for mpox in the UK decreased from 22 days in early May 2022 to 10 days by early June and 8 days in August 2022. When we account for these dynamic delays, the time-varying growth rate declined gradually and continuously in the UK during the May-August 2022 period. Not accounting for varying time delays would have incorrectly characterised the growth rate by a sharp increase followed by a rapid decline in mpox cases. Our results highlight the importance of correctly quantifying the delay between symptom onset to healthcare presentation when characterising the epidemic growth of mpox in the UK. The gradual reduction in the rate of epidemic spread, which pre-dated the vaccine roll-out, is consistent with gradual risk reduction or acquired immunity amongst the highest risk individuals. Our study highlights the need for public health agencies to record the delays from symptom onset to healthcare presentation early in an outbreak.

Secure control design for cooperative adaptive cruise control with a time-varying input delays under false data injection attacks

ABSTRACT Connected and Autonomous Vehicles (CAVs) are shaping the future of transportation systems; however, their future development requires consideration of the upcoming challenges with cyber-physical attacks. Cooperative Adaptive Cruise Control (CACC) is one of the features used in CAVs. Using CACC increases the vulnerability of such systems to False Data Injection (FDI) attacks. To address this, this paper proposes a novel mitigation approach to compensate for FDI attacks and noise in real-time. In addition to FDI attacks, the current CACC algorithm suffers from input delay and disturbance. Here, we develop a nonlinear controller and an FDI attacks estimation technique to mitigate the effects of FDI attacks, noise, input delay and additive disturbance. Lyapunov–Krasovskii functionals are used in the Lyapunov-based stability analysis to ensure semi-global uniformly ultimately bounded tracking. In order to demonstrate the performance of the proposed approach, we validate it through simulation analysis.

Robust PID controller design for positioning systems with hysteresis and time-varying delay

This paper presents Linear Matrix Inequalities (LMIs) conditions for designing Proportional-Integral-Derivative (PID) controllers that guarantee asymptotic stability with exponential convergence rate for positioning systems affected by hysteresis nonlinearity and time-varying delay. The hysteresis is modelled using the Prandtl-Ishlinskii operator, and the effects of both the time-varying delay and hysteresis are encapsulated into a bounded uncertain parameter confined within a known convex polytope. Numerical results support the theoretical developments, confirming that the controller effectively mitigates the effects of disturbances while suppressing both the hysteresis and time-varying delay influences.

Event-triggered secure control for Markov jump neural networks with time-varying delays and subject to cyber-attacks via state estimation fuzzy approach

The investigation uses a state estimation fuzzy technique to address the problem of dynamic event-triggered secure control in Markov jump neural networks with time-varying delays subject to cyber-attacks. Two different deception attacks are given, each employing stochastic variables with a Bernoulli distribution. Specifically, this article presents a dynamic event-triggered strategy and energy restrictions to reduce network traffic and protect network resources during deception attacks. To prevent the system state from becoming unavailable, a state estimator is concurrently developed using the output signal. The application of Lyapunov stability theory yields sufficient criteria that ensure neural network stability. The study also accurately describes the controller gain's by solving Linear matrix inequality. Numerical examples are provided to demonstrate the theoretical results.

Unknown input observer design for uncertain nonlinear systems with time-varying delay: application to online fault estimation

This paper recommends an unknown input observer (UIO) for uncertain nonlinear time-delay dynamics that enables online fault estimation. The main novelty of this paper is designing UIO to fault estimation for nonlinear systems that include time-varying delays in states and time-varying uncertainties in all matrices of the system. The other advantage of the proposed method is that both abrupt and incipient faults are considered. Furthermore, the state and output disturbances, as well as actuator and sensor faults, are considered. The Lyapunov–Krasovskii concept is used to guarantee the stability of the augmented closed-loop system. Calculating observer gains and stabilisation of estimation error dynamics are accomplished by utilising a new linear matrix inequality (LMI). Finally, an uncertain continuous-stirred tank reactor (CSTR) with a time-varying delay is used to evaluate the performance of the suggested technique.

Feedback Control Design Strategy for Stabilization of Delayed Descriptor Fractional Neutral Systems with Order 0 < ϱ < 1 in the Presence of Time-Varying Parametric Uncertainty

Descriptor systems are more complex than normal systems, which are modeled by differential equations. This paper derives stability and stabilization criteria for uncertain fractional descriptor systems with neutral-type delay. Through the Lyapunov–Krasovskii functional approach, conditions subject to time-varying delay and parametric uncertainty are formulated as linear matrix inequalities. Based on the established criteria, static state- and output-feedback control laws are designed to ensure regularity and impulse-free properties, together with robust stability of the closed-loop system under permissible uncertainties. Numerical examples illustrate the effectiveness of the control methods and show that the results depend on the range of variation in the delays and on the fractional order, leading to stability analysis results that are less conservative than those reported in the literature.

Image encryption hiding algorithm based on digital time-varying delay chaos model and compression sensing technique

Most of the existing image encryption algorithms encrypt images as meaningless cryptographic images, which can easily attract the attention of attackers during transmission. To address this problem, scholars have proposed to hide the cipher image in a meaningless carrier image. However, larger carrier images are often required, which occupy more bandwidth. In order to solve this problem, this paper realizes embedding the color secret image into the carrier image whose size is equal to or even smaller than the original image by combining the chaotic compressed sensing model. First of all, the original image is sparsely processed using discrete wavelet transform. Then the time varying delay chaotic model is used to generate pseudo random sequence and then the measurement matrix is constructed to compress and encrypt the image. In the end, using singular value decomposition to achieve image embedding, the carrier image carrying information is obtained.

Observer-based control of uncertain nonlinear Markovian jump systems with time-varying delay and actuator failures via sliding mode technique

This paper focuses on the discussion of asynchronous sliding mode control (SMC) design for uncertain Markovian jump systems (MJSs) in which nonlinearities, time-varying delays, and actuator failures are considered. At first, the study establishes an asynchronous observer and correspondingly constructs a sliding mode switching function in which the controller gain operates asynchronously with the original system. Then the observer-based SMC law is designed through Lyapunov stability theory to achieve reachability of the specified sliding surface, resulting in mean-square stability of the closed-loop system. In addition, we extend the aforementioned findings to a more practical case where the conditional probability is only partially known. Eventually, numerical examples and tunnel-diode-circuit examples are provided to demonstrate the merits of the summarized results.