Time-varying Delays Research Articles

Finite-Time Stabilization of Inertial Memristive Neural Networks via Nonreduced Order Method.

This article investigates the finite-time stabilization problem of inertial memristive neural networks (IMNNs) with bounded and unbounded time-varying delays, respectively. To simplify the theoretical derivation, the nonreduced order method is utilized for constructing appropriate comparison functions and designing a discontinuous state feedback controller. Then, based on the controller, the state of IMNNs can directly converge to 0 in finite time. Several criteria for finite-time stabilization of IMNNs are obtained and the setting time is estimated. Compared with previous studies, the requirement of differentiability of time delay is eliminated. Finally, numerical examples illustrate the usefulness of the analysis results in this article.

Two-dimensional iterative learning hybrid robust fuzzy predictive control for nonlinear multi-phase batch processes with asynchronous switching

For nonlinear multi-phase batch processes with uncertainties, time-varying delays, and unknown bounded disturbances, an iterative learning hybrid robust fuzzy predictive control approach is developed within the context of two-dimensional systems. First, a two-dimensional T-S fuzzy Fornasini-Marchesini comprehensive feedback error model is constructed, which includes a state increment and an output error. Based on the established model and considering an asynchronous switching situation between a controller and a system state, a feedback error switching model, including match and mismatch cases, is developed. Then, a two-dimensional iterative learning hybrid robust fuzzy predictive controller is built, based on the established switching model. Second, building on related theories and methodologies, the stability conditions are derived by a linear matrix inequality form, while the system's asymptotic and exponential stability are analyzed. Next, the stability conditions are calculated to get the control law gains, minimum and maximum dwelling times. The acquired gains of control law greatly minimize the controller's learning cycle, while the advanced switching signal based on the obtained dwelling times is dynamically adjusted to ensure a smooth transition and the system's stability during switching. Ultimately, a simulation case is utilized to validate the proposed method's effectiveness and feasibility.

Exponential stabilization of stochastic quantum systems based on time-delay noise-assisted feedback

The exponential stabilization of stochastic quantum systems (SQS) under time-delay noise-assisted feedback is addressed based on the exponential stability of the stochastic differential delay equation (SDDE) in this paper. We show that if the stochastic differential equation (SDE), which covers the dynamical models of SQS under noise-assisted feedback, is exponentially stable, then the corresponding SDDE is also exponentially stable when the time-varying delay is bounded by a positive number, which is given in an implicit expression and can be computed numerically. On this basis, the results for the general SDDE are applied to the SQS under time-delay noise-assisted feedback, and the corresponding time-delay boundary is obtained. Furthermore, we show the time-delay boundary in numerical simulations.

Master–slaves synchronization of teleoperation systems with the Try‐Once‐Discard protocol under event‐triggered communication

AbstractIn this paper, a class of single‐master‐multiple‐slaves (SMMS) bilateral teleoperation systems with the limitation of communication bandwidth is investigated. The signals are exchanged between the master and the slaves through delayed communication. Besides, to avoid data collisions, the Try‐Once‐Discard (TOD) scheduling protocol is utilized to decide which slave gets the network access at each triggered instant. A control algorithm with the event‐triggered mechanism is proposed to ensure the master–slaves synchronization. Furthermore, the closed‐loop system's stability criterion associated with the controller gains, the varying time delays' bounds, and the maximum transmission interval is established on the basis of the Lyapunov–Krasovskii analysis. Finally, the presented algorithm's performance is demonstrated by the simulation and experiment results.

Stability and stabilization for the hydraulic automatic gauge control system of cold rolling mill with time delay and saturation

This paper studies the stability and stabilization of hydraulic automatic gauge control (HAGC) systems with time-varying delay and actuator saturation. First, a mathematical model of HAGC systems is established considering the measurement delay and saturation factors. With the help of state transformation, the measurement delay is transformed into input delay and the generalized sector condition is adopted to deal with the saturation problem in HAGC systems. Then, a new augmented L–K functional is constructed to contain more delay information to reduce the conservativeness of the stability criteria. Furthermore, by combining the proposed L–K functional with some advanced inequalities, the stability conditions and controller are derived with the aid of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed control algorithm is verified by simulation results.

Distributed delayed impulsive control for [formula omitted]-synchronization of multi-link structure networks with bounded uncertainties and time-varying delays of unmeasured bounds: A novel Halanay impulsive inequality approach

This study discusses the μ−synchronization of multi-link structure networks with parameter uncertainties and nonlinear couplings. Three types of variable delays, including internal, coupling, and distributed delays at sampling moments are deliberated in the synchronization control process. Different from existing multi-link models, the bulk of delays can be non-differentiable and unmeasured, which also brings new challenges to our research. To conquer the difficulties caused by such multiple generalized time delays, a novel Halanay-like impulsive inequality is established by utilizing the properties of μ−function and mathematical induction recipes. For letting the multi-link networks achieve μ−synchronization, a distributed-delay impulsive controller is designed, and multiple coupling matrices are decomposed into diagonal matrices and residual matrices. Based on the stability function method, the derived impulsive inequality, and matrix decomposition techniques, important synchronization conditions for the concerning multi-link networks are obtained, which releases the traditional constraints that delays should be smaller than impulsive intervals, and popularizes the existing synchronization results respecting multi-link systems with unbounded delays.

The global Mittag-Leffler synchronization problem of Caputo fractional-order inertial memristive neural networks with time-varying delays

The global Mittag-Leffler synchronization problem of Caputo fractional-order inertial memristive neural networks with time-varying delays

A Degree-Dependent Polynomial-Based Reciprocally Convex Matrix Inequality and Its Application to Stability Analysis of Delayed Neural Networks.

In this article, several improved stability criteria for time-varying delayed neural networks (DNNs) are proposed. A degree-dependent polynomial-based reciprocally convex matrix inequality (RCMI) is proposed for obtaining less conservative stability criteria. Unlike previous RCMIs, the matrix inequality in this article produces a polynomial of any degree in the time-varying delay, which helps to reduce conservatism. In addition, to reduce the computational complexity caused by dealing with the negative definite of the high-degree terms, an improved lemma is presented. Applying the above matrix inequalities and improved negative definiteness condition helps to generate a more relaxed stability criterion for analyzing time-varying DNNs. Two examples are provided to illustrate this statement.

Exponential State Estimation for Delayed Competitive Neural Network Via Stochastic Sampled-Data Control with Markov Jump Parameters Under Actuator Failure

Abstract This article examines the problem of estimating the states of Markovian jumping competitive neural networks, where the estimation is done using stochastic sampled-data control with time-varying delay. Instead of continuously measuring the states, the network relies on sampled measurements, and a sampled-data estimator is proposed. The estimator uses probabilistic sampling during two sampling periods, following a Bernoulli distribution. The article also takes into account the possibility of actuator failure in real systems. To ensure the exponentially mean-square stability of the delayed neural networks, the article constructs a Lyapunov-Krasovskii functional (LKF) that includes information about the bounds of the delay. The sufficient conditions for stability are derived in the form of linear matrix inequalities (LMIs) by employing modified free matrix-based integral inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Robust Switched H$\infty$ Control of T–S Fuzzy-Based MRF Suspension Systems Subject to Input Saturation and Time-Varying Delay

Robust Switched H$\infty$ Control of T–S Fuzzy-Based MRF Suspension Systems Subject to Input Saturation and Time-Varying Delay

Existence and asymptotic behavior of a nonlinear axially moving string with variable tension and subject to disturbances

In this paper, we consider the stabilization question for a nonlinear model of an axially moving string. The model is assumed to undergo the variable tension and variable disturbances. The Hamilton principle is used to describe the dynamic of transverse vibrations. We establish the well-posedness by means of the Faedo-Galerkin method. A boundary control with a time-varying delay is designed to stabilize uniformly the string. Then, we derive a decay rate of the solution assuming that the retarded term be dominated by the damping one. Some examples are given to clarify when the rate is exponential or polynomial.

Exponential stability of system with time delay based on matrix-refined weighted functions

Exponential stability of system with time-varying delay is studied in this paper. By taking intermediate polynomials and slack variables, we propose novel matrix-refined weighted functions (MRWFs). Then, based on the MRWFs, we construct a suitable Lyapunov-Krasovskii functional (LKF) and propose an exponential stability condition. Finally, numerical examples verify that the stability condition proposed in this paper is more effective, which is less conservative than some past criteria.

Observer-Based Finite-Time Adaptive Fault-Tolerant Control for Nonlinear System with Unknown Time-Varying Delay

Observer-Based Finite-Time Adaptive Fault-Tolerant Control for Nonlinear System with Unknown Time-Varying Delay

Unified analysis on multistablity of fraction-order multidimensional-valued memristive neural networks

This article provides a unified analysis of the multistability of fraction-order multidimensional-valued memristive neural networks (FOMVMNNs) with unbounded time-varying delays. Firstly, based on the knowledge of fractional differentiation and memristors, a unified model is established. This model is a unified form of real-valued, complex-valued, and quaternion-valued systems. Then, based on a unified method, the number of equilibrium points for FOMVMNNs is discussed. The sufficient conditions for determining the number of equilibrium points have been obtained. By using 1-norm to construct Lyapunov functions, the unified criteria for multistability of FOMVMNNs are obtained, these criteria are less conservative and easier to verify. Moreover, the attraction basins of the stable equilibrium points are estimated. Finally, two numerical simulation examples are provided to verify the correctness of the results.

Adaptive-neural command filtered synchronization control of tele-robotic systems using disturbance observer with safety enhancement

Due to the nature of the tele-robotic systems, some main problems are imposed, such as external disturbances, time-varying delays and external torques. However, some applications such as tele-surgery systems, require high precision, safety and accurate transmission of information between the leader and follower robots. In order to facilitate the imposed restrictions and to guarantee transient-state, and even steady-state performances in the presence of external disturbances and system uncertainties, the time-varying full state constrained control is employed by applying the Barrier Lyapunov function (BLF). In this regard, a new adaptive neural network torque observer is proposed to make the system independent from the force sensors. Moreover, the independence of the proposed algorithm from perfect knowledge of the manipulator dynamics and time-delay’s derivative of communication channels are advantages of this paper. Furthermore, the key idea of this paper is to lessen the computational complexity in the backstepping-based adaptive neural controller by means of the command filter strategy and the BLF approach is combined to converge the synchronization error signals into a predefined constraint. In order to consider practical limitations, time-varying delays in the communication channel and input saturation constraint are also considered in the design mechanism. Finally, the stability analysis of the observer and controller together is conducted and the evaluation of the performance of the proposed method is performed through a series of various scenarios and comparisons.

Quasi-projective synchronization of non-identical time-varying delayed quaternion-valued neural networks with interaction terms: Direct method

This article investigates the quasi-projective synchronization (QPS) of non-identical quaternion-valued neural networks (QVNNs) with time-varying delays and interaction terms. Due to parameter mismatches between the drive and response systems, complete projective synchronization is not possible. As a result, a novel idea, known as QPS, is explored up to a small error bound. The direct method is used to derive several general criteria to achieve QPS. The Lyapunov stability theory is employed to estimate the error bound. The numerical simulation results are presented graphically for various special cases to demonstrate the synchronization of time-varying delayed QVNNs with mismatched parameters and interaction terms, which confirm the efficiency of the presented research results. The second example showcases the application of QVNNs coupled with associative memory to illustrate its efficacy in accurately restoring the original color image patterns.

A new inequality and its application in descriptor Markovian jump systems with time-varying delays

This paper is focused on the dissipativity analysis of descriptor Markovian jump systems with time-varying delays. For achieving this aim, an augmented mode-dependent Lyapunov-Krasovskii functional (LKF) is constructed on the basis of the state decomposition method. Next, a novel integral inequality is proposed through the generalized free-weighting-matrix (GFWM) method as well as zero-valued equalities to estimate single integral terms more precisely. Then, an ameliorative stochastic admissibility and dissipative criterion is derived by utilizing the proposed integral inequality, the augmented LKF and other bounding techniques. Finally, the effectiveness and superiority of the presented results are confirmed with some numerical examples.

Distributed secondary frequency control scheme with A-symmetric time varying communication delays and switching topology

A distributed control of a Microgrid (MG) depends on the communication network for the exchange of information among the Distributed Generators (DGs). Most of the control schemes consider ideal communication among the DGs; however, in practical systems, delays are inherited in a system that can affect the dynamic performance and even destabilize an MG. Therefore, in this research work, delay independent distributed secondary frequency control for MGs is presented. Sufficient delay independent conditions for robust stability of the buffer-free Distributed Averaging Integral (DAI) control scheme is proposed while considering A-symmetric time varying communication delays and switching network topology. Moreover, in this work, slow as well as fast varying delays are analyzed using Lyapunov Krasovskii and Lyapunov Razumikhin's approach. Furthermore, a Lyapunov function based adaptive control approach is employed that updates the constant gain parameters to compensate for the uncertain or varying parameters. Finally, the efficacy of the controller is demonstrated through simulation studies that validate its performance in different scenarios.

Resonating Electrostatically Guided Electrons.

An essential component for quantum-enhanced measurements with free electrons is an electron resonator. We report stable guiding of free electrons at 50eV energy for up to seven round trips in a linear autoponderomotive guiding structure, which is realized with two microstructured printed circuit boards that generate the required electromagnetic fields. Free electrons are laser triggered from a sharp tungsten needle tip and coupled in at the front of the electron resonator with the help of sub-nanosecond-fast switchable electron mirrors. After a variable time delay, we open the rear electron mirror and measure the number of trapped electrons with a delay-line detector. We demonstrate, simulate, and show ways of optimizing an electron resonator in simulations, which will help enable "interaction-free" measurement setups, including multipass and quantum-Zeno effect based schemes, helping to realize the quantum electron microscope.

Improved-equivalent-input-disturbance-based preview repetitive control for Takagi–Sugeno fuzzy system with state delay

This paper designs a preview repetitive control (PRC) policy for a class of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay and external disturbances. First, the T–S fuzzy model is employed to represent a nonlinear plant, once the nonlinear plant is represented by a T–S fuzzy model, a fuzzy improved-equivalent-input-disturbance (IEID)-based PRC law can be designed to achieve better tracking performance and disturbance rejection. Next, based on a new equality constraint, we derive a continuous-discrete two-dimensional (2D) system that paves the way to solve the design problem of the IEID-based PRC law using linear matrix inequality (LMI) approach. Then, by solving LMIs, the gains of the controller and state observer can be obtained. Finally, a numerical example is included to show the effectiveness of the proposed method.