Modeling of temperature-humidity for wood drying based on time-delay neural network

The temperature-humidity models of wood drying were developed based on Time-delay neural network and the identification structures of Time-delay neural network were given. The controlling model and the schedule model, which revealed the relation between controlling signal and temperature-humidity and the relation between wood moisture content and temperature-humidity of wood drying, were separately presented. The models were simulated by using the measured data of the experimental drying kiln. The numerical simulation results showed that the modeling method was feasible, and the models were effective.

Behavioral modeling of RF power amplifiers with time-delay feed-forward neural networks

A novel behavioral model using three-layer time-delay feed-forward neural networks （TDFFNN）is adopted to model radio frequency （RF）power amplifiers exhibiting memory nonlinearities. In order to extract the parameters, the back- propagation algorithm is applied to train the proposed neural networks. The proposed model is verified by the typical odd- order-only memory polynomial model in simulation, and the performance is compared with different numbers of taped delay lines（TDLs） and perceptrons of the hidden layer. For validating the TDFFNN model by experiments, a digital test bench is set up to collect input and output data of power amplifiers at a 60 × 10^6 sample/s sampling rate. The 3.75 MHz 16-QAM signal generated in the vector signal generator（VSG） is chosen as the input signal, when measuring the dynamic AM/AM and AM/PM characteristics of power amplifiers. By comparisons and analyses, the presented model provides a good performance in convergence, accuracy and efficiency, which is approved by simulation results and experimental results in the time domain and frequency domain.

Robust model predictive control for discrete uncertain nonlinear systems with time-delay via fuzzy model

An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is presented. In this approach, the minimization problem of the “worst-case” objective function is converted into the linear objective minimization problem in- volving linear matrix inequalities (LMIs) constraints. The state feedback control law is obtained by solving convex optimization of a set of LMIs. Sufficient condition for stability and a new upper bound on robust performance index are given for these kinds of uncertain fuzzy systems with state time-delay. Simulation results of CSTR process show that the proposed robust predictive control approach is effective and feasible.

Generating Li-Yorke chaos in a stable continuous-time T-S fuzzy model via time-delay feedback control

This paper investigates the chaotification problem of a stable continuous-time T S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then, the asymptotically approximate relationship between the controlled continuous-time T-S fuzzy system with time-delay and a discrete-time T-S fuzzy system is established. Based on the discrete-time T-S fuzzy system, it proves that the chaos in the discrete- time T-S fuzzy system satisfies the Li-Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.

RobustL_1 model reduction for stochastic time-delay systems

This paper investigates the problem of robust L1 model reduction for continuous-time uncertain stochastic time-delay systems. For a given mean-square stable system, our purpose is to construct reduced-order systems, such that the error system between these two models is mean-square asymptotically stable and has a guaranteed L1 (also called peak-to-peak) performance. The peak-to-peak gain criterion is first established for stochastic time-delay systems, and the corresponding model reduction problem is solved by using projection lemma. Sufficient conditions are obtained for the existence of admissible reduced-order models in terms of linear matrix inequalities (LMIs) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by standard numerical software. In addition, the development of reduced-order models with special structures, such as the delay-free model, is also presented. The efficiency of the proposed methods is demonstrated via a numerical example.

A Kind of Time-Delayed COVID-19 Dynamical Model with Vaccination

In the paper, we study a kind of time-delayed novel coronavirus pneumonia dynamical model with vaccination. This model considers that people are vaccinated, and the human immune system has a series of processes, which need a certain time. We first obtain the disease-free equilibrium and the basic reproduction number R0, and the system has a unique endemic equilibrium when R0 > 1. Then we discuss the stability of the disease-free equilibrium and the endemic equilibrium with different delays τ. For τ = 0, using the Lyapunov function approach, we obtained the stability of disease-free equilibrium and the endemic equilibrium, respectively. For any delay τ ≠ 0, using the Routh-Hurwitz Criteria, we obtained that the disease-free equilibrium is locally asymptotically stable. We also find the critical value τ0 at the endemic equilibrium, and obtain the condition that the system has a Hopf bifurcation at the endemic equilibrium. Finally, with the suitable choices of the parameters, some numerical simulations are presented in order to verify the effectiveness of the obtained theoretical results.

IMC-PID tuning method based on sensitivity specification for process with time-delay

To overcome the deficiencies addressed in the conventional PID control and improve the dynamic performance and robustness of the system, a simple design and parameters tuning approach of internal model control-PID （IMC-PID） controller was proposed for the first order plus time-delay （FOPTD） process and the second order plus time-delay （SOPTD） process. By approximating the time-delay term of the process model with the first-order Taylor series, the expressions for IMC-PID controller parameters were derived, and they had only one adjustable parameter 2 which was directly related to the dynamic performance and robustness of the system. Moreover, an analytical approach of selecting 2 was given based on the maximum sensitivity Ms. Then, the robust tuning of the system could be achieved according to the value of Ms. In addition, the proposed method could be extended to the integrator plus time-delay （IPTD） process and the first order delay integrating （FODI） process. Simulation studies were carried out on various processes with time-delay, and the results show that the proposed method could provide a better dynamic performance of both the set-point tracking and disturbance rejection and robustness against parameters perturbation.

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function, At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop svstems is guaranteed bv the proposed design method. A numerical example is given to illustrate the main results.

Stability and stabilization of discrete T-S fuzzy time-delay system based on maximal overlapped-rules group

The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.

Stability analysis and controller design of T-S fuzzy systems with time-delay under imperfect premise matching

The issue of the stability and controller design of Takagi-Sugeno（T-S） fuzzy control systems with time-delay is investigated under imperfect premise matching when the T-S fuzzy time-delay model and fuzzy controller do not share the same membership functions.A new stability criterion which contains the information of membership functions is derived.The new stability criterion is less conservative,and enhances the design flexibility.Two numerical examples are presented to illustrate the conservativeness and effectiveness of the proposed method.

Hopf Bifurcation Analysis for a Modified Time-Delay Predator-Prey System with Harvesting

In this paper, we consider the direction and stability of time-delay induced Hopf bifurcation in a delayed predator-prey system with harvesting. We show that the positive equilibrium point is asymptotically stable in the absence of time delay, but loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold. Furthermore, using the norm form and the center manifold theory, we investigate the stability and direction of the Hopf bifurcation.

Bifurcation control of solid angle car-following model through a time-delay feedback method

In order to alleviate unstable factor-caused bifurcation and reduce oscillations in traffic flow,a feedback control with consideration of time delay is designed for the solid angle model(SAM).The stability and bifurcation condition of the new SAM is derived through linear analysis and bifurcation analysis,and then accurate range of stable region is obtained.In order to explore the mechanism of the influence of multiple parameter combinations on the stability of controlled systems,a definite integral stabilization method is provided to determine the stable interval of time delay and feedback gain.Numerical simulations are explored to verify the feasibility and effectiveness of the proposed model,which also demonstrate that feedback gain and delay are two key factors to alleviate traffic congestion in the SAM.

Modeling and Control of Telerobotic Systemswith Time-delays

Telerobotic systems become more and more important due to emerging hi-technologyand practical requirement in modern society. This paper studies+ and integrates the modeling, taskscheduling, action planning and control of telerobot systems. Such hybrid syStems often involve coalmunication, command and control, and are so complex that no efficient and simple method could befound to analyze and design systems. To increase the efficiency, reliability and safety oftelrobot syStems,the consideration of task scheduling and action planning in a unified framework could be an importantstep. The discrete-event dynamics is modeled as a linear state-spare equation in Mad-Algebra sense.Performance evaluation can be carried out efficiently. Then analysis about time-delay continuous-timedynamics is given for the scheduling and control, which shows that, to simplify the design procedure,it is necessary to present a good delay scheduling, for example, by changing multi-time-delays to singleones in advance. Robustness conditions are derived using graph theory for dipcrete-event dynamics andmatrix analysis for continuous-time dynamics.

Bifurcation analysis for Hindmarsh-Rose neuronal model with time-delayed feedback control and application to chaos control

This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback control.By stability and bifurcation analysis,we find that the excitable neuron can emit spikes via the subcritical Hopf bifurcation,and exhibits periodic or chaotic spiking/bursting behaviors with the increase of external current.For the purpose of control of chaos,we adopt the time-delayed feedback control,and convert chaos control to the Hopf bifurcation of the delayed feedback system.Then the analytical conditions under which the Hopf bifurcation occurs are given with an explicit formula.Based on this,we show the Hopf bifurcation curves in the two-parameter plane.Finally,some numerical simulations are carried out to support the theoretical results.It is shown that by appropriate choice of feedback gain and time delay,the chaotic orbit can be controlled to be stable.The adopted method in this paper is general and can be applied to other neuronal models.It may help us better understand the bifurcation mechanisms of neural behaviors.

Fault detection for nonlinear networked control systems based on fuzzy observer

Security and reliability must be focused on control sys- tems firstly, and fault detection and diagnosis （FDD） is the main theory and technology. Now, there are many positive results in FDD for linear networked control systems （LNCSs）, but nonlinear networked control systems （NNCSs） are less involved. Based on the T-S fuzzy-modeling theory, NNCSs are modeled and network random time-delays are changed into the unknown bounded uncertain part without changing its structure. Then a fuzzy state observer is designed and an observer-based fault detection approach for an NNCS is presented. The main results are given and the relative theories are proved in detail. Finally, some simulation results are given and demonstrate the proposed method is effective.

Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks

The robust exponential stability of a larger class of discrete-time recurrent neural networks (RNNs) is explored in this paper. A novel neural network model, named standard neural network model (SNNM), is introduced to provide a general framework for stability analysis of RNNs. Most of the existing RNNs can be transformed into SNNMs to be analyzed in a unified way. Applying Lyapunov stability theory method and S-Procedure technique, two useful criteria of robust exponential stability for the discrete-time SNNMs are derived. The conditions presented are formulated as linear matrix inequalities (LMIs) to be easily solved using existing efficient convex optimization techniques. An example is presented to demonstrate the transformation procedure and the effectiveness of the results.

Determination of Parameters of Time-delayed Embedding Algorithm Using Koopman Operator-based Model Predictive Frequency Control

Power systems around the world have been registering a degenerating inertial response in view of the growth of inverter-based resources along with the withdrawal of conventional coal units.Therefore,there is a need for swift frequency support and its control,preferably by means of power electronic-interfaced storage devices,owing to their beneficial capabilities.Despite being particularly efficient,pragmatically,the traditional model-based non-linear control techniques are not highly popular in power system control design,primarily due to the complications faced in obtaining accurately suitable models for certain power system components.Lately,the modelfree Koopman operator-based model predictive control(KMPC)has proven to be highly conducive for data-driven non-linear control design.The principle behind KMPC is to change the coordinates in a manner to get an approximately linear model,which can then be controlled using a linear model predictive control.In this study,we employed time-delayed embedding of measurements to reconstruct a new set of preferable coordinates,thereby suggesting an approach for finding the optimal number of time lags and the embedding dimensions which are the key parameters of this algorithm.The efficacy of this KMPC framework is established by adopting a decentralized frequency control problem through a decoupled synchronous machine system,which we proposed for both the Kundur two-area system as well as the IEEE 39-bus test system.

Controlling uncertain fuzzy neutral dynamic systems with Markov jumps

The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems（MJSs） with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and time varying,and the uncertain parameters are assumed to be norm bounded.By means of Takagi-Sugeno fuzzy models,the overall closed-loop fuzzy dynamics are constructed through selected membership functions.By selecting the appropriate Lyapunov-Krasovskii functions,the sufficient condition is given such that the uncertain fuzzy neutral MJSs are stochastically stability for all admissible uncertainties and satisfies the given H∞ control index.The stability and H∞ control criteria are formulated in the form of linear matrix inequalities,which can be easily checked in practice.Practical examples illustrate the effectiveness of the developed techniques.

A Hybrid Time-delay Prediction Method for Networked Control System

This paper presents an Ethernet based hybrid method for predicting random time-delay in the networked control system.First,db3 wavelet is used to decompose and reconstruct time-delay sequence,and the approximation component and detail components of time-delay sequences are fgured out.Next,one step prediction of time-delay is obtained through echo state network(ESN)model and auto-regressive integrated moving average model(ARIMA)according to the diferent characteristics of approximate component and detail components.Then,the fnal predictive value of time-delay is obtained by summation.Meanwhile,the parameters of echo state network is optimized by genetic algorithm.The simulation results indicate that higher accuracy can be achieved through this prediction method.

Simultaneous Identification of Process Structure, Parameters and Time-delay Based on Non-negative Garrote

In practice,the model structure,parameters and time-delay of the actual process may vary simultaneously.However,the general identification methods of the 3 items are performed with separate procedures which is very inconvenient in practical application.In view of the fact that variable selection procedure can ensure a compact model with robust input-output,relation and in order to explore the feasibility of variable selection algorithm for the simultaneous identification of process structure,parameters and time-delay,non-negative garrote(NNG)algorithm is introduced and applied to system identification and the corresponding procedures are presented.The application of NNG variable selection algorithm to the identification of single input single output(SISO)system,multiple input multiple output(MIN1O)system and Wood-Berry tower industry are investigated.The identification accuracy and the time-series variable selection results are analyzed and compared between NNG and ordinary least square(OLS)algorithms.The derived excellent results show that the proposed NNG-based modeling algorithm can be utilized for simultaneous identification of the model structure,parameters and time-delay with high precision.