Multiple model approach to linear parameter varying time-delay system identification with EM algorithm

This paper is concerned with the identification problem of linear parameter varying (LPV) time-delay systems. Due to inherent nonlinearity, the industrial processes are often approximately described by an LPV model constructed by synthesizing multiple local models. Time-delay is commonly experienced in industrial processes and it can be parameter varying or constant in the process model. The multiple model identification of LPV systems with parameter varying or constant time-delay is formulated in the scheme of the expectation-maximization (EM) algorithm and the parameter varying property and the time-delay property of the process are handled simultaneously. The irrigation channel example and high purity distillation column example are used to present the effectiveness of the proposed method.     

Robust identification of Wiener time-delay system with expectation-maximization algorithm

This paper considers the parameter estimation for Wiener time-delay systems with the output data contaminated with outliers. The time-delay and corrupted output data bring great challenges to the parameter estimation problem. The statistical model of the estimation problem is constructed based on the Laplace distribution and the identification problem is formulated in the scheme of the expectation-maximization (EM) algorithm. The negative effect of outliers imposed on the parameter estimation problem is sufficiently suppressed and the unknown time-delay and model parameters can be estimated simultaneously. The simulation example is given to demonstrate the effectiveness of the proposed algorithm.     

Closed-loop identification of stable and unstable processes with time-delay

This article concerned with the parametric identification problem of continuous-time process dynamics with unknown time-delay. An improved closed-loop approach is developed to carryout process identification in terms of generalized first and second order plus time-delay (GFOPTD & GSOPTD) process models. These generalized models can include both stable and unstable plant dynamics. The key feature of the proposed method over existing techniques is its effective indirect nature, where the mathematical formulation is developed to identify continuous process dynamics and time-delay parameters, indirectly in terms of discrete parameters. The advantage of the proposed indirect method is that it not only allows to accurately identify process parameters but helps in achieving the single parameter based convergence, which is also proved mathematically. The identification accuracy and robustness of the proposed technique in the presence of measurement noise and modeling uncertainties is corroborated with the help of simulation examples on benchmark problems and by using a practical tank process experiment.     

Necessary conditions of exponential stability for a class of linear uncertain systems with a single constant delay

In this paper, we will investigate the necessary conditions, described by the Lyapunov matrix, for the robust exponential stability for a class of linear uncertain systems with a single constant delay and time-invariant parametric uncertainties, which are some generalizations of the existing results on uncertain linear time-delay systems. As a medium step, several pivotal properties of parameter-dependent Lyapunov matrix are proposed, which set up the relationships between fundamental matrix and Lyapunov matrix for the considered system. In addition, to calculate the parameter-dependent Lyapunov matrix, we introduce the differential equation method and the Lagrange interpolation method, respectively. Furthermore, it is noted that the proposed necessary conditions can be used to estimate the range of time delay, when the linear uncertain time-delay system is robust exponential stability. Finally, the validity of the obtained theoretical results is illustrated via numerical examples.     

Internet of health things encryption via master-slave synchronization for stochastic quaternion-valued neural networks

This paper investigates the problem of master-slave synchronization of stochastic quaternion-valued neural networks (SQVNNs) with mixed time-varying delays. A linear feedback controller is developed to explore the global synchronization of the proposed system by utilizing the complete information of the time-delay state. Sufficient conditions for synchronization of the proposed model are derived by constructing appropriate Lyapunov–Krasovskii functional by applying the master-slave synchronization method of master-slave and some integral inequality techniques. Finally, a corresponding numerical simulation is presented to demonstrate the accuracy of the theoretical results. This paper introduces a unique and efficient image encryption algorithm based on SQVNNs. This technique utilizes the solution set of SQVNNs to generate the high-level randomness secret keys to encrypt the source image. Finally, we conclude that the algorithm yields a source image cipher with excellent diffusion and confusion properties. A few test clinical images are utilized to show the validity of the proposed method. Several performance analyses show that the proposed algorithm for image encryption gives an efficient and secure way to deal with the Internet of Health Things (IoHT).     

Robust suboptimal feedback control for a fed-batch nonlinear time-delayed switched system

The optimal control strategy constructed in the form of a state feedback is effective for small state perturbations caused by changes in modeling uncertainty. In this paper, we investigate a robust suboptimal feedback control (RSPFC) problem governed by a nonlinear time-delayed switched system with uncertain time delay arising in a 1,3-propanediol (1,3-PD) microbial fed-batch process. The feedback control strategy is designed based on the radial basis function to balance the two (possibly competing) objectives: (i) the system performance (concentration of 1,3-PD at the terminal time of the fermentation) is to be optimal; and (ii) the system sensitivity (the system performance with respect to the uncertainty of the time-delay) is to be minimized. The RSPFC problem is subject to the continuous state inequality constraints. An exact penalty method and a novel time scaling transformation approach are used to transform the RSPFC problem into the one subject only to box constraints. The resulting problem is solved by a hybrid optimization algorithm based on a filled function method and a gradient-based algorithm. Numerical results are given to verify the effectiveness of the developed hybrid optimization algorithm.     

Identification of Gaussian process with switching noise mode and missing data

In traditional system identification methods, it is often assumed that the output data are corrupted by Gaussian white noise which is independent and identically distributed (i.i.d.). However, this assumption may lead to poor robustness since the noise characteristic often varies throughout the sampling process. In this work, output measurements affected by switching Gaussian noise are considered. In addition, a Markov chain model is utilized to describe the multi-mode behavior of the noises. Meanwhile, the collected data are usually incomplete in practice. Taking these circumstances into account, a new algorithm for Gaussian process regression (GPR) with switching noise mode and missing data is introduced. The parameters of the model are estimated by expectation maximization (EM) algorithm via conjugate gradient (CG) method. Two numerical examples along with a continuous stirred tank reactor simulation are employed to verify the effectiveness of the proposed algorithm. The superior performance is demonstrated by comparing the proposed algorithm with other existing relevant methods.     

Fractional-order partial pole assignment for time-delay systems based on resonance and time response criteria analysis

In this paper, a novel fractional-order partial pole assignment (FPPA) control algorithm is proposed for systems with time-delay. The FPPA control algorithm is essentially an extension of the original pole assignment, which could change undesired pole locations into desired pole locations. The presented control scheme can be used on open loop poorly damped or unstable systems, which is superior to most other time-delay compensation schemes. The discussion on choosing desirable pole locations is presented based on stability and resonance conditions in the frequency domain. The controlled system is also studied in the time domain based on different transient performance indicators, namely overshoot, settling time, and rising time. In addition, the parameters of the proposed FPPA control algorithm are tunable, thus the control scheme can be used to satisfy different control requirements. Simulation results of stable and unstable fractional-order plants with time-delay are shown to verify the effectiveness and practicability of the FPPA control algorithm.     

Sampled-data control for time-delay systems

The sampled-data systems are hybrid ones involving continuous time and discrete time signals, which makes the traditional analysis and synthesis methodologies of time-delay systems unable to be directly used in the cases of hybrid systems with time-delay. The primary disadvantages of current design techniques of sampled-data control are their inabilities to deal effectively with time-delay and the model uncertainty. In this paper, we generalized the analysis methodology of time-delay systems to that of the hybrid systems with time-delay and uncertainty, which developed a design procedure of sampled-data control for time-delay systems. Asymptotic stability of the time-delay hybrid systems was developed. The time-delay dependent robust sampled-data control for the time-varying delay of an uncertain linear system was then discussed. The results were described as linear matrix inequalities, which can be solved using newly released LMITool.     

Moving horizon estimation for multirate systems with time-varying time-delays

This paper presents a moving horizon estimation approach for the multirate sampled-data system with unknown time-delay sequence. To estimate the unknown variables of interest, two main challenging issues need to be addressed: (a) synthesizing the multirate input and output data for state estimation, (b) simultaneously estimating the continuous state and discrete time-delay sequence. In this work a moving horizon estimation based approach is developed to tackle these issues. The proposed approach can simultaneously estimate both the continuous states and discrete time-delay sequence for dynamic systems. The effects of different noise level on the estimation of continuous states and discrete time-delay sequence are analyzed. The effectiveness of this method is illustrated through a simulation study.     

Comparison principle for positive time-delay systems: An extension and its application

This paper proposes an extended comparison principle for continuous-time linear positive time-delay systems. Unlike the existing comparison principle, which uses a constant initial function for the comparison system, instead, we propose a time-varying initial function in order to derive a more general solution comparison. Based on this extended comparison principle, we develop a novel computational method, which exploits more effectively the information of the initial value function, to derive tighter exponential estimates for the state vector of positive time-delay systems. The effectiveness of our developed method is illustrated through two numerical examples.     

Control of a time-varying hypersonic vehicle model subject to inlet un-start condition

A performance-guaranteed fault-tolerant controller is proposed for air-breathing hypersonic vehicles (AHVs) with synthetical consideration on time-varying uncertain parameters and inlet un-start condition. Different from most of the existing strategies for AHVs, the possible time-varying uncertain parameters in the control-oriented model are accommodated, which makes the resulting controller more adaptable to a real flight. Moreover, the velocity-dependent constraint on angle-of-attack, which is an important factor keeping the scramjet away from inlet un-start, is taken into account. With the utilization of barrier functions in adaptive design, velocity and altitude tracking errors are bounded by specific performance functions. Relevant analysis shows that the tracking performance can be further improved by proper adjustments on design parameters. The effectiveness of our proposed controller is evaluated through a simulation study.     

Modeling and solution of two-dimensional input time-delay system

The discrete-time model of the two-dimensional continuous-time input time-delay system is newly presented in this paper, and the solution of the continuous-time input time-delay system is then solved based on the newly presented discrete-time model. The presented discrete-time model significantly facilitates analysis and design of a system when it faces the unavoidable inherent time delay and the computation time delay which can be modeled as a part of delay at the system input, in practice.     

A robust global approach for LPV FIR model identification with time-varying time delays

Robust identification of the linear parameter varying (LPV) finite impulse response (FIR) model with time-varying time delays is considered in this paper. A robust observation model based on Laplace distribution is established to deal with the output data contaminated with the outliers, which are commonly existed in modern industries. A Markov chain model is utilized to model the correlation between the time delays as they do not simply change randomly in reality. A transition probability matrix and an initial probability distribution vector are used to govern the switching mechanism of the time delays. Since it is difficult to optimize the complex log likelihood function directly, the derivations of the proposed algorithm are performed under the framework of Expectation-Maximization (EM) algorithm. A numerical example and a chemical process are utilized to verify the effectiveness of the proposed approach.     

Tracking control algorithms for plants with input time-delays based on state and disturbance predictors and sub-predictors

The novel control algorithm for linear time invariant plants with input time-delays and presence of external disturbances is proposed. The algorithm based on the state and disturbance predictors ensures the tracking control with unknown reference model parameters. The accuracy in steady state depends on the highest derivative of disturbance and reference model signals, therefore, the magnitude of these signals can be sufficiently large. Further, the proposed algorithm are extended on the state and disturbance sub-predictors which implement multi-step prediction. Compared with the predictor based algorithm the sub-predictor based algorithm allows to control plants with a larger input time-delay and allows to predict the disturbance in less time. The sufficient conditions in terms of linear matrix inequalities (LMIs) provide the estimate of the maximum time-delay that preserves the closed-loop system stability. Numerical examples illustrate the efficiency of the designed method compared with some existing ones.     

混合指数分布定数结尾时参数估计的Monte Carlo EM加速算法

应用Monte Carlo EM加速算法对于单参数混合指数分布在定数结尾场合的参数估计问题做了较深入的探讨,做出了模拟试验。     

Robust identification of linear ARX models with recursive EM algorithm based on Student’s t-distribution

This paper considers the robust identification issue of linear systems represented by autoregressive exogenous models using the recursive expectation-maximization (EM) algorithm. In this paper, a recursive Q-function is formulated based on the maximum likelihood principle. Meanwhile, the outliers that frequently appear in practical processes are accommodated with the Student’s t-distribution. The parameter vector, variance of noise, and the degree of freedom are recursively estimated. Finally, a numerical example, as well as a simulated continuous stirred tank reactor (CSTR) system, is performed to verify the effectiveness of the proposed recursive EM algorithm.     

Event-triggered consensus of nonlinear multi-agent systems with stochastic switching topology

This paper is concerned with a leader-follower consensus problem for networked Lipschitz nonlinear multi-agent systems. An event-triggered consensus controller is developed with the consideration of discontinuous state feedback. To further enhance the robustness of the proposed controller, modeling uncertainty and switching topology are also considered in the stability analysis. Meanwhile, a time-delay equivalent approach is adopted to deal with the discrete-time control problem. Particularly, a sufficient condition for the stochastic stabilization of the networked multi-agent systems is proposed based on the Lyapunov functional method. Furthermore, an optimization algorithm is developed to derive the parameters of the controller. Finally, numerical simulation is conducted to demonstrate the effectiveness of the proposed control algorithm.     

LMI based sampled-data controller for synchronization on the time-delay Darcy-Brinkman model

This paper analyzed the sampled-data controller for using time-delay nonlinear systems with a bounded uncertainty approach. Based on the Lyapunov stability theory, some synchronization criteria are first obtained. Here, the time-delay is assumed to be constant and known. Instead of solving a nonlinear optimization problem, it will be developed by solving a set of linear matrix inequalities (LMIs). The controller gains can be obtained by solving a set of LMIs. During the development of the Darcy-Brinkman model, numerical examples are used to demonstrate the accuracy and dependability of the presented approaches. Finally, numerical simulations show that the proposed solutions are effective and feasible.