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.     

Time-optimal control problem for a linear parameter varying system with nonlinear item

In this paper, we considered a time-optimal control problem for a new type of linear parameter varying (LPV) system which is obtained through data identification in the process of dealing with actual problems. The addition of non-linear terms is compensation for the method that does not require linear expansion at the equilibrium point. Since the objective function is the terminal time which is an implicit function concerning decision variables, it is a non-standard optimal control problem with uncertain terminal time. To find the global optimal solution to this problem, firstly, the control parameterization method is used to transform it into a nonlinear optimization problem of parameter selection, and then the modifed particle swarm optimization (PSO) algorithm is combined to solve the equivalent nonlinear programming problem. Numerical examples are used to illustrate the effectiveness of the proposed algorithm.     

A neutral system approach to stability of singular time-delay systems

This paper is concerned with the problem of delay-dependent stability for a class of singular time-delay systems. By representing the singular system as a neutral form, using an augmented Lyapunov–Krasovskii functional and the Wirtinger-based integral inequality method, we obtain a new stability criterion in terms of a linear matrix inequality (LMI). The criterion is applicable for the stability test of both singular time-delay systems and neutral systems with constant time delays. Illustrative examples show the effectiveness and merits of the method.     

Robust identification of nonlinear time-delay system in state-space form

This paper puts forward a robust identification solution for nonlinear time-delay state-space model (NDSSM) with contaminated measurements. To enhance the robustness of the developed method for outliers, the heavy-tailed Laplace distribution is employed to describe and protect the output measurement process. The undetermined time-delay is considered to be uniformly distributed and the boundary of it is known as a priori. In the developed solution, the uncertain time-delay is treated as a latent process variable and it is iteratively calculated with the expectation–maximization (EM) algorithm. The EM algorithm is actually an iterative optimization algorithm and it is effective for the hidden variable problems. The particle filter is introduced to numerically approximate the cost function (Q-function) in the EM algorithm since it is difficult to calculate directly. The efficacy of the developed solution is evaluated via a numerical test and a two-link robotic manipulator.     

Frequency-shifting-based stable on-line algebraic parameter identification of linear systems

In this paper a new approach to algebraic parameter identification of the linear SISO systems is proposed. The standard approach to the algebraic parameter identification is based on the algebraic derivatives in Laplace domain as the main tool for algebraic manipulations like elimination of the initial conditions and generation of linearly independent equations. This approach leads to the unstable time-varying state-space realization of the filters for the on-line parameter estimation. In this paper, the finite difference and shift operators in combination with the frequency-shifting property of Laplace transform is applied instead of algebraic derivatives. Resulting state-space realization of the estimator filters is asymptotically stable and doesn’t require switch-of mechanism to prevent overflow of the estimator variables. The proposed method is especially suitable for applications in closed-loop on-line identification where the stable behavior of the estimators is a necessary requirement. The efficiency of the proposed algorithm is illustrated on three simulation examples.     

State space model identification of multirate processes with time-delay using the expectation maximization

This paper presents the problems of state space model identification of multirate processes with unknown time delay. The aim is to identify a multirate state space model to approximate the parameter-varying time-delay system. The identification problems are formulated under the framework of the expectation maximization algorithm. Through introducing two hidden variables, a new expectation maximization algorithm is derived to estimate the unknown model parameters and the time-delays simultaneously. The effectiveness of the proposed algorithm is validated by a simulation example.     

Sliding mode state and parameter identification for linear stochastic systems

This paper presents the sliding mode mean-square and mean-module state filtering and parameter identification problems for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered Wiener processes. The original problems are reduced to the sliding mode mean-square and mean-module filtering problems for an extended state vector that incorporates parameters as additional states. The obtained sliding mode filters for the extended state vector also serve as the optimal identifiers for the unknown parameters. Performance of the designed sliding mode mean-square and mean-module state filters and parameter identifiers are verified for both, stable and unstable, linear uncertain systems.     

New finite-time stability for fractional-order time-varying time-delay linear systems: A Lyapunov approach

The primary goal of this paper is to examine the finite-time stability and finite-time contractive stability of the linear systems in fractional domain with time-varying delays. We develop some sufficient criteria for finite-time contractive stability and finite-time stability utilizing fractional-order Lyapunov-Razumikhin technique. To validate the proposed conditions, two different types of dynamical systems are taken into account, one is general time-delay fractional-order system and another one is fractional-order linear time-varying time-delay system, furthermore the efficacy of the stability conditions is demonstrated numerically.     

基于时变参数模型的能源回弹效应研究

在能源增进型技术进步的假设前提下,以内生经济增长理论为基础,构建劳动和能源效率内生化的新古典C-D生产函数。结合时变参数模型和卡尔曼滤波迭代估计等方法对北京市1981—2014年的短期和长期能源回弹效应进行了实证分析。研究发现,北京市短期能源回弹效应均值为149.29%,整体上处于逆反效应;长期能源回弹效应均值为79.21%,存在较强的部分回弹效应。从长期来看,北京市以能效改进为核心的节能减排政策是可行的,但要注意短期内由于城市经济规模扩张带来的能源回弹效应。最后,从技术创新、产业结构、要素投入及要素价格改革方面提供了限制能源回弹效应的政策思路。     

Exponential stability for linear time-delay systems with delay dependence

This paper focuses on the problem of advancing a theorem to estimate the stability bound of delay decay rate α and upper bound delay time τ to guarantee the stability of time-delay systems. Based on the Lyapunov–Krasovskii functional techniques and linear matrix inequality tools, exponential stability and decaying rate for linear time-delay systems are also derived. These results are shown to be less conservative than those reported in the literature. Examples are included to illustrate our results.     

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence.     

Output stabilization of a class of second-order linear time-delay systems: An eigenvalue approach

This paper studies linear time-invariant systems with an input delay and two repeated or distinct real poles. The closed-loop system eigenvalue-loci with respect to the output feedback controller gain are investigated by using the Lambert function and root-locus construction techniques. Output feedback stabilization conditions and stability robustness with respect to the delay time uncertainty are established. Also, the response performance is discussed. Three examples and related simulations are presented to illustrate the analysis results.     

Auxiliary model based least squares parameter estimation algorithm for feedback nonlinear systems using the hierarchical identification principle

This paper presents a decomposition based least squares estimation algorithm for a feedback nonlinear system with an output error model for the open-loop part by using the auxiliary model identification idea and the hierarchical identification principle and by decomposing a system into two subsystems. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm has a smaller computational burden. The simulation results indicate that the proposed algorithm can estimate the parameters of feedback nonlinear systems effectively.     

Walsh series approach to lumped and distributed system identification

This paper considers the problem of identifying the parameters of dynamic systems from input-output records. Both lumped-parameter and distributed-parameter systems, deterministic and stochastic, are studied. The approach adopted is that of expanding the system variables in Walsh series. The key point is an operational matrix P which relates the coefficient matrix Г of the Walsh series of a given function with the coefficient matrix of its first derivative. Using this operational matrix P one overcomes the necessity to use differentiated data, a fact that usually is avoided either by integration of the data or by using discrete-time models. Actually, the original differential input-output model is converted to a linear algebraic (or regression) model convenient for a direct (or a least squares) solution. A feature of the method is that it permits the identification of unknown initial conditions simultaneously with the parameter identification. The results are first derived for single-input single-output systems and then are extended to multi-input multi-output systems. The case of non-constant parameters is treated by assuming polynomial forms. Some results are also included concerning the identification of state-space and integral equation models. The theory is supported by two examples, which give an idea of how effective the method is expected to be in the real practice.     

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.     

Tracking control of nonlinear automobile idle-speed time-delay system via differential geometry approach

This paper is concerned with the problem of global asymptotical tracking of single-input single-output (SISO) nonlinear time-delay control systems. Based on the input-output feedback linearization technique and Lyapunov method for nonlinear state feedback synthesis, a robust globally asymptotical output tracking controller design methodology for a broad class of nonlinear time-delay control systems is developed. The underlying theoretical approaches are the differential geometry approach and the composite Lyapunov approach. One utilizes the parameterized co-ordinate transformation to transform the original nonlinear system into singularly perturbed model and the composite Lyapunov approach is then applied for output tracking. For the view of practical application, the proposed control methodology has been successfully applied to the famous nonlinear automobile idle-speed control system.