Computational relaxed TP model transformation: restricting the computation to subspaces of the dynamic model

The tensor‐product (TP) model transformation is a recently proposed numerical method capable of transforming linear parameter varying state‐space models to the higher order singular value decomposition (HOSVD) based canonical form of polytopic models. It is also capable of generating various types of convex TP models, a type of polytop models, for linear matrix inequality based controller design. The crucial point of the TP model transformation is that its computational load exponentially explodes with the dimensionality of the parameter vector of the parameter‐varying state‐space model. In this paper we propose a modified TP model transformation that leads to considerable reduction of the computation. The key idea of the method is that instead of transforming the whole system matrix at once in the whole parameter space, we decompose the problem and perform the transformation element wise and restrict the computation to the subspace where the given element of the model varies. The modified TP model transformation can readily be executed in higher dimensional cases when the original TP model transformation fails. The effectiveness of the new method is illustrated with numerical examples. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

COMPLEXITY RELAXATION OF THE TENSOR PRODUCT MODEL TRANSFORMATION FOR HIGHER DIMENSIONAL PROBLEMS

The Tensor Product (TP) model transformation method was proposed recently as an automated gateway between a class of non‐linear models and linear matrix inequality based control design. The core of the TP model transformation is the higher order singular value decomposition of a large sized tensor, which requires high computational power that is usually outside of a regular computer capacity in cases of higher dimensionality. This disadvantage restricts the utilization of the TP model transformation to models having smaller dimensionality. The aim of this paper is to propose a computationally relaxed version of the TP model transformation. The paper also presents a 6 dimensional example to show the effectiveness of the modified transformation.     

Incorporating domain-specific knowledge into a genetic algorithm to implement case-based reasoning adaptation

In case-based reasoning systems the adaptation phase is a notoriously difficult and complex step. The design and implementation of an effective case adaptation algorithm is generally determined by the type of application which decides the nature and the structure of the knowledge to be implemented within the adaptation module, and the level of user involvement during this phase. A new adaptation approach is presented in this paper which uses a modified genetic algorithm incorporating specific domain knowledge and information provided by the retrieved cases. The approach has been developed for a CBR system (CBEM) supporting the use and design of numerical models for estuaries. The adaptation module finds the values of hundreds of parameters for a selected numerical model retrieved from the case-base that is to be used in a new problem context. Without the need of implementing very specific adaptation rules, the proposed approach resolves the problem of acquiring adaptation knowledge by combining the search power of a genetic algorithm with the guidance provided by domain-specific knowledge. The genetic algorithm consists of a modifying version of the classical genetic operations of initialisation, selection, crossover and mutation designed to incorporate practical but general principles of model calibration without reference to any specific problems. The genetic algorithm focuses the search within the parameters' space on those zones that most likely contain the required solutions thus reducing computational time. In addition, the design of the genetic algorithm-based adaptation routine ensures that the parameter values found are suitable for the model approximation and hypotheses, and complies with the problem domain features providing correct and realistic model outputs. This adaptation method is suitable for case-based reasoning systems dealing with numerical modelling applications that require the substitution of a large number of parameter values.     

基于PSO算法的probit模型参数估计

针对二值probit回归模型中的参数估计问题,提出一种基于粒子群优化（PSO）的参数估计算法。该算法采用以最大似然准则作为PSO的适应度函数,建立二值probit回归模型中的参数估计计算模型。数值仿真分析表明,该算法性能较好,回归结果具有较高的拟合优度。     

Influence of the Tensor Product Model Representation of qLPV Models on the Feasibility of Linear Matrix Inequality Based Stability Analysis

The paper investigates and proves the statement, that the convex hull of the polytopic tensor product (TP) model representation influences the feasibility of linear matrix inequality (LMI) based stability analysis methods. The proof is based on a complex stability analysis example of a given quasi linear parameter varying (qLPV) state‐space model. Specifically, the three degree of freedom (3‐DoF) aeroelastic wing section model including Stribeck friction is used as the tool for the example model. The proof is achieved by utilizing TP model transformation and LMI based tools. As a first step, numerous TP model type control solutions holding different convex hulls are systematically derived of the qLPV model via LMI based control design methods. As a second step, each control solution is further equivalently transformed for different TP model representations holding different convex hulls. Finally, the stability of all solutions over all TP model representations are checked via LMI based stability analysis methods. As a result of the two steps, a two dimensional (2D) convex hull space is attained for the 3‐DoF aeroelastic wing section model. The two dimensions are denoted by the LMI based control design and the LMI based stability analysis for different convex hulls. Based on the numerical results, a detailed, comprehensive analysis is provided. The paper as a novelty proves the statement, that the polytopic TP model representation of a given control solution strongly influences the feasibility of LMI based stability analysis methods.     

Synchronizing concurrent model updates based on bidirectional transformation

Model-driven software development often involves several related models. When models are updated, the updates need to be propagated across all models to make them consistent. A bidirectional model transformation keeps two models consistent by updating one model in accordance with the other. However, it does not work when the two models are modified at the same time. In this paper we first examine the requirements for synchronizing concurrent updates. We view a synchronizer for concurrent updates as a function taking the two original models and the two updated models as input, and producing two new models where the updates are synchronized. We argue that the synchronizer should satisfy three properties that we define to ensure a reasonable synchronization behavior. We then propose a new algorithm to wrap any bidirectional transformation into a synchronizer with the help of model difference approaches. We show that synchronizers produced by our algorithm are ensured to satisfy the three properties if the bidirectional transformation satisfies the correctness property and the hippocraticness property. We also show that the history ignorance property contributes to the symmetry of our algorithm. An implementation of our algorithm shows that it worked well in a practical runtime management framework.     

APPROXIMATION PROPERTIES OF TP MODEL FORMS AND ITS CONSEQUENCES TO TPDC DESIGN FRAMEWORK

Tensor Product Distributed Compensation (TPDC) is a recently established controller design framework, that links TP model transformation and Parallel Distributed Compensation (PDC) framework. TP model transformation converts different models to a common representational form: the TP model form. The primary aim of this paper is to investigate the approximation capabilities of TP model forms, because the universal applicability of TPDC framework strongly relies on it. We point out that the set of functions that can be approximated arbitrarily well by TP forms with bounded number of components lies no‐where dense in the set of continuous functions. Consequently, in a class of control problems this property necessitates the usage of tradeoff techniques between the accuracy and the complexity of the TP form, which is easily feasible within the TPDC framework unlike in analytic models.     

Augmented TP model transformation‐based parallel distributed compensation control design

The usual sampled hyper grid points of uniform sampling method are distributed equally in the TP model transformation, thus, the sampling results often omit the local extrema when the sampling step is not fine‐tuned. Then the resultant tensor which is used for controller design can not fully cover the state space, although the gain which is the feasible solution of the linear matrix inequalities. In this paper, we proposed a non‐uniform sampling method for tensor product model transformation, local extrema are considered in the sampling step, while the sampling step can vary dynamically for different function entries. In this paper, TP model transformation‐based parallel distributed compensation (PDC) controller is extended in three folds: (i) The existing TP model transformation‐based PDC controller with uniform sampling method is extended to TP model transformation‐based PDC tracking controller with the uniform sampling method and an extended signal. (ii) A new TP model transformation‐based PDC tracking controller is proposed based on a new sampling method, that is, the Hammersley sampling method. (iii) TP model transformation‐based PDC tracking controller is also proposed based on the non‐uniform sampling method. The proposed adaptive TP model transformation‐based PDC tracking controller is able to enhance the performance of the TP model transformation‐based PDC controller, and the adaptive TP model transformation‐based PDC controller obtains the best results due to the nearly exact sampling of the system.     

限定记忆参数估计的Householder变换快速递推算法

利用Householder变换推导出一个新的最小二乘估计的限定记忆快速递推算法(RHFM). 该算法具有运算量小,数值稳定性好、占用内存少的优点,可以用于各种静、动态模型的参 数估计.     

Stochastic Control of Linear and Nonlinear Econometric Models: Some Computational Aspects

This paper considers the optimal control of small econometric models applying the OPTCON algorithm. OPTCON determines approximate numerical solutions to optimum control problems for nonlinear stochastic systems. These optimum control problems consist in minimizing a quadratic objective function for linear and nonlinear econometric models with additive and multiplicative (parameter) uncertainties. The algorithm was programmed in C# and in MATLAB and allows for stochastic control with open-loop and passive learning (open-loop feedback) information patterns. Here we compare the results of applying the OPTCON2 version of the algorithm to two macroeconomic models for Slovenia, the nonlinear model SLOVNL and the linear model SLOVL. The results for both models are similar, with open-loop feedback controls giving better results on average and less outliers than open-loop controls. The number of outliers is higher in the nonlinear case and especially under high parameter uncertainty.     

Novel techniques in parameter estimation for fractional dynamical models arising from biological systems

In recent years, both parameter estimation and fractional calculus have attracted a considerable interest. Parameter estimation of the fractional dynamical models is a new topic. In this paper, we consider novel techniques for parameter estimation of fractional nonlinear dynamical models in systems biology. First, a computationally effective fractional Predictor-Corrector method is proposed for simulating fractional complex dynamical models. Second, we convert the parameter estimation of fractional complex dynamical models into a minimization problem of the unknown parameters. Third, a modified hybrid simplex search (MHSS) and a particle swarm optimization (PSO) is proposed. Finally, these techniques are applied to a dynamical model of competence induction in a cell with measurement error and noisy data. Some numerical results are given that demonstrate the effectiveness of the theoretical analysis.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Incorporation of prior knowledge in neural network model for continuous cooling of steel using genetic algorithm

Artificial neural network model is developed for the prediction of phase transformation of steel from austenite, and thus construction of the continuous cooling transformation (CCT) diagram. The model for prediction of transformation temperatures from steel composition is developed using data from published CCT diagrams. The trained network sometimes fails to predict the sequence of the phase transformation, contradicting the fundamentals of metallurgy. To avoid such limitations of data driven models and to make the models truthful and reasonable from metallurgical standpoint, prior knowledge is incorporated using genetic algorithm, through modifying the weights and biases of a trained neural network. The conventionally backpropagated multi-layered perceptron is modified from error minimization as well as knowledge incorporation point of view through formulation of the problem in both single and multi-objective optimization domains. The predictions of six transformation temperatures by the new models are found to be significantly better than the conventionally trained model.     

GLOBAL ASYMPTOTIC STABILIZATION OF THE PROTOTYPICAL AEROELASTIC WING SECTION VIA TP MODEL TRANSFORMATION

A comprehensive analysis of aeroelastic systems has shown that these systems exhibit a broad class of pathological response regimes when certain types of non‐linearities are included. In this paper, we propose a design method of a state‐dependent non‐linear controller for aeroelastic systems that includes polynomial structural non‐linearities. The proposed method is based on recent numerical techniques such as the Tensor Product (TP) model transformation and the Linear Matrix Inequality (LMI) control design methods within the Parallel Distributed Compensation (PDC) frameworks. In order to link the TP model transformation and the LMI's in the proposed design method, we extend the TP model transformation with a further transformation. As an example, a controller is derived that ensures the global asymptotic stability of the prototypical aeroelastic wing section via one control surface, in contrast with previous approaches which have achieved local stability or applied additional control actuator on the purpose of achieving global stability. Numerical simulations are used to provide empirical validation of the control results. The effectiveness of the controller design is compared with a former approach.     

单相热工对象的一种解析--数值仿真方法

该文针对热力系统中常见的单相分布参数热工对象,建立了分布参数数学模型;在指定的控制微元内,通过对模型的假设和简化以及对系数T,X的常数化,并对该模型进行双拉普拉斯变换,获得了模型的解析解;并以此为基础,构造了单相分布参数热工对象的一种解析一数值混合仿真方法。利用此方法,既可以进行单相分布参数换热系统的动态过程分析,又能够完成此类对象的静态热力特性校核。与其他分布参数模型的处理方法相比较,该文的仿真方法不仅具有较高的运算精度,而且在较大的时间步长下也有非常好的数值稳定性。通过调节步长可以提高计算速度,以满足不同仿真目的的需要。     

基于SVD的推广卡尔曼滤波及其在飞行状态和参数估计中的应用

基于矩阵的奇异值分解技术，本文提出一种鲁棒推广卡尔曼波新算法，并将该算法应用于飞行状态和参数估计中，该算法不仅具有很好的数值稳定性，而且无需任何变换即可处理相关噪声，且适于并行计算。两种不同型号飞机飞行数据计算结果表明；与ＥＫＦ相比，本文算法对不同初始值的不同噪声均可获得更准确的估计结果，并且对飞机机动形式、噪声水平，数据长度等要求不高，收敛性好。     

An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models

In this study, an enhanced Kalman Filter formulation for linear in the parameters models with inherent correlated errors is proposed to build up a new framework for nonlinear rational model parameter estimation. The mechanism of linear Kalman filter (LKF) with point data processing is adopted to develop a new recursive algorithm. The novelty of the enhanced linear Kalman filter (EnLKF in short and distinguished from extended Kalman filter (EKF)) is that it is not formulated from the routes of extended Kalman Filters (to approximate nonlinear models by linear approximation around operating points through Taylor expansion) and also it includes LKF as its subset while linear models have no correlated errors in regressor terms. No matter linear or nonlinear models in representing a system from measured data, it is very common to have correlated errors between measurement noise and regression terms, the EnLKF provides a general solution for unbiased model parameter estimation without extra cost to convert model structure. The associated convergence is analysed to provide a quantitative indicator for applications and reference for further research. Three simulated examples are selected to bench-test the performance of the algorithm. In addition, the style of conducting numerical simulation studies provides a user-friendly step by step procedure for the readers/users with interest in their ad hoc applications. It should be noted that this approach is fundamentally different from those using linearisation to approximate nonlinear models and then conduct state/parameter estimate.     

一种支持向量回归机自动模型选择方法

为解决SVR(支持向量回归)自动模型选择的问题,提出一种基于梯度下降算法的支持向量回归机模型参数优化方法.通过最小化模型选择准则R2w2,对核参数集采用梯度下降算法得到局部最优的模型参数.依据黎曼几何为理论,提出一种适合于SVR的保角变换,对核函数进行数据依赖的改进,进一步提高SVR的泛化能力.仿真试验的结果验证了该方...     

Speaker identification using multi-step clustering algorithm with transformation-based GMM

To improve the performance of speaker recognition, the embedded linear transformation is used to integrate both transformation and diagonal-covariance Caussian mixture into a unified framework. In the case, the mixture number of GMM must be fixed in model training. The cluster expectation-maximization (EM) algorithm is a well-known technique in which the mixture number is regarded as an estimated parameter. This paper presents a new model structure that integrates a multi-step cluster algorithm into the estimating process of GMM with the embedded transformation. In the approach, the transformation matrix, the mixture number and model parameters are simultaneously estimated according to a maximum likelihood criterion. The proposed method is demonstrated on a database of three data sessions for text independent speaker identification. The experiments show that this method outperforms the traditional GMM with cluster EM algorithm. This text was submitted by the authors in English.     

模型在线辨识方法及其应用

本文提出了一种有效的非线性模型和参数在线估计方法。为了实现模型在线辨识，本文根据误差性能指标，给出了模型判据及计算式。根据递推加权最小二乘算法和优选判据，导出了模型和参数同时在线估计的有效算法。为了提高计算效率和数值稳定性，模型辨识和参数辨识均采用了Ｕ－Ｄ分解方法。新方法可用于飞行器非线性气动模型和参数的实时估计。实际应用结果表明，使用该方法可以有效地确定多项式、样条函数模型结构，参数辨识的结果满