Experiment design for grey box identification

Grey box models are characterized by their physical significance e.g. in parametrization and by the partial prior information that is available about e.g. the parameter values. These aspects of the grey box model affect the design of optimal excitations for identification and we study the extension of classical theory for experiment design to input design for identification of grey box models. Partial prior information is expressed as a probability distribution and is employed in the design of optimal excitations through optimization of Bayesian criteria.     

Stable adaptive identification of fully-coupled second-order 6 degree-of-freedom nonlinear plant models for underwater vehicles: Theory and experimental evaluation

This article reports the development, stability analysis, and experimental evaluation of a novel adaptive identification (AID) algorithm for underwater vehicles (UVs) for on-line estimation of plant parameters (hydrodynamic mass, quadratic drag, righting moment, and buoyancy parameters) that enter linearly into 6 degree-of-freedom (6-DOF) second-order rigid-body UV plant dynamic models. The reported UV AID method does not require instrumentation of vehicle acceleration as is required of other standard plant parameter identification methods such as conventional least squares. All but one previously reported adaptive methods for second-order nonlinear plants have addressed the problem of model-based adaptive tracking control—approaches in which adaptive plant model identification is performed simultaneously with model-based trajectory-tracking control of fully-actuated second-order plants; however, these approaches are not applicable when the plant is either uncontrolled, under open-loop control, underactuated, or using any control law other than an algorithm-specific adaptive tracking controller. The UV AID algorithm reported herein does not require simultaneous reference trajectory-tracking control, nor does it require instrumentation of linear acceleration or angular acceleration; thus this novel approach complements previously reported adaptive tracking methods and is applicable to a broader class of UV applications for which fully-actuated tracking control is impractical or infeasible. We report a experimental performance analysis of the UV AID algorithm in comparison to conventional least-square identification methods, including comparison in cross-validation where the performance of the experimentally identified plant models obtained in identification trials are compared to experimental trials differing from the identification trials.     

Generalized Wiener system identification: General backlash nonlinearity and finite impulse response linear part

In this paper, we develop an algorithm for identification of the finite impulse response linear part of a block‐oriented Wiener System. The nonlinear block is a general backlash function with nonlinear ascending and descending functions. Only the horizontal axis intersection points are assumed known a priori. We propose an identification algorithm and establish identifiability. Simulation results are also presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Maximum likelihood hierarchical least squares-based iterative identification for dual-rate stochastic systems

For a dual-rate sampled-data stochastic system with additive colored noise, a dual-rate identification model is obtained by using the polynomial transformation technique, which is suitable for the available dual-rate measurement data. Based on the obtained model, a maximum likelihood least squares-based iterative (ML-LSI) algorithm is presented for identifying the parameters of the dual-rate sampled-data stochastic system. In order to improve the computation efficiency of the algorithm, the identification model of a dual-rate sampled-data stochastic system is divided into two subidentification models with smaller dimensions and fewer parameters, and a maximum likelihood hierarchical least squares-based iterative (H-ML-LSI) algorithm is proposed for these subidentification models by using the hierarchical identification principle. The simulation results indicate that the proposed algorithms are effective for identifying dual-rate sampled-data stochastic systems and the H-ML-LSI algorithm has a higher computation efficiency than the ML-LSI algorithm.     

Maximum likelihood-based adaptive differential evolution identification algorithm for multivariable systems in the state-space form

Parameter estimation plays an important role in the field of system control. This article is concerned with the parameter estimation methods for multivariable systems in the state-space form. For the sake of solving the identification complexity caused by a large number of parameters in multivariable systems, we decompose the original multivariable system into some subsystems containing fewer parameters and study identification algorithms to estimate the parameters of each subsystem. By taking the maximum likelihood criterion function as the fitness function of the differential evolution algorithm, we present a maximum likelihood-based differential evolution (ML-DE) algorithm for parameter estimation. To improve the parameter estimation accuracy, we introduce the adaptive mutation factor and the adaptive crossover factor into the ML-DE algorithm and propose a maximum likelihood-based adaptive differential evolution algorithm. The simulation study indicates the efficiency of the proposed algorithms.     

Adaptive control of stochastic nonlinear systems with uncontrollable linearization

For a class of high‐order stochastic nonlinear systems with uncontrollable linearization, this paper investigates the problem of adaptive global stability in probability. By using the tool of adaptive adding a power integrator, a feedback domination design approach is presented and a smooth controller is constructed. The closed‐loop stochastic system is proved to be globally stable in probability and the states can be regulated to the origin almost surely. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive control of stochastic nonlinear systems with Markovian switching

This paper is concerned with the problem of adaptive control for a class of stochastic nonlinear systems with Markovian switching, where the upper bounds of nonlinearities of stochastic Markovian jump systems are assumed to be unknown. Firstly, an adaptation law is developed to estimate these unknown parameters. Then, a class of adaptive state feedback controller is proposed such that not only the estimated errors are bounded almost surely but also, the states of the resulting closed‐loop system are asymptotically stable almost surely. Finally, a numerical example is given to show the validity of the results.Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive fixed-time tracking control for stochastic pure-feedback nonlinear systems

The article discusses the adaptive fixed-time control problems for the stochastic pure-feedback nonlinear systems. Different from the existing results, the priori information of unknown virtual control coefficients (UVCC) is no longer needed in this article, which is realized by emplying the bound estimation method and well-defined smooth functions. A novel semi-global practical fixed-time stability criterion for the stochastic nonlinear systems is presented. Correspondingly, a new construction of Lyapunov function is proposed for the nonlinear stochastic system by adding the lower bounds of the UVCC. Based on the fuzzy logical system and fixed time stability theorem, a novel adaptive fuzzy fixed-time tracking control algorithm for stochastic nonlinear system is raised firstly. By theoretical analysis, we can conclude that the whole variables of the controlled system are bounded almost surely and the output can track the desired reference signal to a very small compact set within a predefined fixed-time interval. Finally, the raised method is illustrated by two simulation examples.     

Hierarchical recursive least squares algorithms for Hammerstein nonlinear autoregressive output-error systems

This article considers the parameter estimation problem of Hammerstein nonlinear autoregressive output-error systems with autoregressive moving average noises. Applying the key term separation technique, the original system is decomposed into three subsystems: the first subsystem contains the unknown parameters related to the output, the second subsystem contains the unknown parameters related to the input, and the third subsystem contains the unknown parameters related to the noise model. A hierarchical recursive least squares algorithm is proposed based on the hierarchical identification principle for interactively identifying each subsystem. The simulation results confirm that the proposed algorithm is effective in estimating the parameters of Hammerstein nonlinear autoregressive output-error systems.     

Parameter estimation using simultaneous perturbation stochastic approximation

The simultaneous perturbation stochastic approximation (SPSA) is an extension of the Kiefer–Wolfowitz stochastic approximation algorithm. In SPSA, since all parameters are perturbed simultaneously, it is possible to modify parameters with only two measurements of an evaluation function regardless of the dimension of the parameter. We propose a parameter estimation algorithm using the SPSA. A convergence theorem for the proposed algorithm is shown. A simulation result also reveals the feasibility of the identification scheme proposed here. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 154(2): 30–39, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20239     

Self-triggered adaptive prescribed-time tracking control for stochastic nonlinear systems

This paper proposes a self-triggered (ST) adaptive prescribed-time tracking control method for a class of stochastic nonlinear systems. Different from the existing results, an improved ST mechanism is proposed by adding a judgment condition to reduce the negative effect of excessive design interval on system performance. Based on the one-to-one mapping and backstepping technique, an adaptive prescribed-time tracking control method is proposed, which can make the error converge to the predefined precision set within the predetermined time. Simultaneously, applying the Lyapunov stability method, the boundedness of all signals in the closed-loop system can be ensured. Finally, a detailed simulation example is provided to show the effectiveness of the proposed control strategy.     

Separable multi-innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems

This article is concerned with the parameter identification problem of nonlinear dynamic responses for the linear time-invariant system by means of an impulse excitation signal and discrete observation data. Using the impulse signal as the input, the impulse response experiment is carried out and the dynamical moving sampling is designed to generate the measured data for deriving new identification algorithms. By applying the moving window data that contain the dynamical information of the system to be identified, an objective function with respect to the parameters of the systems is constructed according to the impulse response. In accordance with different functional relations between the system parameters and the system output response, the unknown parameter vector of the system is separated into a linear parameter vector and a nonlinear parameter vector. Based on the separated parameter vectors, two subidentification models are constructed and a separable identification algorithm is presented through the gradient search to improve the accuracy. Moreover, for the purpose of enhancing the estimation accuracy and capturing the dynamical feature of the systems, the moving window data are employed to develop the separable identification algorithm. The performance of the proposed separable identification method is illustrated via a numerical example.     

具有非线性扰动的网络化随机系统鲁棒控制

针对具有非线性扰动的网络化随机系统的鲁棒控制问题,考虑到反馈控制环中由于实时通讯网络的存在会不可避免地出现网络诱导时延和数据丢失现象,建立了连续时间网络化随机系统模型.在此基础上,设计了状态反馈控制器,使得闭环系统最终均方有界.利用广义系统变换和Lyapunov-Krasovskii泛函方法,得到了闭环系统最终均方有界的充分条件,证明了理想的状态反馈控制器可以通过求解线性矩阵不等式得到.该方法可推广到以双线性随机系统为受控对象的网络化控制系统的镇定控制器设计中.     

基于t-分布邻域嵌入的同调机群无监督识别

当系统发生严重级联故障导致失稳时,快速搜索同调机群是进行解列控制平息振荡的前提。针对发电机严重受扰后功角信号的非平稳、非线性的特点,以及需要根据经验人为决断同调分群类数的问题,提出一种基于t-分布邻域嵌入的同调机群无监督识别新方法。采用广域量测环境下发电机功角信号作为源数据,引入t-分布邻域嵌入算法将发电机功角信号进行建模并映射到二维子空间中。通过二维坐标下映射点之间的聚集程度衡量受扰动后发电机运行特性的相似性。随后利用仿射传播算法对发电机组进行无监督聚类分群。研究表明所提方法原理简单,易于解决实际问题。基于实测数据进行计算分析,可避免模型参数对分群的影响。通过2014年湖南省网73台发电机系统仿真,并与传统分群方法对比结果,验证了所提方法的有效性和快速性。     

随机最优非线性网络控制系统设计

针对网络控制非线性系统中存在的不确定时延,利用Delta算子方法,研究了基于T-S模糊模型的随机最优网络控制问题。采用T-S模型模糊动态逼近非线性系统,将非线性模型模糊化为局部线性模型,设计了本质为非线性的具有时延补偿功能的状态反馈控制器,并进行了稳定性分析,并仿真。结果表明,所提出的建模方法是可行的,实质为非线性的状态反馈的控制器能够有效地补偿时延对系统性能的影响,且补偿效果好。     

基于递推随机子空间的电力系统低频振荡辨识

为实时提取低频振荡模式信息,采用基于随机子空间的低频振荡递推辨识方法。引入基于双边迭代的子空间递推方法实现随机子空间递推辨识,以提高辨识快速性和灵活性。利用递推误差并结合低频振荡数据的特点,提出一种能够保证快速平稳递推的遗忘因子和加权因子选择策略。对理想数据、仿真数据和WAMS数据分别采用所提方法进行分析,验证了该方法的可行性。     

A new paradigm for parameter estimation in system modeling

In this paper, we consider a basic problem in system identification, that of estimating the unknown parameters of a given model by using input/output data. Available methods (extended Kalman filtering, unscented Kalman filtering, particle filtering, maximum likelihood, prediction error method, etc.) have been extensively studied in the literature, especially in relation to consistency analysis. Yet, other important aspects, such as computational complexity, have been somewhat overlooked so that, when such methods are used in practical problems, remarkable drawbacks may arise. This is why parameter estimation is often performed using empirical procedures. This paper aims to revisit the issue of setting up an estimator that is able to provide reliable estimates at low computational cost. In contrast to other paradigms, the main idea in the new introduced two‐stage estimation method is to retrieve the estimator through simulation experiments in a training phase. Once training is terminated, the user is provided with an explicitly given estimator that can be used over and over basically with no computational effort. The advantages and drawbacks of the two‐stage approach as well as other traditional paradigms are identified with an illustrative example. A more concrete example of tire parameter estimation is also provided. Copyright © 2012 John Wiley & Sons, Ltd.     

基于改进遗传算法的非线性励磁系统参数辨识

将大变异遗传算法应用于非线性发电机励磁系统的参数辨识,利用其较强的全局寻优能力辨识出发电机励磁系统参数估计值。其原理为:当某一代中所有个体集中在一起时就以一个远大于通常变异概率的概率执行一次变异操作,随机、独立地产生许多新的个体,使种群脱离早熟。比较每代中所有个体的最大适应度与平均适应度的接近程度,判断当代中所有个体的集中程度;对当代适应度最高的2个个体不进行大变异操作,以保证具有最大适应度的个体不被破坏掉。采用Matlab的Simulink模块建立仿真模型,算例试验结果表明,基于大变异遗传算法的励磁系统参数辨识方法速度快、精度高。     

Recursive least squares estimation methods for a class of nonlinear systems based on non-uniform sampling

Many dynamic processes in practice have nonlinear characteristics and must be described by using nonlinear models. It remains to be a challenging problem to build the models of such nonlinear systems and to estimate their parameters. This article studies the parameter estimation problem for a class of Hammerstein-Wiener nonlinear systems based on non-uniform sampling. By means of the auxiliary model identification idea, an auxiliary model-based recursive least squares algorithm is derived for the systems. In order to enhance the computational efficiency, an auxiliary model-based hierarchical least squares algorithm is proposed by utilizing the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms.     

Adaptive filtering‐based multi‐innovation gradient algorithm for input nonlinear systems with autoregressive noise

In this paper, by means of the adaptive filtering technique and the multi‐innovation identification theory, an adaptive filtering‐based multi‐innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi‐innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering‐based multi‐innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm.