基于虚假最近邻点GT准则的化工模型变量选择

针对传统变量选择方法对复杂非线性化工模型进行变量选择时,由于缺乏输出变量的有效监督,导致所选择输入变量不能有效解释输出变量的问题,提出基于虚假最近邻点Gamma检验(Gamma test,GT)准则的变量选择方法。首先借鉴虚假最近邻点法,实现对所有变量的全面搜索;再采用能够在输出变量监督下进行非线性系统噪声估计的GT准则,计算各输入变量置零前后数据噪声的伽马统计量,得到输出变量对各输入变量的敏感度,以此为依据进行变量选择。使用线性、非线性模型验证了该方法的有效性。最后对氢氰酸复杂非线性化工过程建模进行变量选择,结果表明合理的变量选择有效地提高了模型精度。     

基于相空间重构和进化高斯过程的短期风速预测

提出一种基于相空间重构和进化高斯过程的短期风速预测方法。首先,运用自相关法和假近邻法分别得出原始风速时间序列的延迟时间和嵌入维数,实现混沌风速时间序列的相空间重构;然后,运用进化高斯过程回归模型进行建模,通过高斯过程模型确定输入量和输出量之间的关系,并用改进粒子群算法求取最优超参数。根据某实测风速数据进行了风速预测,结果表明本文所提出的方法能有效提高风速预测精度。     

Adaptive Learning Control of Nonlinear Systems by Output Error Feedback

This paper addresses the problem of designing an output error feedback control for single-input, single-output nonlinear systems with uncertain, smooth, output-dependent nonlinearities whose local Lipschitz constants are known. The considered systems are required to be observable, minimum phase with known relative degree and known high frequency gain sign: linear systems are included. The reference output signal is assumed to be smooth and periodic with known period. By developing in Fourier series expansion a suitable periodic input reference signal, an output error feedback adaptive learning control is designed which ldquolearnsrdquo the input reference signal by identifying its Fourier coefficients: bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the Fourier series expansion is finite, while arbitrary small tracking errors are exponentially achieved otherwise. The resulting control is not model based, is independent of the system order and depends only on the relative degree, the reference signal period and the high frequency gain sign.     

Acceleration of finite‐time stable homogeneous systems

Stabilization rates of power‐integrator chains are easily regulated. It provides a framework for acceleration of uncertain multiple‐input–multiple‐output dynamic systems of known relative degrees (RDs). The desired rate of the output stabilization (sliding‐mode control) is ensured for an uncertain system if its RD is known, and a rough approximation of the high‐frequency gain matrix is available. The uniformly bounded convergence time (fixed‐time stability) is obtained as a particular case. The control can be kept continuous everywhere except the sliding‐mode set if the partial RDs are equal. Similarly, uncertain smooth systems of complete multiple‐input–multiple‐output RDs (ie, lacking zero dynamics) are stabilized by continuous control at their equilibria in finite time and are accelerated. Output‐feedback controllers are constructed. Computer simulation demonstrates the efficiency of the proposed approach.     

Robust adaptive DSC of directly input‐coupled nonlinear systems with input unmodeled dynamics and time‐varying output constraints

In this paper, an adaptive robust dynamic surface control is proposed for a class of uncertain nonlinear interconnected systems with time‐varying output constraints and dynamic input and output coupling. The directly coupled inputs and control inputs are both of nonlinear input unmodeled dynamics. To counteract the instable impact of the nonlinear input unmodeled dynamics, normalization signals are designed on the basis of the convergence rates of their Lyapunov functions. With new state variables and control variables being defined, the real control inputs are obtained through solving the equations of intermediate control laws. The time‐varying constraints on output signals are implemented by introducing asymmetric barrier Lyapunov functions. In addition, dynamic signals and decentralized K‐filters are used to deal with the state unmodeled dynamics and to estimate the unmeasurable states, respectively. By the theoretical analysis, the signals in the closed‐loop system are proved to be semi‐globally uniformly ultimately bounded, and the output constraints are guaranteed simultaneously. A numerical example is provided to show the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive tracking control of MIMO nonlinear nonminimum phase system with unknown input nonlinearity

This paper proposes a nonlinear adaptive control for output tracking of multi‐input multi‐output nonlinear nonminimum phase system with input nonlinearity. The parameters of the input nonlinearity are assumed to be unknown. This problem is challenging, not only because of the unstable internal dynamics of nonminimum phase system, but also the existence of the unknown input nonlinearity. The partially linearized model of the original system is obtained through input/output linearization, and a states tracking model is constructed based on the computed ideal internal dynamics. A nonlinear adaptive controller, which can guarantee the bounded of output tracking error in the existence of unknown input nonlinearity, is proposed. Finally, a numerical simulation on vertical takeoff and landing aircraft is given to show the effectiveness of the proposed control methods.     

Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Asymptotic output‐feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher‐order sliding mode observer/differentiator is used for the exact estimation of the input–output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output‐feedback tracking approach developed for causal nonminimum phase nonlinear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Automated fault diagnosis in nonlinear multivariable systems usinga learning methodology

The paper presents a robust fault diagnosis scheme for detecting and approximating state and output faults occurring in a class of nonlinear multiinput-multioutput dynamical systems. Changes in the system dynamics due to a fault are modeled as nonlinear functions of the control input and measured output variables. Both state and output faults can be modeled as slowly developing (incipient) or abrupt, with each component of the state/output fault vector being represented by a separate time profile. The robust fault diagnosis scheme utilizes on-line approximators and adaptive nonlinear filtering techniques to obtain estimates of the fault functions. Robustness with respect to modeling uncertainties, fault sensitivity and stability properties of the learning scheme are rigorously derived and the theoretical results are illustrated by a simulation example of a fourth-order satellite model.     

On the consistency of Bayesian variable selection for high dimensional binary regression and classification

Modern data mining and bioinformatics have presented an important playground for statistical learning techniques, where the number of input variables is possibly much larger than the sample size of the training data. In supervised learning, logistic regression or probit regression can be used to model a binary output and form perceptron classification rules based on Bayesian inference. We use a prior to select a limited number of candidate variables to enter the model, applying a popular method with selection indicators. We show that this approach can induce posterior estimates of the regression functions that are consistently estimating the truth, if the true regression model is sparse in the sense that the aggregated size of the regression coefficients are bounded. The estimated regression functions therefore can also produce consistent classifiers that are asymptotically optimal for predicting future binary outputs. These provide theoretical justifications for some recent empirical successes in microarray data analysis.     

Learning to transform time series with a few examples

We describe a semi-supervised regression algorithm that learns to transform one time series into another time series given examples of the transformation. This algorithm is applied to tracking, where a time series of observations from sensors is transformed to a time series describing the pose of a target. Instead of defining and implementing such transformations for each tracking task separately, our algorithm learns a memoryless transformation of time series from a few example input-output mappings. The algorithm searches for a smooth function that fits the training examples and, when applied to the input time series, produces a time series that evolves according to assumed dynamics. The learning procedure is fast and lends itself to a closed-form solution. It is closely related to nonlinear system identification and manifold learning techniques. We demonstrate our algorithm on the tasks of tracking RFID tags from signal strength measurements, recovering the pose of rigid objects, deformable bodies, and articulated bodies from video sequences. For these tasks, this algorithm requires significantly fewer examples compared to fully-supervised regression algorithms or semi-supervised learning algorithms that do not take the dynamics of the output time series into account.     

Robust adaptive output feedback control for uncertain nonlinear systems with quantized input

In this paper, we study the input quantization problem for a class of uncertain nonlinear systems. The quantizer adopted belongs to a class of sector‐bounded quantizers, which basically include all the currently available static quantizers. Different from the existing results, the quantized input signal, rather than the input signal itself, is used to design the state observers, which guarantees that the state estimation errors will eventually converge to zero. Because the resulting system may be discontinuous and non‐smooth, the existence of the solution in the classical sense is not guaranteed. To cope with this problem, we utilize the non‐smooth analysis techniques and consider the Filippov solutions. A robust way based on the sector bound property of the quantizers is used to handle the quantization errors such that certain restrictive conditions in the existing results are removed and the problem of output feedback control with input signal quantized by logarithmic (or hysteresis) quantizers is solved for the first time. The designed controller guarantees that all the closed‐loop signals are globally bounded and the tracking error exponentially converges towards a small region around zero, which is adjustable. Copyright © 2016 John Wiley & Sons, Ltd.     

A note on the Gamma test

This note describes a simple technique, the Gamma (or Near Neighbour) test, which in many cases can be used to considerably simplify the design process of constructing a smooth data model such as a neural network. The Gamma test is a data analysis routine, that (in an optimal implementation) runs in time O(MlogM)as M,where Mis the number of sample data points, and which aims to estimate the best Mean Squared Error (MSError) that can be achieved by any continuous or smooth (bounded first partial derivatives) data model constructed using the data.First presented at NCAF seminar, Portsmouth, UK on 20 September 1995     

Adaptive learning control of linear systems by output error feedback

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output uncertain linear systems when the reference output signal is smooth and periodic with known period T. The considered systems are required to be observable, minimum phase, with known relative degree and known high frequency gain sign. By developing in Fourier series expansion a suitable unknown periodic input reference signal, an output error feedback adaptive learning control is designed which ‘learns’ the input reference signal by identifying its Fourier coefficients: bounded closed-loop signals and global exponential tracking of both the input and the output reference signals are obtained when the Fourier series expansion is finite, while global exponential convergence of the input and output tracking errors into arbitrarily small residual sets is achieved otherwise. The structure of the proposed controller depends only on the relative degree, the reference signal period, the high frequency gain sign and the number of estimated Fourier coefficients.     

Model dissection from earthquake time series: A comparative analysis using modern non-linear forecasting and artificial neural network approaches

This study utilizes two non-linear approaches to characterize model behavior of earthquake dynamics in the crucial tectonic regions of Northeast India (NEI). In particular, we have applied a (i) non-linear forecasting technique to assess the dimensionality of the earthquake-generating mechanism using the monthly frequency earthquake time series (magnitude ?4) obtained from NOAA and USGS catalogues for the period 1960–2003 and (ii) artificial neural network (ANN) methods—based on the back-propagation algorithm (BPA) to construct the neural network model of the same data set for comparing the two. We have constructed a multilayered feed forward ANN model with an optimum input set configuration specially designed to take advantage of more completely on the intrinsic relationships among the input and retrieved variables and arrive at the feasible model for earthquake prediction. The comparative analyses show that the results obtained by the two methods are stable and in good agreement and signify that the optimal embedding dimension obtained from the non-linear forecasting analysis compares well with the optimal number of inputs used for the neural networks.The constructed model suggests that the earthquake dynamics in the NEI region can be characterized by a high-dimensional chaotic plane. Evidence of high-dimensional chaos appears to be associated with “stochastic seasonal” bias in these regions and would provide some useful constraints for testing the model and criteria to assess earthquake hazards on a more rigorous and quantitative basis.     

Robust Adaptive Neural Network Control For A Class Of Multiple‐Input Multiple‐Output Nonlinear Time Delay System With Hysteresis Inputs And Dynamic Uncertainties

This paper studies an adaptive neural control for nonlinear multiple‐input multiple‐output systems with dynamic uncertainties, hysteresis input, and time delay. The studied systems are composed of N nonlinear time‐delay subsystems and the interconnection terms are contained in every equation of each subsystem. Adaptive neural control algorithms are developed by introducing a well‐defined smooth function. The unknown time‐varying delays and the unmodeled dynamics are dealt with by constructing appropriate Lyapunov–Krasovskii functions and introducing an available dynamic signal. The main advantage of the proposed controllers is that they contain fewer parameter estimates that need to be updated online. Consequently, the accuracy of ultimate tracking errors asymptotically approaches a pre‐defined bound, and all signals in the closed‐loop systems are also ensured to be uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed adaptive neural network control schemes.     

多元混沌时间序列的相关状态机预测模型研究

针对多元混沌时间序列预测存在的过拟合问题及高维输入变量冗余问题,提出一种新型的多变量稀疏化预测模型——多元相关状态机.该模型采用主成分分析方法对相空间重构后的高维输入变量进行低维表示,将动态储备池作为相关向量机的核函数,充分映射多元混沌时间序列的动力学特性,使得模型具有丰富的动态机制和良好的稀疏性能,有效避免过拟合问题,提高预测精度.基于两组多元混沌时间序列的仿真实验验证了模型的有效性.     

不确定未知界的相似组合系统分散自适应输出反馈控制

研究一类具有加性振动的不确定相似组合大系统的分散自适应输出反馈镇定问题,给出了该系统输出反馈镇定的条件。受控系统的不确定项可以是非线性的或时变的,输入通道不确定性满足一般限制,系统的不确定项的界是存在的但却是未知的。所设计的确定性非线性控制器能保证受控系统渐近收敛于系统的平衡点,并且自适应律保持有界。最后进行了仿真研究,表明所得结论是正确脯效的。     

A hybrid linear-neural model for time series forecasting

This paper considers a linear model with time varying parameters controlled by a neural network to analyze and forecast nonlinear time series. We show that this formulation, called neural coefficient smooth transition autoregressive model, is in close relation to the threshold autoregressive model and the smooth transition autoregressive model with the advantage of naturally incorporating linear multivariate thresholds and smooth transitions between regimes. In our proposal, the neural-network output is used to induce a partition of the input space, with smooth and multivariate thresholds. This also allows the choice of good initial values for the training algorithm.