Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity (K...Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity (Kantz and Schreiber (1997)). Tsai (1986) introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR(1) errors. Liu (2003) introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL(p, 0, 1) errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL(p, q, 1) random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai (1986), Wei, et al (1995), and Liu, et al (2003).展开更多
This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power ...This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data (Ratkowsky, 1983). Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.展开更多
The pneumatic artificial muscles are widely used in the fields of medicalrobots, etc. Neural networks are applied to modeling and controlling of artificial muscle system. Asingle-joint artificial muscle test system is...The pneumatic artificial muscles are widely used in the fields of medicalrobots, etc. Neural networks are applied to modeling and controlling of artificial muscle system. Asingle-joint artificial muscle test system is designed. The recursive prediction error (RPE)algorithm which yields faster convergence than back propagation (BP) algorithm is applied to trainthe neural networks. The realization of RPE algorithm is given. The difference of modeling ofartificial muscles using neural networks with different input nodes and different hidden layer nodesis discussed. On this basis the nonlinear control scheme using neural networks for artificialmuscle system has been introduced. The experimental results show that the nonlinear control schemeyields faster response and higher control accuracy than the traditional linear control scheme.展开更多
This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on th...This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].展开更多
Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real pla...Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.展开更多
This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed m...This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed model, the size of the input space is directly related to the system order. By monitoring the identification error characteristic curve, we are able to determine the system order and subsequently an appropriate network structure for systems identification. Simulation results are promising and show that generic nonlinear systems can be identified, different cases of the same system can also be discriminated by our model.展开更多
In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal con...In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.展开更多
为同时考虑多种不确定因素对非线性结构模型修正的影响,提出了一种基于模块化贝叶斯推理的随机非线性模型修正方法。为了描述具有时变特性的非线性动力响应,提取结构动力响应主分量的瞬时加速度幅值作为非线性指标,基于贝叶斯方法,将整...为同时考虑多种不确定因素对非线性结构模型修正的影响,提出了一种基于模块化贝叶斯推理的随机非线性模型修正方法。为了描述具有时变特性的非线性动力响应,提取结构动力响应主分量的瞬时加速度幅值作为非线性指标,基于贝叶斯方法,将整个模型修正过程分为3个相互独立的模块:首先建立非线性模型的高斯过程替代模型记为模块一;同时,为考虑模型误差对非线性结构随机模型修正的影响,将设计变量作为输入,模型误差作为输出,建立关于模型误差的高斯过程替代模型,记为模块二;最后,结合贝叶斯推理方法与模块一和模块二中的高斯过程模型,利用过渡马尔可夫链蒙特卡罗(transitional Markov Chain Monte Carlo,TMCMC)随机采样方法估计待修正参数后验概率密度函数,实现基于模块化贝叶斯推理的随机非线性模型修正研究。采用三跨连续梁桥数值算例来验证所提出的随机非线性模型修正方法的准确性,并对比了不同噪声水平、不同程度模型误差条件下的模型修正结果。研究结果表明,基于模块化贝叶斯推理的随机非线性模型修正方法能够有效地实现非线性结构的随机模型修正,并具有较好的鲁棒性。展开更多
In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and ...In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.展开更多
We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained.
In this paper, the stabilization problem of a stochastic nonlinear system with modeling errors is considered. An augmented observer is first presented to counteract the unmeasurable states as well as modeling errors. ...In this paper, the stabilization problem of a stochastic nonlinear system with modeling errors is considered. An augmented observer is first presented to counteract the unmeasurable states as well as modeling errors. An adaptive output feedback controller is designed such that all signals in the closed-loop system are bounded in probability and the output is regulated to the origin almost surely.展开更多
文摘Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity (Kantz and Schreiber (1997)). Tsai (1986) introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR(1) errors. Liu (2003) introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL(p, 0, 1) errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL(p, q, 1) random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai (1986), Wei, et al (1995), and Liu, et al (2003).
基金Supported by SSFC(04BTJ002),the National Natural Science Foundation of China(10371016) and the Post-Doctorial Grant in Southeast University.
文摘This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data (Ratkowsky, 1983). Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.
基金This project is supported by Foundation of Public Laboratory on Robotics of Chinese Academy of Sciences.
文摘The pneumatic artificial muscles are widely used in the fields of medicalrobots, etc. Neural networks are applied to modeling and controlling of artificial muscle system. Asingle-joint artificial muscle test system is designed. The recursive prediction error (RPE)algorithm which yields faster convergence than back propagation (BP) algorithm is applied to trainthe neural networks. The realization of RPE algorithm is given. The difference of modeling ofartificial muscles using neural networks with different input nodes and different hidden layer nodesis discussed. On this basis the nonlinear control scheme using neural networks for artificialmuscle system has been introduced. The experimental results show that the nonlinear control schemeyields faster response and higher control accuracy than the traditional linear control scheme.
基金Supported by the NSSFC(02BTJ001) Supported by the NSSFC(04BTJ002) Supported by the Grant for Post-Doctorial Fellows in Southeast University
文摘This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].
文摘Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.
文摘This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed model, the size of the input space is directly related to the system order. By monitoring the identification error characteristic curve, we are able to determine the system order and subsequently an appropriate network structure for systems identification. Simulation results are promising and show that generic nonlinear systems can be identified, different cases of the same system can also be discriminated by our model.
文摘In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.
文摘为同时考虑多种不确定因素对非线性结构模型修正的影响,提出了一种基于模块化贝叶斯推理的随机非线性模型修正方法。为了描述具有时变特性的非线性动力响应,提取结构动力响应主分量的瞬时加速度幅值作为非线性指标,基于贝叶斯方法,将整个模型修正过程分为3个相互独立的模块:首先建立非线性模型的高斯过程替代模型记为模块一;同时,为考虑模型误差对非线性结构随机模型修正的影响,将设计变量作为输入,模型误差作为输出,建立关于模型误差的高斯过程替代模型,记为模块二;最后,结合贝叶斯推理方法与模块一和模块二中的高斯过程模型,利用过渡马尔可夫链蒙特卡罗(transitional Markov Chain Monte Carlo,TMCMC)随机采样方法估计待修正参数后验概率密度函数,实现基于模块化贝叶斯推理的随机非线性模型修正研究。采用三跨连续梁桥数值算例来验证所提出的随机非线性模型修正方法的准确性,并对比了不同噪声水平、不同程度模型误差条件下的模型修正结果。研究结果表明,基于模块化贝叶斯推理的随机非线性模型修正方法能够有效地实现非线性结构的随机模型修正,并具有较好的鲁棒性。
基金Supported by National Natural Science Foundation of China(Grant Nos.11101014 and 11002005)the Beijing Natural Science Foundation(Grant No.1142002)+2 种基金the Doctoral Fund of Innovation of Beijing Universityof Technologythe Science and Technology Project of Beijing Municipal Education Commission(Grant No.KM201410005010)the Training Programme Foundation for the Beijing Municipal Excellent Talents(GrantNo.2013D005007000005)
文摘In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19971001).
文摘We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained.
基金supported by the National Natural Science Foundations of China(Nos.60974028,10971256)the China Postdoctoral Science Foundation(No.200904501289)+3 种基金the Shandong Postdoctoral Science Foundation(No.200903042)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20103705110002)the Shandong Provincial Natural Science Foundation(Nos.ZR2009GM008,ZR2009AL014)the Natural Science Foundation of Jiangsu Province(No.BK2009083)
文摘In this paper, the stabilization problem of a stochastic nonlinear system with modeling errors is considered. An augmented observer is first presented to counteract the unmeasurable states as well as modeling errors. An adaptive output feedback controller is designed such that all signals in the closed-loop system are bounded in probability and the output is regulated to the origin almost surely.