发酵过程混合建模及带动态补偿的非线性预测控制方法研究
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摘要
微生物发酵是生物工程和现代生物技术及其产业化的基础。随着生物工程技术的进步和发酵工业生产规模的不断扩大,迫切需要提高发酵过程控制系统的控制性能和鲁棒性。发酵过程是典型的非线性、非平稳、高维数、慢时变的复杂系统,且缺乏足够的先验知识,难以构建准确描述发酵过程特性的数学模型。随着对发酵过程控制性能要求的不断提高,研究能准确表征发酵过程特性的混合建模方法及有效的自适应控制策略具有重要的理论意义和应用价值。
本文在分析现有发酵过程建模和控制方法研究现状基础上,以系统的未知动态不确定性为主要研究对象,针对模型失配和未知动态等不确定性影响发酵过程控制品质的难题,研究了发酵过程的混合模型结构、在线快速建模、状态抗差估计、鲁棒预测控制等问题,并进行了青霉素发酵过程预测控制的仿真实验研究。
发酵过程机理十分复杂,已有的建模方法对过程的描述并不全面。本文提出了一种带未知动态的非线性系统混合状态空间模型,未知动态的引入使得该模型不但具备一般非线性系统的优点，还能表征更广泛领域的非线性过程特性。在此基础上,设计了带动态补偿的输出反馈非线性模型预测控制(Nonlinear Model Predictive Control, NMPC)的整体实现框架,并分析了未知动态对系统动态特性的影响,为后续研究打下了坚实的理论基础。
基于核方法的在线建模研究方面,为提高支持向量回归(Support Vector Regression, SVR)建模的实时性和运算速度,本文首次从在特征空间复制训练样本的角度证明了SVR和支持向量分类(Support Vector Classification, SVC)的等价性问题,部分消除了SVC和SVR训练算法的差异,将简洁快速的几何训练算法推广用于SVR训练,有效提高了SVR的实时性和运算速度。基于核独立元分析(Kernel Independent Component Analysis, KICA)和递推最小二乘支持向量机(Recursive Least Square Support Vector Machine, RLS-SVM)的未知动态回归估计满足了在线建模和预测估计的实时性要求,且具有较低的计算复杂度。
基于滤波器的自适应控制器设计方面,基于过程混合模型,研究了基于环路传递复现(Loop Transfer Recovery, LTR)非线性二次调节(Nonlinear Quadratic Regulation with LTR, NQG/LTR)的、带一步动态补偿的NMPC (NMPC with Dynamic Compensation, NMPC/DC)设计方法,考虑到高斯和非高斯扰动的情况,本文在不敏粒子滤波(Unscented Particle Filter, UPF)和不敏变换抗差Kalman滤波(Unscented Transformation based Robust Kalman Filter, UT-RKF)状态估计的基础上,构建了完整的基于NQR/LTR的发酵过程NMPC/DC控制系统,并给出了控制系统的详细执行步骤。
以青霉素发酵过程为实验对象,仿真实验表明：用基于不同训练算法的SVR对青霉素发酵过程大规模数据进行回归训练,在相同的实验条件和相当的回归精度情况下,基于几何训练算法的SVR具有更快的运算速度和更好的收敛性,有效提高了SVR的数据实时处理能力；在初始值和噪声方差存在偏差的情况下,比较EKF、RKF、UT-RKF和RPF的状态估计性能可知,UT-RKF和RPF算法具有更好的估计精度和数值稳定性,高斯扰动情况下,UT-RKF可在计算复杂度较低的情况下得到较好的状态估计结果,便于在线计算；同开环控制、不带未知动态补偿的控制和只考虑未知动态补偿的控制相比,提出的基于模型在线更新的发酵过程NMPC/DC控制能很好的跟踪最优轨迹,具有更好的控制性能和鲁棒性。
本文提出的基于模型在线更新的NMPC/DC系统具有坚实的理论基础,大幅度提高了控制系统鲁棒性和控制性能,为复杂非线性控制系统性能的提高提供了有效的途径,具有重要的指导意义,在化工、机电等复杂非线性领域有着广泛的应用前景。
Fermentation is one of the most important technical elements of biological engineering and modern biotechnology. Because of the progress on biotechnology and increasing scale of industrial fermentation production, it became an urgent need to improve the fermentation process control performance and system robustness. Fermentation process is typically non-linear, non-stationary, high-dimension, time-varying, and lack of adequate prior knowledge. It is difficult to establish an accurate mathematical model to describe the process characteristics. As advancement of the fermentation process control performance requirements, the studies on hybrid modeling methods and efficient adaptive control strategies have important theoretical significance and potential application value.
In this paper, the existing fermentation process modeling and process control methods are analyzed in detail. Aim at the problems in fermentation process control, the nonlinear systems with uncertainties, which include model mismatching and unknown dynamics, were mainly studied. The research issues include hybrid model structure, on-line fast modeling, robust state estimation, robust predictive control, etc. A simulation study of Penicillin fermentation was made to confirm the proposed methods.
As the fermentation process is very complex process, it is difficult to obtain good results based on traditional modeling method. Therefore, the paper presents a hybrid state space model to describe a nonlinear system with uncertainties. By introducing local dynamics, makes the model not only has the advantages of general nonlinear systems, but also characterized a wider field of nonlinear process. This paper discusses the stability of the nonlinear system with unknown dynamics, and the corresponding compensation methods with an output feedback nonlinear model predictive control (NMPC). The overall implementation framework laid a solid theoretical basis.
In the kernel-based online modeling studies, in order to enhance the support vector regression (SVR) modeling speed, this paper presented the geometric interpretation of support vector machine (SVM). It was proved that SVR and support vector classification (SVC) are the equivalence problem by duplicating the training samples in the feature space. Some of the geometric training algorithms were introduced to speed up SVR training, which are simpler and faster than other QP-based algorithms but only suit for SVC earlier. In addition, kernel independent component analysis (KICA) was introduced to decomposition unknown dynamics of the independent impact, and a novel in-place moving-window recursive least square SVM (RLS-SVM) algorithm with lower computational complexity was used to model and forecast the unknown dynamics.
In the studies of filter-based adaptive controller design, the remodeling strategies based on hybrid model were discussed firstly. The controller design methods based on nonlinear quadratic regulator with loop transfer recovery (NQR/LTR) were studied. Further, based on robust particle filter (RPF) and unscented transformation based robust Kalman filter (UT-RKF) algorithm, two dynamic compensator inbuilt NQR/LTR algorithms were proposed, and gave the complete adaptive output feedback predictive control algorithm system of fermentation process.
By the penicillin fermentation process control simulation experiment, the results show that, for SVR training on large-scale data in the same experimental conditions, the regression based on geometric algorithm was quite precise with faster computing speed and better convergence, and effectively improve the SVR for real-time processing. The comparative studies of EKF, RKF, UT-RKF and RPF for state estimation under different initial value, noise variance cases show that, UT-RKF algorithm has higher estimation accuracy and better numerical stability when the noise is Gaussian, and UT-RKF has lower computational complexity. Comparing with the open-loop control and NMPC without dynamic compensation, the proposed dynamic compensator inbuilt NMPC could track the optimal trajectory very well, and have a better control performance and robustness.
This paper presents a dynamic compensator inbuilt NMPC system for fermentation process, it has good robustness and control performance, provides a significance method to improve the complex non-linear process control system performance, and has a broad application prospects.
本文在分析现有发酵过程建模和控制方法研究现状基础上,以系统的未知动态不确定性为主要研究对象,针对模型失配和未知动态等不确定性影响发酵过程控制品质的难题,研究了发酵过程的混合模型结构、在线快速建模、状态抗差估计、鲁棒预测控制等问题,并进行了青霉素发酵过程预测控制的仿真实验研究。
发酵过程机理十分复杂,已有的建模方法对过程的描述并不全面。本文提出了一种带未知动态的非线性系统混合状态空间模型,未知动态的引入使得该模型不但具备一般非线性系统的优点，还能表征更广泛领域的非线性过程特性。在此基础上,设计了带动态补偿的输出反馈非线性模型预测控制(Nonlinear Model Predictive Control, NMPC)的整体实现框架,并分析了未知动态对系统动态特性的影响,为后续研究打下了坚实的理论基础。
基于核方法的在线建模研究方面,为提高支持向量回归(Support Vector Regression, SVR)建模的实时性和运算速度,本文首次从在特征空间复制训练样本的角度证明了SVR和支持向量分类(Support Vector Classification, SVC)的等价性问题,部分消除了SVC和SVR训练算法的差异,将简洁快速的几何训练算法推广用于SVR训练,有效提高了SVR的实时性和运算速度。基于核独立元分析(Kernel Independent Component Analysis, KICA)和递推最小二乘支持向量机(Recursive Least Square Support Vector Machine, RLS-SVM)的未知动态回归估计满足了在线建模和预测估计的实时性要求,且具有较低的计算复杂度。
基于滤波器的自适应控制器设计方面,基于过程混合模型,研究了基于环路传递复现(Loop Transfer Recovery, LTR)非线性二次调节(Nonlinear Quadratic Regulation with LTR, NQG/LTR)的、带一步动态补偿的NMPC (NMPC with Dynamic Compensation, NMPC/DC)设计方法,考虑到高斯和非高斯扰动的情况,本文在不敏粒子滤波(Unscented Particle Filter, UPF)和不敏变换抗差Kalman滤波(Unscented Transformation based Robust Kalman Filter, UT-RKF)状态估计的基础上,构建了完整的基于NQR/LTR的发酵过程NMPC/DC控制系统,并给出了控制系统的详细执行步骤。
以青霉素发酵过程为实验对象,仿真实验表明：用基于不同训练算法的SVR对青霉素发酵过程大规模数据进行回归训练,在相同的实验条件和相当的回归精度情况下,基于几何训练算法的SVR具有更快的运算速度和更好的收敛性,有效提高了SVR的数据实时处理能力；在初始值和噪声方差存在偏差的情况下,比较EKF、RKF、UT-RKF和RPF的状态估计性能可知,UT-RKF和RPF算法具有更好的估计精度和数值稳定性,高斯扰动情况下,UT-RKF可在计算复杂度较低的情况下得到较好的状态估计结果,便于在线计算；同开环控制、不带未知动态补偿的控制和只考虑未知动态补偿的控制相比,提出的基于模型在线更新的发酵过程NMPC/DC控制能很好的跟踪最优轨迹,具有更好的控制性能和鲁棒性。
本文提出的基于模型在线更新的NMPC/DC系统具有坚实的理论基础,大幅度提高了控制系统鲁棒性和控制性能,为复杂非线性控制系统性能的提高提供了有效的途径,具有重要的指导意义,在化工、机电等复杂非线性领域有着广泛的应用前景。
Fermentation is one of the most important technical elements of biological engineering and modern biotechnology. Because of the progress on biotechnology and increasing scale of industrial fermentation production, it became an urgent need to improve the fermentation process control performance and system robustness. Fermentation process is typically non-linear, non-stationary, high-dimension, time-varying, and lack of adequate prior knowledge. It is difficult to establish an accurate mathematical model to describe the process characteristics. As advancement of the fermentation process control performance requirements, the studies on hybrid modeling methods and efficient adaptive control strategies have important theoretical significance and potential application value.
In this paper, the existing fermentation process modeling and process control methods are analyzed in detail. Aim at the problems in fermentation process control, the nonlinear systems with uncertainties, which include model mismatching and unknown dynamics, were mainly studied. The research issues include hybrid model structure, on-line fast modeling, robust state estimation, robust predictive control, etc. A simulation study of Penicillin fermentation was made to confirm the proposed methods.
As the fermentation process is very complex process, it is difficult to obtain good results based on traditional modeling method. Therefore, the paper presents a hybrid state space model to describe a nonlinear system with uncertainties. By introducing local dynamics, makes the model not only has the advantages of general nonlinear systems, but also characterized a wider field of nonlinear process. This paper discusses the stability of the nonlinear system with unknown dynamics, and the corresponding compensation methods with an output feedback nonlinear model predictive control (NMPC). The overall implementation framework laid a solid theoretical basis.
In the kernel-based online modeling studies, in order to enhance the support vector regression (SVR) modeling speed, this paper presented the geometric interpretation of support vector machine (SVM). It was proved that SVR and support vector classification (SVC) are the equivalence problem by duplicating the training samples in the feature space. Some of the geometric training algorithms were introduced to speed up SVR training, which are simpler and faster than other QP-based algorithms but only suit for SVC earlier. In addition, kernel independent component analysis (KICA) was introduced to decomposition unknown dynamics of the independent impact, and a novel in-place moving-window recursive least square SVM (RLS-SVM) algorithm with lower computational complexity was used to model and forecast the unknown dynamics.
In the studies of filter-based adaptive controller design, the remodeling strategies based on hybrid model were discussed firstly. The controller design methods based on nonlinear quadratic regulator with loop transfer recovery (NQR/LTR) were studied. Further, based on robust particle filter (RPF) and unscented transformation based robust Kalman filter (UT-RKF) algorithm, two dynamic compensator inbuilt NQR/LTR algorithms were proposed, and gave the complete adaptive output feedback predictive control algorithm system of fermentation process.
By the penicillin fermentation process control simulation experiment, the results show that, for SVR training on large-scale data in the same experimental conditions, the regression based on geometric algorithm was quite precise with faster computing speed and better convergence, and effectively improve the SVR for real-time processing. The comparative studies of EKF, RKF, UT-RKF and RPF for state estimation under different initial value, noise variance cases show that, UT-RKF algorithm has higher estimation accuracy and better numerical stability when the noise is Gaussian, and UT-RKF has lower computational complexity. Comparing with the open-loop control and NMPC without dynamic compensation, the proposed dynamic compensator inbuilt NMPC could track the optimal trajectory very well, and have a better control performance and robustness.
This paper presents a dynamic compensator inbuilt NMPC system for fermentation process, it has good robustness and control performance, provides a significance method to improve the complex non-linear process control system performance, and has a broad application prospects.
引文
[1]史仲平,潘丰.发酵过程解析、控制与检测技术[M].北京：化学工业出版社,2005
[2]Patnaik P R, An integrated hybrid neural system for noise filtering simulation and control of a fed-batch recombinant fermentation[J]. Biochem. Eng. J.,2003,9,15(3):165-175
[3]Cihan K, Mustafa T, Sitki O. Modelling on-line state estimation and fuzzy control of production scale fed-batch baker's yeast fermentation[J]. Contr Eng Pract.,2006,14:959-974
[4]杨梁,徐保国.基因工程菌高密度发酵过程中PH值模糊控制的实现[J].计算机工程,2005,1,31(1)：206-208
[5]王建林,于涛,杨敬杰.基于模糊集的流加发酵控制方法及其实现[J].仪器仪表学报,2007,2：28(2)
[6]Ray I D, Basu S, Chattopadhyay P. Fault detecting intelligent system for baker's yeast fermentation[J]. Journal of Food Science and Technology.,2001,38(4):329-333
[7]Alford J. Automatic control system [A]. Drug biotechnology regulation scientific basis and practices[C]. Washington DC, US Food and Drug Administration.,1991:59-65
[8]Guerreiro M A, Andrietta S R, Maugeri F. Expert system for the design of an industrial fermentation plant for the production of alcohol[J]. J Chem Tech. Biotechnol.,1997,68(2):163-170
[9]石贤爱.卡那霉素发酵过程专家控制节能系统[J].福州大学学报(自然科学版)，2000,28(1)：102-105
[10]须文波.智能控制在发酵过程中的应用[J].无锡轻工大学学报,2000,19(5)：455-457
[11]Ezequiel F L, Weuster B D. Estimation of optimal feeding strategies for fed-batch bioprocesses[J]. Bioprocess Biosyst. Eng.,2005,27:255-262
[12]姚仲舒,杨成梧.迭代学习控制在烟叶发酵系统中的应用[J].自动化仪表,2002,12(23)：41-43
[13]储炬,李友荣.现代工业发酵调控学(第二版)[M].北京：化学工业出版社,2006.8
[14]O'Connor G M, Sanchez R F, Cooney C L. Design and evaluation of control strategies for high cell density fermentations[J]. Biotechnol. Bioeng.,1992,39:293-304 Azimzadeh F, Palizban H A, Romagnoli J A. On line optimal control of a batch
fermentation process using multiple model approach[J].37th IEEE Conference on Decision and Control Tampa.,1998,12:455-460
[16]Montague G A, Morris A J, Wright A R, et al. Online estimation and adaptive control of penicillin fermentation [J]. IEE Proc.,1986,5:240-246
[17]Amalendu P, Ranjan, J G. Simultaneous dissolved oxygen and glucose regulation in fed-batch methionine production using decoupled input-output linearizing control [J]. J Process Contr.,2009,19,664-677
[18]Peng H, Tohru O, Yukihiro T, et al. RBF-ARX model-based nonlineat system modeling and predictive control with application to a NOx decomposition precess[J]. Contr Eng Pract.,2004,12:191-203
[19]Ahmad A, Behzad M, Ali K S, et al. Optimal control of a nonlinear fed-batch fermentation process using model predictive approach[J]. J Process Contr.,2009:1-12
[20]Ignatova M N, Lyubenova V N, Garci'ab M R, et al. Indirect adaptive linearizing control of a class of bioprocesses-Estimator tuning procedure[J]. J Process Contr.,2008,18:27-35
[21]Meleiro L A C, Von Zuben F J, Filho R M. Constructive learning neural network applied
to identification and control of a fuel-ethanol fermentation process[J]. Eng. Appl. Artif. Intell.,2009,22:201-215
[22]Landau I D, Samaan M, Saad M. Further evaluation of the partial bio technological processes[J]. Proc Am Control Conf San Diego.,1990:2684-2691
[23]Szederke'nyi G, Kristensen N R, Hangos K. M, et al. Nonlinear analysis and control of a continuous fermentation process [J]. Comput. Chem. Eng.,2006,26:659-670
[24]Marcos J A B, Jose M C I, Eduardo G S, et al. Automatization of a penicillin production process with soft sensors and an adaptive controller based on neuron fuzzy systems[J]. Contr Eng Pract.,2004,12:1073-1090
[25]Szederkenyi G, Kristensen N R, Hangos K M, et al. Nonlinear analysis and control of a continuous fermentation process[J]. Comput. Chem. Eng.,2002,26(4):659-670
[26]宋毅芳,任元,杨虹.生物发酵过程的微分几何变结构控制[J].微计算机信息,2007,23(4)：44-46
[27]Saha P, Patwardhan S C, Ramachandra R V S. Maximizing productivity of a continuous fermenter using nonlinear adaptive optimizing control[J]. Bioprocess Engineering.,1999,20:15-21
[28]Assoudi A El, Yaagoubi E H El, Hammouri H. Observer design for a class of differential-algebraic systems application to a bioprocess model[J]. Proceedings of the 13th Mediterranean Conference on Control and Automation Limas.,2005,6:1143-1149
[29]张嗣良,储炬,庄英萍.抗生素发酵过程优化技术研究[J].中国抗生素杂志,2002,27(9)：572-576
[30]Gulnur B, Cenk U, Ali C. A modular simulation package for fed-batch fermentation: penicillin production[J]. Comput. Chem. Eng.,2002,26:1553-1565
[31]Ratkov A I, Georgiev T, Ivanova V, et al. Investigation of L-lysine fed-batch fermentation process with droppings by mathematical modeling[J]. Information Technology Interfaces., 2004,10(10):543-547
[32]Zhang H W, Barry L. Integrated condition monitoring and control of fed-batch fermentation process[J]. J Process Contr.,2004,14(1):41-50.
[33]Massimo C D, Montague G A, Willis M J, et al. Towards improved penicillin fermentation via artificial neural networks [J]. Comput. Chem. Eng.,1992,16(4):283-291
[34]王健,陈宁,杨海军,等.基于BP神经网络的L-色氨酸发酵过程建模[J].天津轻工业学院学报,2003,18(3)：1-4
[35]Chen B H, Woodley J M. Wavelet shrinkage data processing for neural networks in bioprocess modeling[J]. Comput. Chem. Eng.,2002,26(11):1611-1620
[36]Liu G H, Xu H X, Zhou D W, et al. On-Line Estimation of Biomass Concentration Based on ANN and Fuzzy C-Means Clustering[J]. Lecture Notes in Computer Science.,2008,12,306-314
[37]Tan Z P, Wang ST, Du J C. Fermentation Process Modeling Based on CCTSK Fuzzy Neural Network[J]. Biotechnology,2008,7(l):73-79
[38]Chen L Z, Nguang S K, Chen X D, et al. Modeling and optimization of fed-batch fermentation processes using dynamic neural networks and genetic algorithms [J]. Biochem. Eng. J.,2004,22(1):51-61
[39]Vapnik V N. The Nature of Statistical Learning Ttheory [M]. New York, Springer,1995
[40]David M, Johan H, Rudy S, et al. Rule Extraction from Support Vector Machines:An Overview of Issues and Application in Credit Scoring[J].Studies in Computational Intelligence.,2007,12:33-63
[41]许光.俞欢军，陈德钊.基于支持向量机的柠檬酸发酵过程统计建模[J].化学反应工 程与工艺,2004,20(1)：59-63
[42]高学金,王普,孙崇正,等.基于动态ε-SVM的发酵过程建模[J].仪器仪表学报,2006,27(11)：1497-1500
[43]张本法,杨赛楠,潘丰.基于支持向量机的发酵过程建模研究[J].控制工程,2006,13(4)：317-319
[44]Zuo K, Wu W T. Semi-real time optimization and control of a fed-batch fermentation system[J]. Comput. Chem. Eng.,2000,24(2-7):1105-1109
[45]Berkholz R, Rohlig D, Guthke R. Data and knowledge based experimental design for fermentation process optimization[J]. Enzyme Microb. Technol.,2000,27(10):784-788
[46]Tholudur A, Ramirez W F, McMillan J D. Interpolated parameter functions for neural network models[J]. Comput. Chem. Eng.,2000,24(11):2545-2553
[47]许光,俞欢军,陶少辉,等.与机理杂交的支持向量机为发酵过程建模[J].化工学报,2005,56(4)：653-658
[48]桑海峰,王福利,何大阔,等.基于最小二乘支持向量机的发酵过程混合建模[J].仪器仪表学报,2006,27(6)：629-633
[49]Nguang S K, Chen X D, Robust H∞ control of a class of continuous fermentation processes[J]. Appl Math Lett.,1999,12:61-69
[50]Renard F, Wouwer A V, Valentinotti S, et al. A practical robust control scheme for yeast fed-batch cultures-An experimental validation[J]. J Process Contr.,2006,16:855-864
[51]Rui H, Victor M. Z, Lorenz T B. Advanced step nonlinear model predictive control for air separation units[J]. Journal of Process Control.,2009,4,19(4):678-685
[52]Lynn W, Ralf H, Wolfgang M. Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization[J]. J Process Contr.,2009,9,19(8):1277-1288
[53]Magni L, Scattolini R, Tracking of non-square nonlinear continuous time systems with piecewise constant model predictive control [J]. J Process Contr.,2007,17:631-640
[54]Ashoori A, Moshiri B, Ali K. S, et al. Optimal control of a nonlinear fed-batch fermentation process using model predictive approach[J]. J Process Contr.,2009,7(19): 1162-1173
[55]Kalman N Z. Model based control of a yeast fermentation bioreactor using optimally designed artificial neural networks[J]. Chem. Eng. J.,2007,127:95-109
[56]Czuk M L. Modelling and nonlinear predictive control of a yeast fermentation biochemical reactor using neural networks[J]. Chem. Eng. J.,2008,145:290-307
[57]Brian D O A, Arvin D. Challenges of adaptive control, past, permanent and future[J]. Annu Rev in Contr.,2008,2(32):123-135
[58]Soons Z I T A, Voogt J A, Straten G V, et al. Constant specific growth rate in fed-batch cultivation of Bordetella pertussis using adaptive control[J]. J. Biotechnol.,2006,125:252-268
[59]Valentinottia S, Srinivasana B, Holmberg U. Optimal operation of fed-batch fermentations via adaptive control of overflow metabolite[J]. Contr Eng Pract.,2003,11:665-674
[60]Youssef C. B, Guillou V, Olmos-Dichara A. Modeling and adaptive control strategy in a lactic fermentation process[J]. Contr Eng Pract.,2000,8:1297-1307
[61]Shengbing Duan, Zhongping Shi, Haojie Feng, et al. An on-line adaptive control based on DO/pH measurements and ANN pattern recognition model for fed-batch cultivation[J]. Biochem. Eng. J.,2006,30:88-96
[62]隋青美，王欧.基于神经网络的多变量发酵过程自适应控制[J].信息与控制,2002,
8,31(4):371-374
[63]Hisbullah, Hussain M A, Ramachandran K B. Design of a fuzzy logic controller for regulating substrate feed to fed-batch fermentation[J]. Food Biopro Process.,2003,81(2):138-146
[64]Dai X Z. He D, Zhang X, et al. MIMO system invertibility and decoupling control strategies based on ANN ath-order inversion[J]. IEE Proc. Control Theory.,2001,4,2 (148):125-136
[65]常玉清,李玉朝,吕哲,等.基于两级神经网络的发酵过程多变量前馈解耦控制[J].东北大学学报,2007,7,28(7)：925-928
[66]Jayati R D, Pranab K D, Rintu B. Modeling and optimization of protease production by a newly isolated Pseudomonas sp. using a genetic algorithm[J]. Process Biochem.,2005, 40(2):879-884
[67]Mandal C, Gudi R D, Suraishkumar G K. Multi-objective optimization in Aspergillus niger fermentation for selective product enhancement[J]. Bioprocess Biosyst Eng.,2005,28(3):149-164
[68]Robert H, Differential Geometry and the Calculus of Variations[M]. New York: Academic,1968
[69]Robert H, Arthur J. K. Nonlinear Controllability and Observability[J].IEEE T ransactions on Nautomatic Control.,1997,AC-22(5)
[70]Wassim M. H, Vijay S C. Nonlinear dynamical systems and control:a Lyapunov-based approach[M]. Princeton:Princeton University Press.,2008,1
[71]Joseph A B, Martin V D, Tungsheng Y, et al.Robust L2-gain control for nonlinear systems with projection dynamics and input constraints. an example from traffic control[J]. Automatica.,1999,35:429-444
[72]Zames G. Feedback and optimal sensitivity:model reference transformations, multiplicative seminorms, and approximate inverses [J]. IEEE Transactions on Automatic Control.,1981(2):301-320
[73]Isaacs R. Differential games:Their scope, nature, and future[J].Journal of Optimization Theory and Applications.,1969,5,3:283-295
[74]Doyle J.C. Nonlinear Robust Control Theory and Applications[J]. Computer Programming and Software.,1998,15(3):358-363
[75]Fernando A. P, Amit B.Control Liapunov function design of neural networks that solve convex optimization and variational inequality problems[J]. Neurocomputing.,2009,10, 72(16):3863-3872
[76]Adiwinata G, Prashant M, Panagiotis D. C. Fault-tolerant control of a polyethylene reactor [J]. Journal of Process Control.,2007,6,17(5):439-451
[77]Keerthi S. S, Gilbert E. G. Optimal infinite-horizon feedback laws for general class of constrained discrete-time systems:Stability and movinghorizon approximations [J]. IEEE Transactions on Automatic Control.,1998,57(2):265-293
[78]Victor M. Z, Lorenz T. B. The advanced-step NMPC controller:Optimality, stability and robustness [J]. Automatica.,2009,45:86-93
[79]Lazara M, D. Munoz de la Pena, Heemelsc W.P.M.H., et al. On input-to-state stability of min-max nonlinear model predictive control[J]. Systems & Control Letters.,2008,57:39-48
[80]Jiang Z P, Wang Y. Input-to-state stability for discrete-time nonlinear systems[J]. Automatica.,2001,6,37(6):857-869
[81]Raimondo D.M, L. Magni, R. Scattolini. Decentralized MPC of Nonlinear Systems:an Input-to-State Stability Approach[J]. International Journal of Robust and Nonlinear Control.,2007,5,17:1651-1667
[82]Doyle J C, Stein G. Multivariable feedback design:concepts for a classical/modern synthesis[J].IEEE Transactions on Automatic Control.,1981(1):4-16
[83]Athans L.M. A tutorial on the LQG/LTR method [J]. American Control Conference,1986, 6:1-8
[84]Scokaert P O M, MayneD Q. Min-max feedback model predictive control for constrained linear systems [J]. IEEE Transactions on Automatic Control.,1998,43(8):1136-1142
[85]Vladimir C, Ma Y Q. Another look at statistical learning theory and regularization[J]. Neural Networks.,2009,9,22(7):958-969
[86]Vapnik V N. Statistical Learning Theory [M]. New York, Wiley,1998
[87]Scholkopf B, Smola A J. Learning with kernels [M].Cambridge:MIT Press,2002.
[88]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1)：32-42
[89]Vapnik V N. Estimation of Dependences Based on Empirical Data[M]. New York, Springer, Verlag,1982
[90]Osuna E, Freund R, Girosi F. Improved training algorithm for support vector machines
[A]. In:Proceedings of IEEE NNSP'97 [C]. Amelia Island.,1997,276-285
[91]Keerthi S S, Shevade S K, Bhattacharyya C. Improvements to Platt's SMO algorithm for SVM classifier design [J]. Neural Comput.,2001,13(3):637-649
[92]Tao Q, Gao-wei W, Jue W. A generalized S-K algorithm for learning v-SVM classifiers[J]. Pattern Recognition Letters.,2004,25(10):1165-1171
[93]Keerthi S S, Shevade S K, Bhattacharyya C, et al. A fast iterative nearest point algorithm for support vector machine classifier design[J]. IEEE Trans Neural Networks.,2000,11(1):124-136
[94]Crisp D J, Burges C J C. A Geometric Interpretation of v-SVM Classifiers[J]. NIPS.,2000
[95]Bi J B, Bennett K P. A Geometric Approach to Support Vector Regression [J]. Neurocomputing.,2003,55:79-108
[96]Bennett K P, Bredesteiner E J. Duality and geometry in SVM classifiers [A]. In: Proceedings of the 17th International Conference on Machine Learning [C].2000:57-64
[97]Mitchell B F, Dem'yanov V F, Malozemov V N. Finding the point of a polyhedron closet to the origin[J]. SIAM J Contr.,1974,12:19-26
[98]Schlesinger M I, Kalmykov V G, Suchorukov A A. Comparative analysis of algorithms synthesising linear decision rule for analysis of complex hypotheses[J]. Automatika.,1981,1:3-9
[99]Gilbert E G. Minimizing the quadratic form on a convex set[J]. SIAM J Contr.,1996,4(1): 61-79
[100]Li Y, Long P M. The relaxed online maximum margin algorithm[C]. in:Solla S A, Leen T K, Muller K R. Chapter Making Large-Scale Support Vector Machine Learning Practical.Cambridge, MIA, MIT Press.,1999,169-184
[101]Tsang I W, Kwok J T, Cheung P M. Core vector machines, Fast SVM training on very large data sets[J]. J. Mach. Learn. Res.,2005,6:363-392
[102]Karacali B, Ranmnath R, Snyder W E. A comparative analysis of structural risk minimization by support vector machines and nearest neighbor rule[J]. Pattern Recognition Letters.,2004,25:63-71
[103]Jutten C, Herault J. Independent component analysis versus PCA [C]. Proc of European Signal Processing Conf.,1988:287-314
[104]Bach F R, Jordan M I. Kernel independent component analysis[J]. J. Mach. Learn. Res.,
2002(3):1-48
[105]Suykens J A K, Vandewalle J. Least squares support vector machine classifiers [J]. Neural Processing Letters.,1999,9 (3):293-300.
[106]Shigeo A, Sparse least squares support vector training in the reduced empirical feature space[J]. Pattern Analysis & Applications.,2007,2,203-214
[107]Mark Hall.A decision tree-based attribute weighting filter for naive Bayes[J].Knowledge-Based Systems.,2007,3,20(2):120-126
[108]Ali A G, Mohammad B M. A neuro-based EM-particle smoothing algorithm for identification of nonlinear state space models[J].Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul., Korea,2008,6:2008
[109]Steffen B, Aurelien G, Eric M. On approximate maximum-likelihood methods for blind identification:how to cope with the curse of dimensionality[J].IEEE Transactions on Signal processing.,2009,11,57(11):4247-4259
[110]Darko M. Bearings only single-sensor target tracking using Gaussian mixtures[J]. Automatica.,2009,9,45(9):2088-2092
[111]Peda V. M, Tansel Y, Farzad P. Adaptive SDRE based nonlinear sensorless speed control for PMSM drives[J].2009 American Control Conference.,2009,6:3866-3871
[112]Haykin S. Adaptive filter theory (4th Edition) [M]. New Jersey, Prentice Hall,2002
[113]Xie X Q, Zhou D H, Jin Y H. Strong tracking filter based adaptive generic model control [J]. Journal of Process Control.,1999, (9):337-350.
[114]文成林,周东华.多尺度估计理论及其应用[M].北京：清华大学出版社,2002
[115]Zhang Z T, Zhang J S. A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking [J]. Science in China Series F:Information Sciences.,2009,4, 52(4):688-694
[116]Deng L, Leo J L, Attias H, et al.Adaptive Kalman filtering and smoothing for tracking vocal tract resonances using a continuous-valued hidden dynamic model[J]. IEEE Transactions on audio, Speech, and Language Processing.,2007,15(1):13-23
[117]Crisan D, Doucet A. A Survey of convergence results on particle filtering methods for practitioners[J]. IEEE Trans Speech and Audio Proc.,2002,10(3):173-185
[118]Slawomir G, Christian P, Giorgio G, et al. Look-ahead proposals for robust grid-based SLAM with Rao-Blackwellized particle filters[J].The International Journal of Robotics Research.,2009,28(2):191-200
[119]Yao A, Wang G J, Lin X G, et al. An incremental Bhattacharyya dissimilarity measure for particle filtering[J].Pattern Recognition,2010,4,43(4):1244-1256
[120]山根恒夫.生物反応工学(第三版)[M].束京：產業図書,2003
[121]Nielsen J, Villadsen J, Liden G Bioreaction Engineering Principles (Second Edition)[M]. New York, Kluwer Academic/Plenum Publishers.,2002
[122]江汉湖.食品微生物学[M].北京：中国农业出版社,2002.8
[123]Coney C L. Proc Biochem.,1979(5):31-33
[124]Lee S.H. Application of tendency modeling to state estimation of fermentation processes [D]. Benthlehem:Lehigh University.,1997
[2]Patnaik P R, An integrated hybrid neural system for noise filtering simulation and control of a fed-batch recombinant fermentation[J]. Biochem. Eng. J.,2003,9,15(3):165-175
[3]Cihan K, Mustafa T, Sitki O. Modelling on-line state estimation and fuzzy control of production scale fed-batch baker's yeast fermentation[J]. Contr Eng Pract.,2006,14:959-974
[4]杨梁,徐保国.基因工程菌高密度发酵过程中PH值模糊控制的实现[J].计算机工程,2005,1,31(1)：206-208
[5]王建林,于涛,杨敬杰.基于模糊集的流加发酵控制方法及其实现[J].仪器仪表学报,2007,2：28(2)
[6]Ray I D, Basu S, Chattopadhyay P. Fault detecting intelligent system for baker's yeast fermentation[J]. Journal of Food Science and Technology.,2001,38(4):329-333
[7]Alford J. Automatic control system [A]. Drug biotechnology regulation scientific basis and practices[C]. Washington DC, US Food and Drug Administration.,1991:59-65
[8]Guerreiro M A, Andrietta S R, Maugeri F. Expert system for the design of an industrial fermentation plant for the production of alcohol[J]. J Chem Tech. Biotechnol.,1997,68(2):163-170
[9]石贤爱.卡那霉素发酵过程专家控制节能系统[J].福州大学学报(自然科学版)，2000,28(1)：102-105
[10]须文波.智能控制在发酵过程中的应用[J].无锡轻工大学学报,2000,19(5)：455-457
[11]Ezequiel F L, Weuster B D. Estimation of optimal feeding strategies for fed-batch bioprocesses[J]. Bioprocess Biosyst. Eng.,2005,27:255-262
[12]姚仲舒,杨成梧.迭代学习控制在烟叶发酵系统中的应用[J].自动化仪表,2002,12(23)：41-43
[13]储炬,李友荣.现代工业发酵调控学(第二版)[M].北京：化学工业出版社,2006.8
[14]O'Connor G M, Sanchez R F, Cooney C L. Design and evaluation of control strategies for high cell density fermentations[J]. Biotechnol. Bioeng.,1992,39:293-304 Azimzadeh F, Palizban H A, Romagnoli J A. On line optimal control of a batch
fermentation process using multiple model approach[J].37th IEEE Conference on Decision and Control Tampa.,1998,12:455-460
[16]Montague G A, Morris A J, Wright A R, et al. Online estimation and adaptive control of penicillin fermentation [J]. IEE Proc.,1986,5:240-246
[17]Amalendu P, Ranjan, J G. Simultaneous dissolved oxygen and glucose regulation in fed-batch methionine production using decoupled input-output linearizing control [J]. J Process Contr.,2009,19,664-677
[18]Peng H, Tohru O, Yukihiro T, et al. RBF-ARX model-based nonlineat system modeling and predictive control with application to a NOx decomposition precess[J]. Contr Eng Pract.,2004,12:191-203
[19]Ahmad A, Behzad M, Ali K S, et al. Optimal control of a nonlinear fed-batch fermentation process using model predictive approach[J]. J Process Contr.,2009:1-12
[20]Ignatova M N, Lyubenova V N, Garci'ab M R, et al. Indirect adaptive linearizing control of a class of bioprocesses-Estimator tuning procedure[J]. J Process Contr.,2008,18:27-35
[21]Meleiro L A C, Von Zuben F J, Filho R M. Constructive learning neural network applied
to identification and control of a fuel-ethanol fermentation process[J]. Eng. Appl. Artif. Intell.,2009,22:201-215
[22]Landau I D, Samaan M, Saad M. Further evaluation of the partial bio technological processes[J]. Proc Am Control Conf San Diego.,1990:2684-2691
[23]Szederke'nyi G, Kristensen N R, Hangos K. M, et al. Nonlinear analysis and control of a continuous fermentation process [J]. Comput. Chem. Eng.,2006,26:659-670
[24]Marcos J A B, Jose M C I, Eduardo G S, et al. Automatization of a penicillin production process with soft sensors and an adaptive controller based on neuron fuzzy systems[J]. Contr Eng Pract.,2004,12:1073-1090
[25]Szederkenyi G, Kristensen N R, Hangos K M, et al. Nonlinear analysis and control of a continuous fermentation process[J]. Comput. Chem. Eng.,2002,26(4):659-670
[26]宋毅芳,任元,杨虹.生物发酵过程的微分几何变结构控制[J].微计算机信息,2007,23(4)：44-46
[27]Saha P, Patwardhan S C, Ramachandra R V S. Maximizing productivity of a continuous fermenter using nonlinear adaptive optimizing control[J]. Bioprocess Engineering.,1999,20:15-21
[28]Assoudi A El, Yaagoubi E H El, Hammouri H. Observer design for a class of differential-algebraic systems application to a bioprocess model[J]. Proceedings of the 13th Mediterranean Conference on Control and Automation Limas.,2005,6:1143-1149
[29]张嗣良,储炬,庄英萍.抗生素发酵过程优化技术研究[J].中国抗生素杂志,2002,27(9)：572-576
[30]Gulnur B, Cenk U, Ali C. A modular simulation package for fed-batch fermentation: penicillin production[J]. Comput. Chem. Eng.,2002,26:1553-1565
[31]Ratkov A I, Georgiev T, Ivanova V, et al. Investigation of L-lysine fed-batch fermentation process with droppings by mathematical modeling[J]. Information Technology Interfaces., 2004,10(10):543-547
[32]Zhang H W, Barry L. Integrated condition monitoring and control of fed-batch fermentation process[J]. J Process Contr.,2004,14(1):41-50.
[33]Massimo C D, Montague G A, Willis M J, et al. Towards improved penicillin fermentation via artificial neural networks [J]. Comput. Chem. Eng.,1992,16(4):283-291
[34]王健,陈宁,杨海军,等.基于BP神经网络的L-色氨酸发酵过程建模[J].天津轻工业学院学报,2003,18(3)：1-4
[35]Chen B H, Woodley J M. Wavelet shrinkage data processing for neural networks in bioprocess modeling[J]. Comput. Chem. Eng.,2002,26(11):1611-1620
[36]Liu G H, Xu H X, Zhou D W, et al. On-Line Estimation of Biomass Concentration Based on ANN and Fuzzy C-Means Clustering[J]. Lecture Notes in Computer Science.,2008,12,306-314
[37]Tan Z P, Wang ST, Du J C. Fermentation Process Modeling Based on CCTSK Fuzzy Neural Network[J]. Biotechnology,2008,7(l):73-79
[38]Chen L Z, Nguang S K, Chen X D, et al. Modeling and optimization of fed-batch fermentation processes using dynamic neural networks and genetic algorithms [J]. Biochem. Eng. J.,2004,22(1):51-61
[39]Vapnik V N. The Nature of Statistical Learning Ttheory [M]. New York, Springer,1995
[40]David M, Johan H, Rudy S, et al. Rule Extraction from Support Vector Machines:An Overview of Issues and Application in Credit Scoring[J].Studies in Computational Intelligence.,2007,12:33-63
[41]许光.俞欢军，陈德钊.基于支持向量机的柠檬酸发酵过程统计建模[J].化学反应工 程与工艺,2004,20(1)：59-63
[42]高学金,王普,孙崇正,等.基于动态ε-SVM的发酵过程建模[J].仪器仪表学报,2006,27(11)：1497-1500
[43]张本法,杨赛楠,潘丰.基于支持向量机的发酵过程建模研究[J].控制工程,2006,13(4)：317-319
[44]Zuo K, Wu W T. Semi-real time optimization and control of a fed-batch fermentation system[J]. Comput. Chem. Eng.,2000,24(2-7):1105-1109
[45]Berkholz R, Rohlig D, Guthke R. Data and knowledge based experimental design for fermentation process optimization[J]. Enzyme Microb. Technol.,2000,27(10):784-788
[46]Tholudur A, Ramirez W F, McMillan J D. Interpolated parameter functions for neural network models[J]. Comput. Chem. Eng.,2000,24(11):2545-2553
[47]许光,俞欢军,陶少辉,等.与机理杂交的支持向量机为发酵过程建模[J].化工学报,2005,56(4)：653-658
[48]桑海峰,王福利,何大阔,等.基于最小二乘支持向量机的发酵过程混合建模[J].仪器仪表学报,2006,27(6)：629-633
[49]Nguang S K, Chen X D, Robust H∞ control of a class of continuous fermentation processes[J]. Appl Math Lett.,1999,12:61-69
[50]Renard F, Wouwer A V, Valentinotti S, et al. A practical robust control scheme for yeast fed-batch cultures-An experimental validation[J]. J Process Contr.,2006,16:855-864
[51]Rui H, Victor M. Z, Lorenz T B. Advanced step nonlinear model predictive control for air separation units[J]. Journal of Process Control.,2009,4,19(4):678-685
[52]Lynn W, Ralf H, Wolfgang M. Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization[J]. J Process Contr.,2009,9,19(8):1277-1288
[53]Magni L, Scattolini R, Tracking of non-square nonlinear continuous time systems with piecewise constant model predictive control [J]. J Process Contr.,2007,17:631-640
[54]Ashoori A, Moshiri B, Ali K. S, et al. Optimal control of a nonlinear fed-batch fermentation process using model predictive approach[J]. J Process Contr.,2009,7(19): 1162-1173
[55]Kalman N Z. Model based control of a yeast fermentation bioreactor using optimally designed artificial neural networks[J]. Chem. Eng. J.,2007,127:95-109
[56]Czuk M L. Modelling and nonlinear predictive control of a yeast fermentation biochemical reactor using neural networks[J]. Chem. Eng. J.,2008,145:290-307
[57]Brian D O A, Arvin D. Challenges of adaptive control, past, permanent and future[J]. Annu Rev in Contr.,2008,2(32):123-135
[58]Soons Z I T A, Voogt J A, Straten G V, et al. Constant specific growth rate in fed-batch cultivation of Bordetella pertussis using adaptive control[J]. J. Biotechnol.,2006,125:252-268
[59]Valentinottia S, Srinivasana B, Holmberg U. Optimal operation of fed-batch fermentations via adaptive control of overflow metabolite[J]. Contr Eng Pract.,2003,11:665-674
[60]Youssef C. B, Guillou V, Olmos-Dichara A. Modeling and adaptive control strategy in a lactic fermentation process[J]. Contr Eng Pract.,2000,8:1297-1307
[61]Shengbing Duan, Zhongping Shi, Haojie Feng, et al. An on-line adaptive control based on DO/pH measurements and ANN pattern recognition model for fed-batch cultivation[J]. Biochem. Eng. J.,2006,30:88-96
[62]隋青美，王欧.基于神经网络的多变量发酵过程自适应控制[J].信息与控制,2002,
8,31(4):371-374
[63]Hisbullah, Hussain M A, Ramachandran K B. Design of a fuzzy logic controller for regulating substrate feed to fed-batch fermentation[J]. Food Biopro Process.,2003,81(2):138-146
[64]Dai X Z. He D, Zhang X, et al. MIMO system invertibility and decoupling control strategies based on ANN ath-order inversion[J]. IEE Proc. Control Theory.,2001,4,2 (148):125-136
[65]常玉清,李玉朝,吕哲,等.基于两级神经网络的发酵过程多变量前馈解耦控制[J].东北大学学报,2007,7,28(7)：925-928
[66]Jayati R D, Pranab K D, Rintu B. Modeling and optimization of protease production by a newly isolated Pseudomonas sp. using a genetic algorithm[J]. Process Biochem.,2005, 40(2):879-884
[67]Mandal C, Gudi R D, Suraishkumar G K. Multi-objective optimization in Aspergillus niger fermentation for selective product enhancement[J]. Bioprocess Biosyst Eng.,2005,28(3):149-164
[68]Robert H, Differential Geometry and the Calculus of Variations[M]. New York: Academic,1968
[69]Robert H, Arthur J. K. Nonlinear Controllability and Observability[J].IEEE T ransactions on Nautomatic Control.,1997,AC-22(5)
[70]Wassim M. H, Vijay S C. Nonlinear dynamical systems and control:a Lyapunov-based approach[M]. Princeton:Princeton University Press.,2008,1
[71]Joseph A B, Martin V D, Tungsheng Y, et al.Robust L2-gain control for nonlinear systems with projection dynamics and input constraints. an example from traffic control[J]. Automatica.,1999,35:429-444
[72]Zames G. Feedback and optimal sensitivity:model reference transformations, multiplicative seminorms, and approximate inverses [J]. IEEE Transactions on Automatic Control.,1981(2):301-320
[73]Isaacs R. Differential games:Their scope, nature, and future[J].Journal of Optimization Theory and Applications.,1969,5,3:283-295
[74]Doyle J.C. Nonlinear Robust Control Theory and Applications[J]. Computer Programming and Software.,1998,15(3):358-363
[75]Fernando A. P, Amit B.Control Liapunov function design of neural networks that solve convex optimization and variational inequality problems[J]. Neurocomputing.,2009,10, 72(16):3863-3872
[76]Adiwinata G, Prashant M, Panagiotis D. C. Fault-tolerant control of a polyethylene reactor [J]. Journal of Process Control.,2007,6,17(5):439-451
[77]Keerthi S. S, Gilbert E. G. Optimal infinite-horizon feedback laws for general class of constrained discrete-time systems:Stability and movinghorizon approximations [J]. IEEE Transactions on Automatic Control.,1998,57(2):265-293
[78]Victor M. Z, Lorenz T. B. The advanced-step NMPC controller:Optimality, stability and robustness [J]. Automatica.,2009,45:86-93
[79]Lazara M, D. Munoz de la Pena, Heemelsc W.P.M.H., et al. On input-to-state stability of min-max nonlinear model predictive control[J]. Systems & Control Letters.,2008,57:39-48
[80]Jiang Z P, Wang Y. Input-to-state stability for discrete-time nonlinear systems[J]. Automatica.,2001,6,37(6):857-869
[81]Raimondo D.M, L. Magni, R. Scattolini. Decentralized MPC of Nonlinear Systems:an Input-to-State Stability Approach[J]. International Journal of Robust and Nonlinear Control.,2007,5,17:1651-1667
[82]Doyle J C, Stein G. Multivariable feedback design:concepts for a classical/modern synthesis[J].IEEE Transactions on Automatic Control.,1981(1):4-16
[83]Athans L.M. A tutorial on the LQG/LTR method [J]. American Control Conference,1986, 6:1-8
[84]Scokaert P O M, MayneD Q. Min-max feedback model predictive control for constrained linear systems [J]. IEEE Transactions on Automatic Control.,1998,43(8):1136-1142
[85]Vladimir C, Ma Y Q. Another look at statistical learning theory and regularization[J]. Neural Networks.,2009,9,22(7):958-969
[86]Vapnik V N. Statistical Learning Theory [M]. New York, Wiley,1998
[87]Scholkopf B, Smola A J. Learning with kernels [M].Cambridge:MIT Press,2002.
[88]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1)：32-42
[89]Vapnik V N. Estimation of Dependences Based on Empirical Data[M]. New York, Springer, Verlag,1982
[90]Osuna E, Freund R, Girosi F. Improved training algorithm for support vector machines
[A]. In:Proceedings of IEEE NNSP'97 [C]. Amelia Island.,1997,276-285
[91]Keerthi S S, Shevade S K, Bhattacharyya C. Improvements to Platt's SMO algorithm for SVM classifier design [J]. Neural Comput.,2001,13(3):637-649
[92]Tao Q, Gao-wei W, Jue W. A generalized S-K algorithm for learning v-SVM classifiers[J]. Pattern Recognition Letters.,2004,25(10):1165-1171
[93]Keerthi S S, Shevade S K, Bhattacharyya C, et al. A fast iterative nearest point algorithm for support vector machine classifier design[J]. IEEE Trans Neural Networks.,2000,11(1):124-136
[94]Crisp D J, Burges C J C. A Geometric Interpretation of v-SVM Classifiers[J]. NIPS.,2000
[95]Bi J B, Bennett K P. A Geometric Approach to Support Vector Regression [J]. Neurocomputing.,2003,55:79-108
[96]Bennett K P, Bredesteiner E J. Duality and geometry in SVM classifiers [A]. In: Proceedings of the 17th International Conference on Machine Learning [C].2000:57-64
[97]Mitchell B F, Dem'yanov V F, Malozemov V N. Finding the point of a polyhedron closet to the origin[J]. SIAM J Contr.,1974,12:19-26
[98]Schlesinger M I, Kalmykov V G, Suchorukov A A. Comparative analysis of algorithms synthesising linear decision rule for analysis of complex hypotheses[J]. Automatika.,1981,1:3-9
[99]Gilbert E G. Minimizing the quadratic form on a convex set[J]. SIAM J Contr.,1996,4(1): 61-79
[100]Li Y, Long P M. The relaxed online maximum margin algorithm[C]. in:Solla S A, Leen T K, Muller K R. Chapter Making Large-Scale Support Vector Machine Learning Practical.Cambridge, MIA, MIT Press.,1999,169-184
[101]Tsang I W, Kwok J T, Cheung P M. Core vector machines, Fast SVM training on very large data sets[J]. J. Mach. Learn. Res.,2005,6:363-392
[102]Karacali B, Ranmnath R, Snyder W E. A comparative analysis of structural risk minimization by support vector machines and nearest neighbor rule[J]. Pattern Recognition Letters.,2004,25:63-71
[103]Jutten C, Herault J. Independent component analysis versus PCA [C]. Proc of European Signal Processing Conf.,1988:287-314
[104]Bach F R, Jordan M I. Kernel independent component analysis[J]. J. Mach. Learn. Res.,
2002(3):1-48
[105]Suykens J A K, Vandewalle J. Least squares support vector machine classifiers [J]. Neural Processing Letters.,1999,9 (3):293-300.
[106]Shigeo A, Sparse least squares support vector training in the reduced empirical feature space[J]. Pattern Analysis & Applications.,2007,2,203-214
[107]Mark Hall.A decision tree-based attribute weighting filter for naive Bayes[J].Knowledge-Based Systems.,2007,3,20(2):120-126
[108]Ali A G, Mohammad B M. A neuro-based EM-particle smoothing algorithm for identification of nonlinear state space models[J].Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul., Korea,2008,6:2008
[109]Steffen B, Aurelien G, Eric M. On approximate maximum-likelihood methods for blind identification:how to cope with the curse of dimensionality[J].IEEE Transactions on Signal processing.,2009,11,57(11):4247-4259
[110]Darko M. Bearings only single-sensor target tracking using Gaussian mixtures[J]. Automatica.,2009,9,45(9):2088-2092
[111]Peda V. M, Tansel Y, Farzad P. Adaptive SDRE based nonlinear sensorless speed control for PMSM drives[J].2009 American Control Conference.,2009,6:3866-3871
[112]Haykin S. Adaptive filter theory (4th Edition) [M]. New Jersey, Prentice Hall,2002
[113]Xie X Q, Zhou D H, Jin Y H. Strong tracking filter based adaptive generic model control [J]. Journal of Process Control.,1999, (9):337-350.
[114]文成林,周东华.多尺度估计理论及其应用[M].北京：清华大学出版社,2002
[115]Zhang Z T, Zhang J S. A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking [J]. Science in China Series F:Information Sciences.,2009,4, 52(4):688-694
[116]Deng L, Leo J L, Attias H, et al.Adaptive Kalman filtering and smoothing for tracking vocal tract resonances using a continuous-valued hidden dynamic model[J]. IEEE Transactions on audio, Speech, and Language Processing.,2007,15(1):13-23
[117]Crisan D, Doucet A. A Survey of convergence results on particle filtering methods for practitioners[J]. IEEE Trans Speech and Audio Proc.,2002,10(3):173-185
[118]Slawomir G, Christian P, Giorgio G, et al. Look-ahead proposals for robust grid-based SLAM with Rao-Blackwellized particle filters[J].The International Journal of Robotics Research.,2009,28(2):191-200
[119]Yao A, Wang G J, Lin X G, et al. An incremental Bhattacharyya dissimilarity measure for particle filtering[J].Pattern Recognition,2010,4,43(4):1244-1256
[120]山根恒夫.生物反応工学(第三版)[M].束京：產業図書,2003
[121]Nielsen J, Villadsen J, Liden G Bioreaction Engineering Principles (Second Edition)[M]. New York, Kluwer Academic/Plenum Publishers.,2002
[122]江汉湖.食品微生物学[M].北京：中国农业出版社,2002.8
[123]Coney C L. Proc Biochem.,1979(5):31-33
[124]Lee S.H. Application of tendency modeling to state estimation of fermentation processes [D]. Benthlehem:Lehigh University.,1997
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