线性不确定中立型时滞系统的鲁棒无源控制与滤波
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摘要
时滞现象普遍存在于实际工程中,如生物系统、通讯系统、电力系统、化工过程。时滞的存在往往是导致系统不稳定和系统性能变差的根本原因。鉴于稳定性是一个动态控制系统的基本要求,稳定性分析成为动态系统理论中的一个重要的研究课题。近年来,时滞微分动态系统的稳定与控制问题受到了学者广泛的关注,结论较多,而中立型时滞系统的研究相对滞后。作为时滞系统的一个特例,中立型时滞系统是一类既可以描述系统状态滞后又可以描述系统状态微商滞后的系统,是一类更为广泛的滞后系统。并且许多时滞系统都可以转化为中立型时滞系统来进行研究。因此,中立型时滞系统的研究成为近几十年来控制领域新兴起的一个热点,对其进行研究具有极大的理论意义和实用价值。
无源性理论在系统稳定性研究中起着重要的作用,它将输入输出的乘积作为能量的供给率,体现了系统在有界输入条件下的能量衰减特性。目前,诸多学者正致力于鲁棒无源控制的研究。本文利用线性矩阵不等式方法和Lyapunov函数方法相结合,研究一类线性不确定中立型时滞系统的鲁棒无源控制问题。给出了中立型系统时滞独立的鲁棒无源控制器的存在条件。系统中所含的不确定性假设是未知且范数有界的。
滤波问题在系统与控制理论、信号处理与信息融合中有很重要的应用。特别著名的估计方法是Kalman滤波方法。在Kalman滤波中,一个平常特性就是模型必须精确。但是,在很多工业应用中,精确的系统模型是很难获得的。进而,鲁棒滤波方法被引入。针对线性不确定中立型时滞系统,本文研究鲁棒无源滤波器设计问题,系统中所含的不确定性假设是未知且范数有界的。利用线性矩阵不等式方法和Lyapunov函数方法相结合,给出了滤波增广系统时滞独立的鲁棒无源滤波器存在条件。基于滤波器的存在条件,将滤波器的设计问题转化为线性矩阵不等式的求解问题。通过对线性矩阵不等式的求解,获得了滤波器的增益矩阵。
Time delay arises quite naturally in industrial and engineering systems, such as biological systems,communication systems,electrical networks and chemical systems.Time delay is frequently a source of instability and performance degradation in many dynamic systems.In view of that the stability is the basic demand of a dynamical system,the study of the system stability is an important issue in the dynamical system theory. The stability and control issues for delay differential systems have received much interest for recent years,while the development of neutral systems is relatively slow.As special case of delay systems,Neutral delay system contains delays both in its states and in the derivatives of its states.It has a moregeneral form and finds application.And many delay systems can be investigated by transforming to neutral delay systems.The study of neutral delay systems became a hotspot for the last decades.It has profound theory significance and practical value to investigate the stability analysis and synthesis problem of the time delay systems of neutral type.
Method based on passivity play an important role in system stability,which takes the product of the input and the output as the supply rate of the energy, which embodies the attenuation property of a system under bounded exogenous input. Now, considerable attention has been focused on the stability analysis of various neutral delay systems. The paper combines the linear matrix inequality with Lyapunov function method, studying robust passive control for a class of linear uncertain neutral delay systems.A sufficient condition on the existence of robust passive controller is derived. The parameter uncertainties of the system are assumed unknown and norm bounded.
Filtering plays an important role in systems and control theory, signal processing and information fusion. Certainly, the most widely used estimation method is the well-known Kalman filtering. A common feature in the Kalman filtering is that an accurate model is available. In some applications, however, when the system is subject to parameter uncertainties, the accurate system model is difficult to be obtained. To overcome this difficulty, robust filtering approaches are proposed. For linear uncertain neutral delay systems, robust passive filtering is proposed. The parameter uncertainties of the system are assumed unknown and norm bounded. By combining the linear matrix inequality with Lyapunov function method, a sufficient condition on the existence of robust passive filters is derived.Filters gain matrices are obtained by solving LMI.
无源性理论在系统稳定性研究中起着重要的作用,它将输入输出的乘积作为能量的供给率,体现了系统在有界输入条件下的能量衰减特性。目前,诸多学者正致力于鲁棒无源控制的研究。本文利用线性矩阵不等式方法和Lyapunov函数方法相结合,研究一类线性不确定中立型时滞系统的鲁棒无源控制问题。给出了中立型系统时滞独立的鲁棒无源控制器的存在条件。系统中所含的不确定性假设是未知且范数有界的。
滤波问题在系统与控制理论、信号处理与信息融合中有很重要的应用。特别著名的估计方法是Kalman滤波方法。在Kalman滤波中,一个平常特性就是模型必须精确。但是,在很多工业应用中,精确的系统模型是很难获得的。进而,鲁棒滤波方法被引入。针对线性不确定中立型时滞系统,本文研究鲁棒无源滤波器设计问题,系统中所含的不确定性假设是未知且范数有界的。利用线性矩阵不等式方法和Lyapunov函数方法相结合,给出了滤波增广系统时滞独立的鲁棒无源滤波器存在条件。基于滤波器的存在条件,将滤波器的设计问题转化为线性矩阵不等式的求解问题。通过对线性矩阵不等式的求解,获得了滤波器的增益矩阵。
Time delay arises quite naturally in industrial and engineering systems, such as biological systems,communication systems,electrical networks and chemical systems.Time delay is frequently a source of instability and performance degradation in many dynamic systems.In view of that the stability is the basic demand of a dynamical system,the study of the system stability is an important issue in the dynamical system theory. The stability and control issues for delay differential systems have received much interest for recent years,while the development of neutral systems is relatively slow.As special case of delay systems,Neutral delay system contains delays both in its states and in the derivatives of its states.It has a moregeneral form and finds application.And many delay systems can be investigated by transforming to neutral delay systems.The study of neutral delay systems became a hotspot for the last decades.It has profound theory significance and practical value to investigate the stability analysis and synthesis problem of the time delay systems of neutral type.
Method based on passivity play an important role in system stability,which takes the product of the input and the output as the supply rate of the energy, which embodies the attenuation property of a system under bounded exogenous input. Now, considerable attention has been focused on the stability analysis of various neutral delay systems. The paper combines the linear matrix inequality with Lyapunov function method, studying robust passive control for a class of linear uncertain neutral delay systems.A sufficient condition on the existence of robust passive controller is derived. The parameter uncertainties of the system are assumed unknown and norm bounded.
Filtering plays an important role in systems and control theory, signal processing and information fusion. Certainly, the most widely used estimation method is the well-known Kalman filtering. A common feature in the Kalman filtering is that an accurate model is available. In some applications, however, when the system is subject to parameter uncertainties, the accurate system model is difficult to be obtained. To overcome this difficulty, robust filtering approaches are proposed. For linear uncertain neutral delay systems, robust passive filtering is proposed. The parameter uncertainties of the system are assumed unknown and norm bounded. By combining the linear matrix inequality with Lyapunov function method, a sufficient condition on the existence of robust passive filters is derived.Filters gain matrices are obtained by solving LMI.
引文
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[44]郭雷,忻欣,冯纯伯.线性对象的正实控制[J].自动化学报,1997, 23(5)：哈尔滨工业大学工学博士学位论文 577-583.
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[2]KALMAN R Z. When is a linear control system optimal Trans [J]. ASME, Set.D, Basic Engr,1964,86:51-60.
[3]Chen Peng, Yuchu Tian, Dong Yue, Jing Guo. Delay-dependent robust stability analysis for neutral systems with discrete and distributed delays[C]. Intelligent Control and Automation,2008:916-921.
[4]Voulgaris,P.G., Hadjicostis, C.N., Touri, R.A.. Robust Control Approach to Perfect Reconstruction of Digital Signals[J]. IEEE, Signal Processing,2007,55 (9):4444-4457.
[5]Rajan, B.A., Devanathan,R. Robust Control of Permanent Magnet Synchronous Motor Nevanlinna-Pick Approach[C]. IEEE Power System Technology and IEEE Power India Conference,2008,1-4.
[6]Jinsheng Jang, Jason L.Speyer. A Class of Nonlinear Game-Theoretic Filters and Controllers Using a Dissipative Approach. Proceedings of the 33rd Conference on Decision and Control Lake Buena Vista, pp799-804,1994.
[7]Z.P.Jiang, D.J.Hill, A.L.Fradkov. Adaptive passive of interconnected nonlinear systems. Conference on Decision and Control Kobe, Japan, pp 1945-1946,1996.
[8]Zhiqiang Tan, YingChai Soh, Lihua Xie. Dissipative control for linear discrete time systems. Automatica.35:1557-1564,1999.
[9]David J.Hill. Disipative nonlinear systems Proceedings of the 31st conference on Decision and control Tucaon, Artzona. pp3259-3269,1992.
[10]Ziegler J. G., Nichols N. B. Optimum settings for automatic controllers[J]. Transaction of ASME,1992,64:759-768.
[11]李会军,陈明军.基于LMI的鲁棒PID控制器设计[J].控制工程,2007,14(3)：294-315.
[12]张卫东,孙优贤.一类Smith预估器及其鲁棒整定[J].自动化学报,1997,23(5)：660-663.
[13]钟庆昌,谢剑英,彭楚武.纯滞后对象的直接补偿外模控制器[J].湖南大学学报(自然科学版),1999,26(1)：53-59.
[14]俞立,潘海天.具有时变不确定线性系统的鲁棒无源控制[J].自动化学报,1998,24(8)：368-372.
[15]俞立,陈国定.线性时滞系统的无源控制[J].控制理论与应用,1999,16(1)：130-133.
[16]Q. L. Han, One stability for a class of neutral delay-differential systems[C].Pro. American Control Conference,2001,4544-4549.
[17]J. H. park. A new delay-dependent criterion for neutral systems with multiple delays[J]. Journal of Computational and Applied Mathematics,2001,136:177-184.
[18]M. S Mahmoud. Robust H∞ control of linear neutral systems[J], Automatic, 2000,36:757-764.
[19]Z. D. Wang, J. Lam, K. J. Bumham. Stability and observer design for neutral delay systems. IEEE Transactions on Automatic Control,2002,47(3):478-483.
[20]莫玉忠.一类中立弄时滞系统的绝对稳定性[J].广西科学,2007,14(2)：113-116.
[21]史玉英,吴保卫.不确定性中立弄时滞系统的鲁棒稳定性[J].云南师范大学学报,2007,2(7)：21-24.
[22]陈贞丰,金朝永,陈德银,范永青.不确定中立时滞系统的鲁棒稳定性[J].广东工业大学学报,2008,25(4)：37-40.
[23]于新刚.不确定中立时滞系统的鲁棒H∞控制[J].湖南工程学院学报,2008,18(4)：26-29.
[24]王降,黄敏.不确定时变中立时滞系统的鲁棒H∞控制[J].江南大学学报(自然科学版),2008,7(6)：641-646.
[25]张冬雯,高峻岭.不确定中立型时滞系统的鲁棒制[J].电机与控制学报,2007,11(6)：666-671.
[26]张友,井元伟,张嗣瀛.不确定线性中立时滞系统的时滞相关鲁棒H∞控制[J].东北师大学报(自然科学版),2005,37(2)：1-8.
[27]石胜利,杨军,张洁.中立型时滞系统的时滞相关鲁棒控制[J].数学的实践与认识,2008,9(17)：160-164.
[28]Wiener, The Extrapolation Interpolation and Smoothing of Stationary Time Series.OSCD370, Report to the Servites, Research Project DIC-6037,MIT.
[29]R.E.Kalman. A New Approach to Linear Filtering and Prediction[J]. Transactions of Asme Journal of Basic Engineering.1960,82:34-45.
[30]F.Caliskan, C.M.Hajiyev. Sensor Fault Detection in Flight Control Systems Based on the Kalman Filter Innovation Sequence. Proceedings of the Institution of Mechanical Engineers Part I-Journal of Systems and Control Engineering[J].1999,213(13):243-248.
[31]F.Yu, J.Zhang, D.A.Crolla. A Study of a Kalman Filter Active Vehicle Suspension System Using Correlation of Front and Real Wheel Road Inputs[J]. Proceedings of the Institution of Mechanical Engineers Part D-Journal of Automobile Engineering.2000,214(5):493-502.
[32]D.D.Siljak, M.B.Vukcevic. Decentralization, Stabilization and Estimation of Large-Scale Linear Systems. IEEE Trans on Auto Control,1976,21:363-366.
[33]K.Malur, D.Sun, C.K.Paul, On the Design of a Decentralized Observation Scheme for Large-Scale Systems. IEEE Trans on Auto Control,1984,29(3): 274-276.
[34]C.Neal, Federated Square Root Filter for Decentralized Parallel Processes. IEEE Trans on Aerospace and Electronic Systems,1990,26(3):17-525.
[35]N.A.Calson, M.P.Berarducci, Federated Kalman Filter Simulation Results[J]. Navigation Journal of the Institute of Navigation,1994,141(3):297-321
[36]C.Neal, Federated Square Root Filter for Decentralized Parallel Processes. IEEE Trans on Aerospace and Electronic Systems,1990,26(3):517-525.
[37]解学书,钟宜生.H∞控制理论[M].北京：清华大学出版社,1994.
[38]申铁龙.H∞控制理论与应用[M].北京：清华大学出版社,1996.
[39]B.D.O.Andeson, S.Vongpanitherd. Network Analysis and Synthesis-A Modem Systems Theory Approach, New Jersey:Prentice-Hall,1979.
[40]W.M.Hadded, D.S.Bernstein. Robust Stabilization with Positive Real Uncertainty Beyond Small Gain Theorem[J]. Systems and Control Letters, 1991,17(3):1914-1918.
[41]M.Vidyasagar. Nonlinear Systems Analysis. New Jersey:Prentice-Hall,1993.
[42]J.C.Willems. Dissipative Dynamical Systems-Part General theory[J]. Arch Rational Mech Anal,1972,5:321-351.
[43]W.Sun, P.P.Phargonekar, D.Shim. Solution to the Positive Real Control Problem for Linear Time-Invariant Systems. IEEE Trans Automatic Control, 1994,39(10):2034-2046.
[44]郭雷,忻欣,冯纯伯.线性对象的正实控制[J].自动化学报,1997, 23(5)：哈尔滨工业大学工学博士学位论文 577-583.
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