。1176 北京科技大学学报 第29卷 信息与控制，2001,18(2)：497 5结论 【4刘贺平，张兰玲，孙一康.基于多层局部回归神经网络的多变 量非线性系统预测控制.控制理论与应用，2001,18(2)：298 本文提出的基于Kautz模型的自适应预测函数 [5 Christos C,Zerovos,Dumout G A.Deterministic adaptive control 控制算法，在实现控制方案时，不需要事先知道系统 based on Laguerre series representation.Int J Control.1988.48 的时延和阶次，需要辨识的参数少，比神经网络模型 (6):2333 容易实现，能够根据系统数据准确辨识模型、调整控 [6 Wahberg B.System identification using Kautz model.IEEE 制规律实现自适应控制，在线计算量小、跟踪速度 Trans Autom Control.1994.39(6):1276 较快. [7 Morvan R.Tanguy N.Vilbe P.Pertinent parameters for Kautz approximation.Electron Lett.2000,36(8):769 参考文献 [8 Targuy N.Morvan R.Vilbe P.Pertinent choice of parameters for discrete Kautz approximation.IEEE Trans Autom Control. [1]Richalet J.Abu El Ata-Doss S.Arber C.Predictive furetional 2002.47(5):783 controk application to fast and accurate mobots //Proceedings of 【身许鸣珠，刘贺平.基于Kauz模型的预测控制仿真研究.系统 10th IFAC World Congress.M urich,1987:251 仿真学报，2007.19(1)：3841 [2]Kuntze H B.Jacubasch A.Hirsch U.On the application of a new [10 Mbarek A.Messaoud H.Favir G.Roubust predictive control method for fast and robust //1988 IEEE International Conference using Kautz model//Proceedings of the 2003 10th IEEE Inter on Robotics and Automation.Scottsdale,1988:1574 national Conference on Ekctronics,Cimuits,and Systems. 【3引张泉灵，王树青.基于神经网络模型的非线性预测函数控制. Sharjah,2003:184 Stability condition of predictive functional control based on Kautz model XU Mingzhu,LIU Heping,LI Xicoli,WANG Yunjian Infomation Engineering Sebol.University of Science and Technology Beijing.Beijng 100083.China ABSTRACT The orthogonal Kautz function was used to obtain the approximate model of a system.An adap- tive predictive functional control algorithm using the Kautz model w as designed.The stability of the algorithm was analyzed,and the sufficient condition to make a closed-loop system stable was presented based on the Lya- punov stability theory.Simulation results show that the proposed algorithm is effective,which can describe the sy stem exactly and reach a high degree of control performance. KEY WORDS predictive functional control;Kautz model;RLS;Lyapunov stability5 结论 本文提出的基于 Kautz 模型的自适应预测函数 控制算法, 在实现控制方案时, 不需要事先知道系统 的时延和阶次, 需要辨识的参数少, 比神经网络模型 容易实现, 能够根据系统数据准确辨识模型、调整控 制规律实现自适应控制, 在线计算量小、跟踪速度 较快 . 参 考 文 献 [ 1] Richalet J, Abu El Ata-Doss S, Arber C .Predicti ve functional control:application to fast and accurat e robots ∥Proceedings of 10th IFAC World Congress.M unich, 1987:251 [ 2] Kuntz e H B, Jacubasch A, Hirsch U, On the application of a new method f or f ast and robust ∥1988 IEEE International Conference on Roboti cs and Aut omation.S cottsdale, 1988:1574 [ 3] 张泉灵, 王树青.基于神经网络模型的非线性预测函数控制. 信息与控制, 2001, 18(2) :497 [ 4] 刘贺平, 张兰玲, 孙一康.基于多层局部回归神经网络的多变 量非线性系统预测控制.控制理论与应用, 2001, 18( 2) :298 [ 5] Christos C, Zerovos, Dumout G A.Det erministic adapti ve control based on Laguerre series represent ation.Int J Control, 1988, 48 ( 6) :2333 [ 6] Wahlberg B .System identification using Kautz models.IEEE Trans Autom Control, 1994, 39( 6) :1276 [ 7] Morvan R, Tanguy N, Vilbe P.Pertinent paramet ers for Kautz approximation.El ectron Lett, 2000, 36( 8) :769 [ 8] Tanguy N, Morvan R, Vilbe P.Pertinent choice of parameters for discrete Kautz approximation.IEEE Trans Autom Control, 2002, 47( 5) :783 [ 9] 许鸣珠, 刘贺平.基于 Kautz 模型的预测控制仿真研究.系统 仿真学报, 2007, 19( 15) :3841 [ 10] Mbarek A, Messaoud H, Favir G .Roubust p redictive control using Kautz model∥Proceedings of the 2003 10th IEEE Inter￾national Conference on Electronics, Circuits, and Systems. Sharjah, 2003:184 S tability condition of predictive functional control based on Kautz model X U Mingzhu, LIU Heping, LI X iaoli, WANG Y unjian Inf ormation Engineering School, Universit y of Science and Technology Beijing, Beijing 100083, China ABSTRACT The orthog onal Kautz function was used to obtain the approximate model of a system .An adap￾tive predictive functional control algorithm using the Kautz model w as designed .The stability of the algorithm w as analyzed, and the sufficient condition to make a closed-loop sy stem stable w as presented based on the Lya￾punov stability theory .Simulation results show that the proposed algorithm is effective, w hich can describe the sy stem exactly and reach a hig h deg ree of control performance. KEY WORDS predictive functional control ;Kautz model ;RLS ;Lyapunov stability · 1176 · 北 京 科 技 大 学 学 报 第 29 卷