不确定非线性跳变系统滑模耗散控制

Journal of Systems Engineering and Electronics ›› 2009, Vol. 31 ›› Issue (3): 653-656,709.

不确定非线性跳变系统滑模耗散控制

唐中一^1,2, 刘飞¹

1. 江南大学自动化研究所, 江苏, 无锡, 214122;
2. 淮阴工学院自动化研究所, 江苏, 淮安, 223003

收稿日期:2007-10-31 修回日期:2008-04-17 出版日期:2009-03-20 发布日期:2010-01-03
作者简介:唐中一(1980- ),男,硕士研究生,主要研究方向为先进控制理论与应用.E-mail:00ltzy@163.com
基金资助:
国家自然科学基金(60574001);新世纪优秀人才支持计划(NCET-05-0485)资助课题

Sliding mode dissipative control for uncertain jumping nonlinear systems

TANG Zhong-yi^1,2, LIU Fei¹

1. Inst. of Automation, Jiangnan Univ., Wuxi 214122, China;
2. Inst. of Automation, Huaiyin Inst. of Technology, Huaian 223003, China

Received:2007-10-31 Revised:2008-04-17 Online:2009-03-20 Published:2010-01-03

摘要/Abstract

摘要： 针对既含有连续时间演化,又含有马尔可夫事件驱动的一类非线性不确定混杂动态跳变系统,研究相异滑模面上的耗散控制问题。对于跳变系统所具有的匹配的不确定性,可根据滑模控制理论,设计比例-积分多滑模面及相应滑模控制器。与此同时利用耗散控制理论并结合线性矩阵不等式,得到存在非线性和非匹配不确定性滑模面的无记忆状态耗散控制器。如此,系统滑模耗散控制器便可给出。最后数值事例验证定理的正确性。

Abstract: The different sliding mode surface dissipative control problems are discussed for a class of Markov jump nonlinear systems with uncertainties.The systems involve both time-evolving and event-driven mechanisms.In terms of sliding mode theory,different sliding mode surfaces and controllers are designed for the matched uncertainties.Dissipative control theory and linear matrix inequality are applied to sliding mode surface with nonlinear and unmatched uncertainties.Thereafter,the memoryless state feedback controllers are given.Finally,a sliding mode dissipative controllers are gained.A numerical example demonstrates the effect of the proposed design approach.

中图分类号:

TP273

唐中一, 刘飞. 不确定非线性跳变系统滑模耗散控制[J]. Journal of Systems Engineering and Electronics, 2009, 31(3): 653-656,709.

TANG Zhong-yi, LIU Fei. Sliding mode dissipative control for uncertain jumping nonlinear systems[J]. Journal of Systems Engineering and Electronics, 2009, 31(3): 653-656,709.

参考文献

[1] Kwan C M.Sliding mode control of linear systems with mismatched uncertainties[J].Automatica,1995,31(2):303-307.
[2] Choi H H.A new method for variable structure control system design:A linear matrix inequality appruach[J].Automatic,1997,33(11):2089-2092.
[3] Choi H H.An explicit formula of linear sliding surface for a class of uncertain dynamic systems with mismatched uncertainties[J].Automatic,1998,34(8):1015-1020.
[4] Choi H H.On the existence of linear siding surface for a class of uncertain dynamic systems with mismatched uncertainties[J].Automatic,1999,35:1707-1715.
[5] Choi H H.Variable structure output feedback control design for a class of uncertain dynamic systems[J].Automatic,2002,38:335-341.
[6] Utkin V,Shi P.Sliding mode in systems operating under uncertainty conditions[C].Proc.of the 39th IEEE Conf.on the Decision and Control,Kobe,Japan,1996,12:4591-4596.
[7] Ackermann J,Ukin V.Sliding mode control design based on ackermann's formula[J].IEEE Trans.on Automatic Control,1998,43(2):234-237.
[8] Cao W J,Xu J X.Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems[J].IEEE Trans.on Automutic Control,2004,49(8):1355-1360.
[9] Choi H H.LMI-Based sliding surface design for integral sliding mode control of mismatched uncertain systems[J].IEEE Trans.on Automatic Control,2007,52(4):736-742.
[10] Li J.Backstepping variable structure control of nonlinear systems with unmatched uncertainties[C].Proc of the 39h IEEE Conf.on the Decision and Control,Sydney,Australia:IEEE Press,2000,12:4234-4239.
[11] Benjelloun K,Boukas E K,Costa O L V.H∞-control for linear time-delay systems with markovian iumping parameters[J].Jounal of Optimization Theory and Applications,2000,105(1):73-95.
[12] 刘飞.不确定跳变系统鲁棒L₂-L_∞滤波[J].控制与决策,2005,20(1):32-35.
[13] Fu Y M,WU D,Duan G R.Robust guaranteed cost control for descriptor systems with Markov jumpirigs parameters ang state delays[J].Australian Mathematic Society,2006,47:569-580.
[14] Xia Y Q,Shi P,Liu G P,et al.Sliding mode control for stochastic jump systems with time-delay[C].Proc.of the 6th World Congress on Control and Automation,Dalian,China,2006,6:354-358.
[15] 刘飞,苏宏业,禇键.线性时滞系统鲁棒严格耗散控制[J].自动化学报,2002,28(6):897-903.
[16] Li Z H,Wang J C,Shao H H.Delay-dependent dissipative control for linear time-delay systems[J].Journal of the Franklin Institute,2002,339:529-542.
[17] Dung X Z.Robust strictly dissipative control for discrete singular systems[J].IET Control Theory Appl.,2007,1(4):1060-1067.
[18] Xie S,Xie L,Souzade C E.Robust dissipative control for linear systems with dissipative uncertainty[J].International Journal of Control,1998,70(2):169-181.