具有离散和分布时滞系统的鲁棒有限时间能量-峰值控制

doi:10.12068/j.issn.1005-3026.2016.11.004

东北大学学报:自然科学版 ›› 2016, Vol. 37 ›› Issue (11): 1536-1540.DOI: 10.12068/j.issn.1005-3026.2016.11.004

具有离散和分布时滞系统的鲁棒有限时间能量-峰值控制

郑连伟

(东北大学理学院，辽宁沈阳110819)

收稿日期:2015-12-28 修回日期:2015-12-28 出版日期:2016-11-15 发布日期:2016-11-18
通讯作者: 郑连伟
作者简介:郑连伟 (1963-)，男，辽宁新民人，东北大学副教授，博士．
基金资助:
辽宁省自然科学基金资助项目(2014020022)．

Robust Finite-Time Energy-to-Peak Control for Systems with Discrete and Distributed Delays

ZHENG Lian-wei

School of Sciences， Northeastern University， Shenyang 110819， China.

Received:2015-12-28 Revised:2015-12-28 Online:2016-11-15 Published:2016-11-18
Contact: ZHENG Lian-wei
About author:-
Supported by:
-

摘要/Abstract

摘要： 研究了不确定线性时滞系统在有限时间能量-峰值性能指标约束下的鲁棒控制问题.系统的系数矩阵包含范数有界的不确定性，状态包含离散时滞和分布时滞.引入一个含参数的Lyapunov泛函，通过检验它的指数增长情况，为状态和输出定界，据此得到了闭环系统对于所有允许的不确定性有限时间有界以及满足预先指定的能量-峰值性能指标的充分条件，同时给出了状态反馈控制率.这些条件是有特征值约束的线性矩阵不等式，通过把特征值约束转换成非线性矩阵不等式，设计了锥补偿线性化(CCL)算法来求解这样的矩阵不等式，最后用数值算例验证了所得方法的有效性.

关键词: 分布时滞, 有限时间有界性, 能量-峰值性能, 锥补偿线性化算法, 线性矩阵不等式

Abstract: The robust finite-time control problem under the constraint of energy-to-peak performance index was investigated for linear systems with delays. Norm-bounded uncertainties was included in the coefficient matrices of systems and discrete and distributed delays were included in the states. A Lyapunov functional involving a parameter was introduced. Its exponential growth was checked for bounding the states and outputs. Then， sufficient conditions were derived guaranteeing that the closed-loop systems are finite-time bounded and satisfy prescribed energy-to-peak performance index for all admissible uncertainties. What’s more， the control law was obtained simultaneously. These conditions were formulated in terms of linear matrix inequalities with an eigenvalue constraint. Through transforming the constraint to nonlinear matrix inequalities， a cone complementarity linearization algorithm was designed to solve such matrix inequalities. An example was presented to show the effectiveness of the proposed method.

Key words: distributed delay, finite-time boundedness, energy-to-peak performance, cone complementarity linearization algorithm, linear matrix inequalities

中图分类号:

TP13

郑连伟. 具有离散和分布时滞系统的鲁棒有限时间能量-峰值控制[J]. 东北大学学报:自然科学版, 2016, 37(11): 1536-1540.

ZHENG Lian-wei. Robust Finite-Time Energy-to-Peak Control for Systems with Discrete and Distributed Delays[J]. Journal of Northeastern University Natural Science, 2016, 37(11): 1536-1540.

参考文献

[1]Amato F，Ariola M，Dorato P.Finite-time control of linear systems subject to parametric uncertainties and disturbances ［J］.Automatica，2001，37(9):1459-1463.
[2]Amato F，Ariola M，Cosentino C.Finite-time stabilization via dynamic output feedback ［J］.Automatica，2006，42(2):337-342.
[3]Lin X Z，Du H B，Li S H.Finite-time boundedness and L₂-gain analysis for switched delay systems with norm-bounded disturbance ［J］.Applied Mathematics and Computation，2011，217(12):5982-5993.
[4]Song J，He S P.Robust finite-time H_∞control for one-sided Lipschitz nonlinear systems via state feedback and output feedback ［J］.Journal of the Franklin Institute，2015，352(8):3250-3266.
[5]Gu K.An improved stability criterion for systems with distributed delays ［J］.International Journal of Robust and Nonlinear Control，2003，13(9):819-831.
[6]Yue D，Han Q L.Robust H_∞ filter design of uncertain descriptor systems with discrete and distributed delays ［J］.IEEE Transactions on Signal Processing，2004，52(11):3200-3212.
[7]Du H P，Lam J.Energy to peak performance controller design for building via static output feedback under consideration of actuator saturation ［J］.Computers & Structures，2006，84(31):2277-2290.
[8]Palhares R M，Peres P L D.Robust filter with guaranteed energy-to-peak performance—an LMI approach ［J］.Automatica，2000，36(6):851-858.
[9]Gu K.Integral inequality in the stability problem of time-delay systems ［C］ // Proceedings of the 39th IEEE Conference on Decision and Control.Sydney:IEEE，2000:2805-2810.
[10]Wang Y，Xie L，de Souza C E.Robust control of a class of uncertain nonlinear systems ［J］.Systems & Control Letters，1992，19(2):139-149.
[11]Ghaoui L E，Oustry F，AitRami M.A cone complementarity linearization algorithm for static output-feedback and related problems ［J］. IEEE Transactions on Automatic Control，1997，42(8):1171-1176.

[1]	张秀华，任佳旭. 带输入饱和的奇异摄动双线性系统的无源控制[J]. 东北大学学报（自然科学版）, 2022, 43(12): 1680-1687.
[2]	张雪峰，靳凯净. 基于LMI的离散广义系统的容许性和鲁棒镇定性[J]. 东北大学学报（自然科学版）, 2021, 42(4): 463-469.
[3]	张雪峰，刘博豪. 带有传感器故障的不确定分数阶系统观测器设计[J]. 东北大学学报:自然科学版, 2019, 40(5): 619-624.
[4]	李武杰，陈从根，郭立新. 基于微分几何法的主动悬架鲁棒H_○∞控制[J]. 东北大学学报:自然科学版, 2019, 40(5): 716-721.
[5]	齐文海，李新，高宪文. 执行器饱和的分段齐次Markov跳变系统的镇定[J]. 东北大学学报:自然科学版, 2017, 38(4): 462-466.
[6]	王建华，张庆灵，逄博. 离散Markovian跳变系统概率转移矩阵部分未知的可靠控制[J]. 东北大学学报:自然科学版, 2015, 36(4): 457-461.
[7]	张丽萍，郭立新. 车辆悬架和座椅悬架的鲁棒H_○∞集成控制策略[J]. 东北大学学报:自然科学版, 2015, 36(12): 1771-1775.
[8]	郑连伟，宋叔尼. 区间时变时滞线性系统的指数稳定性[J]. 东北大学学报:自然科学版, 2014, 35(9): 1225-1228.
[9]	邢伟，孙阳，戴良萃. 基于观测器的时延网络控制系统稳定性[J]. 东北大学学报:自然科学版, 2014, 35(4): 457-460.
[10]	刘丽丽，张庆灵，杜昭平. 切换广义被控对象网络控制系统状态反馈镇定[J]. 东北大学学报:自然科学版, 2014, 35(2): 158-161.
[11]	邢双云，张庆灵，朱宝彦. 随机奇异T-S模糊系统的有限时间鲁棒H∞控制[J]. 东北大学学报:自然科学版, 2014, 35(11): 1521-1524.
[12]	郑连伟，宋叔尼. 具有时变时滞的广义系统的稳定性判别方法[J]. 东北大学学报(自然科学版), 2013, 34(6): 770-773.
[13]	郑连伟，宋叔尼. 线性时变时滞系统新的稳定性准则[J]. 东北大学学报(自然科学版), 2013, 34(4): 457-460.
[14]	杨冬梅，徐文明，崔磊. 广义系统动态输出反馈H∞优化控制[J]. 东北大学学报(自然科学版), 2013, 34(4): 461-464.
[15]	杨冬梅，张静. 不确定时滞Lur’e控制系统的鲁棒H∞观测器设计[J]. 东北大学学报(自然科学版), 2013, 34(3): 305-307.

具有离散和分布时滞系统的鲁棒有限时间能量-峰值控制

Robust Finite-Time Energy-to-Peak Control for Systems with Discrete and Distributed Delays

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价