广义马氏跳变系统在一般转移速率下的控制器设计

王国良; 薄海英

doi:10.16383/j.aas.2015.c140370

广义马氏跳变系统在一般转移速率下的控制器设计

doi: 10.16383/j.aas.2015.c140370

王国良^,,
薄海英

1.
辽宁石油化工大学信息与控制工程学院抚顺 113001

基金项目:

国家自然科学基金(61104066, 61374043);中国博士后科学基金(2012M521 086);辽宁省高等学校优秀人才支持计划(LJQ2013040);辽宁省自然科学基金(2014020106)资助

详细信息

作者简介:
薄海英辽宁石油化工大学硕士研究生.主要研究方向为广义系统,鲁棒控制.E-mail:bohaiying123@163.com

通讯作者:
王国良辽宁石油化工大学副教授.主要研究方向为广义马尔科夫跳变系统的分析与控制.本文通信作者.E-mail:glwang985@163.com

计量
- 文章访问数: 1765
- HTML全文浏览量: 98
- PDF下载量: 747
- 被引次数: 0
出版历程
- 收稿日期: 2014-05-23
- 修回日期: 2014-06-30
- 刊出日期: 2015-01-20

Stabilization of Singular Markovian Jump Systems with General Switching

WANG Guo-Liang^,,
BO Hai-Ying

1.
School of Information and Control Engineering, Liaoning Shihua University, Fushun 113001

Funds:

Supported by National Natural Science Foundation of China (61104066, 61374043), China Postdoctoral Science Foundation Funded Project (2012M521086), the Program for Liaoning Excellent Talents in University (LJQ2013040), and Natural Science Foundation of Liaoning Province (2014020106)

摘要

摘要: 针对转移概率不能精确获得并且部分未知的广义马氏跳变系统, 分别讨论在模态依赖控制器和模态独立控制器条件下的系统镇定问题. 与现有结果相比, 所提研究方法具有较小的保守性, 能够有效地解决实际问题. 首先, 运用自由权矩阵方法, 得到了广义马氏跳变系统在转移速率满足上述一般条件时系统随机容许的充分条件. 在此基础上, 以线性矩阵不等式(Linear matrix inequality, LMI)的形式分别给出了模态依赖和模态独立控制器的求解条件. 最后, 通过数值算例验证设计方法的有效性和优越性.
- 广义马氏跳变系统 /
- 不确定切换率 /
- 转移概率部分未知 /
- 线性矩阵不等式
Abstract: This paper considers the stabilization of singular Markovian jump systems with general switching, where the transition rate matrix is uncertain and partially unknown. Compared with the existing results, the methods proposed in this paper are less conservative and are very suitable to deal with many practical problems. First, a new condition of stochastic admissibility for singular Markovian jump systems with general switching is obtained by exploiting the slack variable method. Then, several conditions for the existence of mode-dependent and mode-independent controllers are developed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is given to show the effectiveness and advantages of the design methods.
- Singular Markovian jump systems /
- uncertain switching probability /
- partially unknown transition rate matrix /
- linear matrix inequality (LMI)

HTML全文

参考文献(27)

[1]	Krasovskii N M, Lidskii E A. Analytical design of controllers in systems with random attributes. Automation and Remote Control, 1961, 22(1-3): 1021-1025, 1141-1146, 1289-1294
[2]	Boukas E K, Liu Z K. Deterministic and Stochastic Time-delay Systems. Boston: Birkhauser, 2002.
[3]	Liu Fei, Cai Yin. Constrained predictive control of Markov jump linear systems based on terminal invariant sets. Acta Automatica Sinica, 2008, 34(4): 496-499 (刘飞, 蔡胤. 基于终端不变集的 Markov 跳变系统约束预测控制. 自动化学报, 2008, 34(4): 496-499)
[4]	Mariton M. Control of nonlinear systems with Markovian parameter changes. IEEE Transactions on Automatic Control, 1991, 36(2): 233-238
[5]	Li Y Y, Zhong M Y. On optimal fault detection for discrete-time Markovian jump linear systems. Acta Automatica Sinica, 2013, 39(6): 926-932
[6]	Kong S L, Zhang Z S. Optimal control of stochastic system with Markovian jumping and multiplicative noises. IEEE Transactions on Automatic Control, 2012, 38(7): 1113- 1118
[7]	Zhao Shun-Yi, Liu Fei. Bayesian filtering of linear nonhomogeneous Markov jump system. Acta Automatica Sinica, 2012, 38(3): 485-490 (赵顺毅, 刘飞. 非线性非齐次Markov跳变系统的贝叶斯滤波. 自动化学报, 2012, 38(3): 485-490)
[8]	Wang Y Y, Shi P, Wang Q B, Duan D P. Exponential H∞ filtering for singular Markovian jump systems with mixed mode-dependent time-varying delay. IEEE Transactions on Circuits and Systems —— I, 2013, 60(9): 2440-2452
[9]	Xu S Y, Lam J. Robust Control and Filtering of Singular Systems. Berlin: Springer-Verlag, 2006.
[10]	Boukas E K. Control of Singular Systems with Random Abrupt Changes. Berlin: Springer-Verlag, 2008.
[11]	Wu Z G, Su H Y, Chu J. Robust exponential stability of uncertain singular Markovian jump time-delay systems. Acta Automatica Sinica, 2010, 36(4): 558-563
[12]	Sheng Li, Yang Hui-Zhong. Stabilization control of a class of discrete-time Markov jump singular systems. Control and Decision, 2010, 2(8): 1189-1194 (盛立, 杨慧中. 一类离散Markov跳变奇异系统的镇定控制. 控制与决策, 2010, 2(8): 1189-1194)
[13]	Wu Z G, Su H Y, Chu J. Delay-dependent H∞ control for singular Markovan jump systems with time delay. Optimal Control Applications and Methods, 2008, 30(5): 443-461
[14]	Wang G L, Zhang Q L, Yang C Y. Dissipative control for singular Markovian jump systems with time delay. Optimal Control Applications and Methods, 2012, 33(4): 415-432
[15]	Wang G L, Zhang Q L. Robust control of uncertain singular stochastic systems with Markovian switching via proportional-derivative state feedback. IET Control Theory and Applications, 2012, 6(8): 1089-1096
[16]	Shi Shu-Hui. H∞ output feedback control for a class of switched singular systems. Control Engineering of China, 2013, 20(2): 357-361 (史书慧. 切换广义系统的H∞输出反馈控制. 控制工程, 2013, 20(2): 357-361)
[17]	Krtolica R, Ozguner U. Stability of linear feedback systems with random communication delays. International Journal of Control, 1994, 59(4): 925-953
[18]	Seiler P, Sengupta R. An H∞ approach to networked control. IEEE Transactions on Automatic Control, 2005, 50(3): 356 -364
[19]	Zhang L, Shi Y, Chen T, Huang B. A new method for stabilization of networked control systems with random delays. IEEE Transactions on Automatic Control, 2005, 50(8): 1177-1181
[20]	Zhang L X. H∞ estimation for piecewise homogeneous Markov jump linear systems. Automatica, 2009, 45(11): 2570-2576
[21]	Zhang L X, Gao H J, Kaynak O. Network-induced constraints in networked control system —— a survey. IEEE Transactions on Industrial Informatics, 2013, 9(1): 403-416
[22]	Kao Y G, Xie J, Wang C, Karimi H R. Stabilisation of singular Markovian jump systems with generally uncertain transition rates. IEEE Transactions Automatic Control, 2014, 59(9): 2604-2610
[23]	Zhang L X, Boukas E K. Mode-dependent filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. Automatica, 2009, 45(6): 1462-1467
[24]	Karan M, Shi P, Kaya C Y. Transition probability bounds for the stochastic stability robustness of continuous and discrete-time Markovian jump linear systems. Automatica, 2006, 42(12): 2159-2168
[25]	Xiong J L, Lam J. On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica, 2005, 41(5): 897-903
[26]	Zhang L X, Lam J. Necessary and sufficient conditions for analysis and synthesis of Markov jump linear systems with incomplete transition descriptions. IEEE Transactions on Automatic Control, 2010, 55(7): 1695-1701
[27]	Zhang L X, Boukas E K, Lam J. Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Transactions on Automatic Control, 2008, 53(10): 2458-2464