具有Markov跳跃参数的一类随机非线性系统逆最优增益设计

李桂林; 王传锐; 季海波

doi:10.3724/SP.J.1004.2014.01285

具有Markov跳跃参数的一类随机非线性系统逆最优增益设计

doi: 10.3724/SP.J.1004.2014.01285

1.
中国科学技术大学自动化系合肥 230027;
2.
江苏师范大学电气工程及自动化学院徐州 221116

基金项目:

国家自然科学基金（61273090）资助

详细信息

作者简介:
王传锐中国科学技术大学自动化系博士研究生. 2009年获得西北工业大学数学与应用专业学士学位. 主要研究方向为非线性控制.E-mail：hugh@mail.ustc.edu.cn

计量
- 文章访问数: 1778
- HTML全文浏览量: 109
- PDF下载量: 814
- 被引次数: 0
出版历程
- 收稿日期: 2013-07-25
- 修回日期: 2013-12-03
- 刊出日期: 2014-07-20

Inverse Optimal Gain Assignment Control for a Class of Stochastic Nonlinear Systems with Markovian Jump Parameters

1.
Department of Automation, University of Science and Technology of China, Hefei 230027;
2.
School of Electrical Engineering and Automation, Institute of Automation, Jiangsu Normal University, Xuzhou 221116

Funds:

Supported by National Natural Science Foundation of China (61273090)

摘要

摘要: 研究了一类随机非线性系统的逆最优增益设计问题，系统中除了方差未知的Wiener噪声之外，还含有Markov跳跃参数. 首先，给出此类系统逆最优增益设计问题可解的一个充分条件. 其次，针对一类具有严格反馈形式的随机非线性系统，利用积分反推法，给出了依概率全局渐近稳定和逆最优控制策略的设计方法. 其中，所设计的Lyapunov函数和控制策略与模态显式无关，克服了由于Markov跳跃模态引起的耦合项所带来的设计困难. 最后，通过仿真验证了控制策略的有效性.
- Markov跳跃 /
- Wiener噪声 /
- 逆最优增益设计 /
- 依概率渐近稳定 /
- 积分反推法
Abstract: In this paper, the inverse optimal gain assignment problem for a class of stochastic nonlinear systems with Markovian jump parameters is investigated. Firstly, a sufficient condition to solve this problem for Markovian jump nonlinear systems with bounded indefinite Wiener noises is given. Then, the control strategies of global asymptotic stability and inverse optimal stabilization in probability are presented for a class of strict feedback nonlinear systems. To avoid dealing with the "interconnected" term caused by Markovian jump, the Lyapunov function and the controller are designed to be independent of the regime. Finally, simulation verifies the effectiveness of the control algorithm.
- Markovian jump /
- Wiener noise /
- inverse optimal gain assignment /
- asymptotic stabilization in probability /
- integrator backstepping

HTML全文

参考文献(22)

[1]	Mariton M. Jump Linear Systems in Automatic Control. New York: Marcel Dekker, 1990. 56-72
[2]	Mao X R, Yuan C G. Stochastic Differential Equations with Markovians Switching. London: Imperial College Press, 2006. 49-104
[3]	Huang H, Feng G, Chen X P. Stability and stabilization of Markovian jump systems with time delay via new Lyapunov functionals. IEEE Transactions on Circuits and Systems, 2012, 59(10): 2413-2421
[4]	Cong Shen, Zhang Hai-Tao, Zou Yun. A new exponential stability condition for delayed systems with Markovian switching. Acta Automatica Sinica, 2010, 36(7): 1025-1029(丛屾, 张海涛, 邹云. 具有状态时滞的Markov切换系统的指数稳定性新结果. 自动化学报, 2010, 36(7): 1025-1029)
[5]	Kong Shu-Lan, Zhang Zhao-Sheng. Optimal control of stochastic system with Markovian jumping and multiplicative Noises. Acta Automatica Sinica, 2012, 38(7): 1113-1118(孔淑兰, 张召生. 带马尔科夫跳和乘积噪声的随机系统的最优控制. 自动化学报, 2012, 38(7): 1113-1118)
[6]	Bolzern P, Colaneri P, De Nicolao G. Almost sure stability of Markov jump linear systems with deterministic switching. IEEE Transactions on Automatic Control, 2013, 58(1): 209 -214
[7]	Luan X L, Zhao S Y, Liu F. H∞ control for discrete-time Markov jump systems with uncertain transition probabilities. IEEE Transactions on Automatic Control, 2013, 58(6): 1566-1572
[8]	Zhao P, Kang Y, Zhai D H. On input-to-state stability of stochastic nonlinear systems with Markovian jumping parameters. International Journal of Control, 2012, 85(4): 343 -349
[9]	Song M K, Park J B, Joo Y H. Stability analysis and synthesis of Markovian jump nonlinear systems with incomplete transition descriptions via fuzzy control. In: Proceedings of the 2011 IEEE International Conference on Fuzzy Systems. Taipei, China: IEEE, 2011. 1007-1012
[10]	Zhao Ping, Kang Yu. Stabilization control for a class of two-dimensional Markovian jumping nonlinear systems with time-delay. Journal of Systems Science and Mathematical Sciences, 2007, 27(3): 451-463(赵平, 康宇. 一类二维Markov 跳跃非线性时滞系统的镇定控制. 统科学与数学, 2007, 27(3): 451-463)
[11]	Wu Z J, Xie X J, Shi P, Xia Y Q. Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching. Automatica, 2009, 45(4): 997-1004
[12]	Wu Z J, Yang J, Shi P. Adaptive tracking for stochastic nonlinear systems with Markovian switching. IEEE Transactions on Automatic Control, 2010, 55(9): 2135-2141
[13]	Freeman R A, Kokotovic P V. Inverse optimality in robust stabilization. SIAM Journal on Control and Optimization, 1996, 34(4): 1365-1391
[14]	Krstić M, Tsiotras P. Inverse optimal stabilization of a rigid spacecraft. IEEE Transactions on Automatic Control, 1999, 44(5): 1042-1049
[15]	Krstić M, Li Z H. Inverse optimal design of input-to-state stabilizing nonlinear controllers. IEEE Transactions on Automatic Control, 1998, 43(3): 336-350
[16]	Wang Chuan-Rui, Wang Xing-Hu, Ji Hai-Bo. Inverse optimal gain assignment control for Markovian jump nonlinear systems. Control Theory and Applications, 2013, 30(5): 537 -542(王传锐, 王兴虎, 季海波. Markov 跳跃非线性系统逆最优增益设计. 控制理论与应用, 2013, 30(5): 537-542)
[17]	Florchinger P. A universal formula for the stabilization of control stochastic differential equations. Stochastic Analysis and Applications, 1993, 11(12): 155-162
[18]	Deng H, Krstić M, Williams R J. Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Transactions on Automatic Control, 2001, 46(8): 1237-1253
[19]	Krstić M, Deng H. Stabilization of Nonlinear Uncertain Systems. New York: Springer, 1998. 47-85
[20]	Zhang Ping, Fang Yang-Wang, Hui Xiao-Bin, Liu Xin-Ai, Li Liang. Near optimal strategy for nonlinear stochastic differential games based on the technique of statistical linearization. Acta Automatica Sinica, 2013, 39(4): 390-399(张平, 方洋旺, 惠晓滨, 刘新爱, 李亮. 基于统计线性化的随机非线性微分对策逼近最优策略. 自动化学报, 2013, 39(4): 390-399)
[21]	Hardy G H, Littlewood J E, Pólya G. Inequalities (2nd edition). Cambridge: Cambridge University Press, 1989. 111-113
[22]	Zhao L Q, Xi F B. Explicit conditions for asymptotic stability of stochastic Liénard-type equations with Markovian switching. Journal of Mathematical Analysis and Applications, 2008, 348(1): 267-273

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1778
HTML全文浏览量: 109
PDF下载量: 814
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

具有Markov跳跃参数的一类随机非线性系统逆最优增益设计

doi: 10.3724/SP.J.1004.2014.01285

作者简介:
王传锐中国科学技术大学自动化系博士研究生. 2009年获得西北工业大学数学与应用专业学士学位. 主要研究方向为非线性控制.E-mail：hugh@mail.ustc.edu.cn

计量

Inverse Optimal Gain Assignment Control for a Class of Stochastic Nonlinear Systems with Markovian Jump Parameters

计量

目录

留言板

具有Markov跳跃参数的一类随机非线性系统逆最优增益设计

doi: 10.3724/SP.J.1004.2014.01285

作者简介: 王传锐 中国科学技术大学自动化系博士研究生. 2009年获得西北工业大学数学与应用专业学士学位. 主要研究方向为非线性控制.E-mail：hugh@mail.ustc.edu.cn

计量

出版历程

Inverse Optimal Gain Assignment Control for a Class of Stochastic Nonlinear Systems with Markovian Jump Parameters

计量

出版历程

目录

作者简介:
王传锐中国科学技术大学自动化系博士研究生. 2009年获得西北工业大学数学与应用专业学士学位. 主要研究方向为非线性控制.E-mail：hugh@mail.ustc.edu.cn