基于编码控制机制的混杂系统半全局实用镇定

楼旭阳; 叶倩

doi:10.3724/SP.J.1004.2014.00862

基于编码控制机制的混杂系统半全局实用镇定

doi: 10.3724/SP.J.1004.2014.00862

楼旭阳¹,
叶倩²

1.
江南大学轻工过程先进控制教育部重点实验室无锡 214122;
2.
无锡职业技术学院无锡 214121

基金项目:

国家自然科学基金（61174021，61104155），中央高校基本科研业务费专项资金（JUSRP51322B），高等学校学科创新引智计划（B12018）资助

详细信息

作者简介:
叶倩无锡职业技术学院讲师，博士.主要研究方向为混杂系统分析与综合.E-mail：yeqian85@gmail.com

计量
- 文章访问数: 1626
- HTML全文浏览量: 61
- PDF下载量: 743
- 被引次数: 0
出版历程
- 收稿日期: 2013-05-02
- 修回日期: 2013-11-01
- 刊出日期: 2014-05-20

Semi-global Practical Stabilization of Hybrid Systems Based on an Encoded Control Mechanism

LOU Xu-Yang¹,
YE Qian²

1.
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122;
2.
Wuxi Institute of Technology, Wuxi 214121

Funds:

Supported by National Natural Science Foundation of China (61174021, 61104155), the Fundamental Research Funds for the Central Universities (JUSRP51322B), and the 111 Project (B12018)

摘要

摘要: 混杂系统的鲁棒镇定是复杂控制系统领域的重要研究课题之一.提出了一种编码机制下的混杂控制策略，它能有效地克服传统连续反馈控制或不连续反馈控制在处理局部鲁棒镇定平衡点或不变集问题中的局限性，获得更好的控制效果.首先针对编码状态反馈，构建了一般的混杂系统模型来描述编码状态反馈作用下非线性系统的闭环系统模型.然后，基于逆Lyapunov定理开展了非线性系统的混杂控制鲁棒性分析，提出了闭环混杂系统的半全局实用渐近稳定性判据.最后，结合一个经典控制问题来说明所提出控制策略的优越性.
- 混杂系统 /
- 编码控制 /
- 半全局稳定 /
- 鲁棒性
Abstract: Robust stabilization of hybrid systems is one of the important research topics in the field of complex control systems. This paper proposes a hybrid control strategy under an encoded control mechanism. It can effectively overcome the limitation in dealing with the problems of local robust stabilizing equilibrium point or invariant set for the traditional continuous feedback control or discontinuous feedback control, and obtain better control effects. We first build a general hybrid system model to describe the closed-loop system of a nonlinear system under the encoded state feedback. Then we carry out the robustness analysis of hybrid control for the nonlinear system based on the inverse Lyapunov theorem, and present a semi-global practical asymptotic stability criterion for the closed-loop hybrid system. Finally, we combine with a classical control problem to illustrate the superiority of the proposed control strategy.
- Hybrid systems /
- encoded control /
- semi-global stability /
- robustness

HTML全文

参考文献(30)

[1]	Wong W S, Brockett R W. Systems with finite communication bandwidth constraints. I: State estimation problems. IEEE Transactions on Automatic Control, 1997, 42(9): 1294-1299
[2]	Elia N, Mitter S K. Stabilization of linear systems with limited information. IEEE Transactions on Automatic Control, 2001, 46(9): 1384-1400
[3]	Liberzon D, Hespanha J P. Stabilization of nonlinear systems with limited information feedback. IEEE Transactions on Automatic Control, 2005, 50(6): 910-915
[4]	Liberzon D. On stabilization of linear systems with limited information. IEEE Transactions on Automatic Control, 2003, 48(2): 304-307
[5]	Nair G N, Fagnani F, Zampieri S, Evans R J. Feedback control under data rate constraints: an overview. Proceedings of the IEEE, 2007, 95(1): 108-137
[6]	Tatikonda S, Mitter S. Control under communication constraints. IEEE Transactions on Automatic Control, 2004, 49(7): 1056-1068
[7]	Tarbouriech S, Gouaisbaut F. Control design for quantized linear systems with saturations. IEEE Transactions on Automatic Control, 2012, 57(7): 1883-1889
[8]	Che Wei-Wei, Yang Guang-Hong. Quantized dynamic output feedback H∞ control for discrete-time systems with quantizer ranges consideration. Acta Automatica Sinica, 2008, 34(6): 652-658 (车伟伟, 杨光红. 离散时间系统量化动态输出反馈的H∞控制. 自动化学报, 2008, 34(6): 652-658)
[9]	Jiang Zhong-Ping, Liu Teng-Fei. Quantized nonlinear control——a survey. Acta Automatica Sinica, 2013, 39(11): 1820-1830 (姜钟平, 刘腾飞. 量化非线性控制—综述. 自动化学报, 2013, 39(11): 1820-1830)
[10]	De Persis C, Isidori A. Stabilizability by state feedback implies stabilizability by encoded state feedback. Systems & Control Letters, 2004, 53(3-4): 249-258
[11]	De Persis C, Nešić D. Practical encoders for controlling nonlinear systems under communication constraints. Systems & Control Letters, 2008, 57(8): 654-662
[12]	Mahmoud M S. Control of linear discrete-time systems by quantised feedback. IET Control Theory & Applications, 2012, 6(13): 2095-2102
[13]	Fu M Y. Lack of separation principle for quantized linear quadratic gaussian control. IEEE Transactions on Automatic Control, 2012, 57(9): 2385-2390
[14]	Hayakawa T, Ishii H, Tsumura K. Adaptive quantized control for nonlinear uncertain systems. Systems & Control Letters, 2009, 58(9): 625-632
[15]	Ryan E P. An integral invariance principle for differential inclusions with applications in adaptive control. SIAM Journal on Control and Optimization, 1998, 36(3): 960-980
[16]	Kellett C M, Shim H, Teel A R. Further results on robustness of (possibly discontinuous) sample and hold feedback. IEEE Transactions on Automatic Control, 2004, 49(7): 1081-1089
[17]	Sontag E D. Clocks and insensitivity to small measurement errors. ESAIM: Control, Optimisation and Calculus of Variations, Cambridge University Press, 1999, 4: 537-557
[18]	Sanfelice R G, Teel A R. Lyapunov analysis of sample-and-hold hybrid feedbacks. In: Proceedings of the 45th IEEE Conference on Decision and Control. San Diego, CA: IEEE, 2006. 4879-4884
[19]	Sanfelice R G, Prieur C. Uniting two output-feedback controllers with different objectives. In: Proceedings of the 29th American Control Conference. Baltimore, MD: IEEE, 2010. 910-915
[20]	Prieur C. Uniting local and global controllers with robustness to vanishing noise. Mathematics of Control, Signals and Systems, 2001, 14(2): 143-172
[21]	Chai Tian-You, Zhang Ya-Jun. Nonlinear adaptive switching control method based on unmodeled dynamics compensation. Acta Automatica Sinica, 2011, 37(7): 773-786 (柴天佑, 张亚军. 基于未建模动态补偿的非线性自适应切换控制方法. 自动化学报, 2011, 37(7): 773-786)
[22]	Sanfelice R G, Teel A R. A “throw-and-catch” hybrid control strategy for robust global stabilization of nonlinear systems. In: Proceedings of the 26th American Control Conference. New York, NY: IEEE, 2007. 3470-3475
[23]	Sanfelice R G, Teel A R, Goebel R, Prieur C. On the robustness to measurement noise and unmodeled dynamics of stability in hybrid systems. In: Proceedings of the 25th American Control Conference. Minneapolis, MN: IEEE, 2006. 4061-4066
[24]	Sanfelice R G, Teel A R. On hybrid controllers that induce input-to-state stability with respect to measurement noise. In: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference. Seville, Spain: IEEE, 2005. 4891-4896
[25]	Sanfelice R G, Messina M J, Tuna S E, Teel A R. Robust hybrid controllers for continuous-time systems with applications to obstacle avoidance and regulation to disconnected set of points. In: Proceedings of the 25th American Control Conference. Minneapolis, MN: IEEE, 2006. 3352-3357
[26]	Prieur C. Asymptotic controllability and robust asymptotic stabilizability. SIAM Journal on Control and Optimization, 2005, 43(5): 1888-1912
[27]	Prieur C, Goebel R, Teel A R. Hybrid feedback control and robust stabilization of nonlinear systems. IEEE Transactions on Automatic Control, 2007, 52(11): 2103-2117
[28]	Goebel R, Teel A R. Solutions to hybrid inclusions via set and graphical convergence with stability theory applications. Automatica, 2006, 42(4): 573-587
[29]	Cai C H, Teel A R, Goebel R. Smooth Lyapunov functions for hybrid systems part II: (pre)asymptotically stable compact sets. IEEE Transactions on Automatic Control, 2008, 53(3): 734-748
[30]	Artstein Z. Stabilization with relaxed controls. Nonlinear Analysis: Theory, Methods & Applications, 1983, 7(11): 1163-1173