基于采样控制的一类本质非线性系统的全局镇定

都海波; 李世华; 钱春江; 何怡刚

doi:10.3724/SP.J.1004.2014.00379

基于采样控制的一类本质非线性系统的全局镇定

doi: 10.3724/SP.J.1004.2014.00379

1.
合肥工业大学电气与自动化工程学院合肥 230009, 中国;
2.
东南大学自动化学院南京 210096, 中国;
3.
美国德克萨斯大学圣安东尼奥分校电子与计算机工程系圣安东尼奥 78249, 美国

基金项目:

国家自然科学基金（61074013，61304007）;国家杰出青年科学基金（509257 27）;教育部博士点基金项目（20130111120007）;中央高校基本科研业务费专项资金项目（2012HGBZ0205，2012HGQC0002）;中国博士后科学基金（2012 M521217）;安徽省自然科学基金（1308085QF106）资助

详细信息

作者简介:
李世华博士，东南大学自动化学院教授. 主要研究方向为非线性系统控制，交流伺服控制和飞控系统. E-mail：lsh@seu.edu.cn

计量
- 文章访问数: 1827
- HTML全文浏览量: 73
- PDF下载量: 922
- 被引次数: 0
出版历程
- 收稿日期: 2012-06-18
- 修回日期: 2012-10-25
- 刊出日期: 2014-02-20

Global Stabilization of a Class of Inherently Nonlinear Systems under Sampled-data Control

1.
School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China;
2.
School of Automation, Southeast University, Nanjing 210096, China;
3.
Department of Electrical and Computer Engineering, the University of Texas at San Antonio, San Antonio 78249, USA

Funds:

Supported by National Natural Science Foundation of China (61074013, 61304007), National Natural Science Funds of China for Distinguished Young Scholar (50925727), Ph.D. Programs Foundation of Ministry of Education of China (20130111120007), Fundamental Research Funds for the Central Universities (2012HGBZ02 05, 2012HGQC0002), China Postdoctoral Science Foundation (2012 M521217), and Natural Science Foundation of Anhui Province (1308 085QF106)

摘要

摘要: 针对一类含不确定参数的本质非线性系统，基于非光滑控制技术，提出了一种基于采样控制的全局非光滑镇定方案. 首先，基于加幂积分技术和递归设计方法，提出了一类采样状态反馈控制器构造性设计方法.然后，通过合理地构造Lyapunvo泛函，严格地证明了存在一个最大采样周期可以保证闭环系统的全局渐近稳定性. 由于控制器是离散形式的，所以在实际中易于用计算机来实现. 仿真结果验证了该方法的有效性.
- 全局镇定 /
- 本质非线性系统 /
- 非光滑控制 /
- 采样控制
Abstract: For a class of inherently nonlinear systems with uncertain parameters, the global stabilization problem via sampled-data control is investigated in this paper. First of all, based on the technique of adding a power integrator and a recursive argument, a class of sampled-data state feedback controllers are proposed. Then under the proposed controller, by using a suitable Lyapunov functional, it is shown that there is a maximum allowable sampling period which can guarantee the global asymptotical stability of the closed-loop system. Since the proposed controller is discrete-time, it can be easily implemented by computers. Finally, an example is given to verify the efficiency of the proposed method.
- Global stabilization /
- inherently nonlinear systems /
- non-smooth control /
- sampled-data control

HTML全文

参考文献(22)

[1]	Hong Y G. Finite-time stabilization and stabilizability of a class of controllable systems. Systems and Control Letters, 2002, 46(4): 231-236
[2]	Li Shi-Hua, Ding Shi-Hong, Tian Yu-Ping. A finite-time state feedback stabilization method for a class of second order nonlinear systems. Acta Automatica Sinica, 2007, 33(1): 101-104 (李世华, 丁世宏, 田玉平. 一类二阶非线性系统的有限时间状态反馈镇定方法. 自动化学报, 2007, 33(1): 101-104)
[3]	Ding Shi-Hong, Li Shi-Hua. Global finite-time stabilization of nonlinear integrator systems subject to input saturation. Acta Automatica Sinica, 2011, 37(10): 1222-1231 (丁世宏, 李世华. 输入饱和下的非线性积分系统的全局有限时间镇定. 自动化学报, 2011, 37(10): 1222-1231)
[4]	Ding S H, Qian C J, Li S H, Li Q. Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations. International Journal of Robust and Nonlinear Control, 2011, 21(3): 271-294
[5]	Rui C L, Reyhangolu M, Kolmanovsky I, Cho S, McClamroch N H. Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system. In: Proceedings of the 36th IEEE Conference on Decision and Control. San Diego, California: IEEE, 1997. 3998-4003
[6]	Qian C J, Lin W. A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Transactions on Automatic Control, 2001, 46(7): 1061-1079
[7]	Qian C J, Lin W. Nonsmooth output feedback stabilization of a class of genuinely nonlinear systems in the plane. IEEE Transactions on Automatic Control, 2003, 48(10): 1824-1829
[8]	Qian C J, Lin W. Recursive observer design, homogeneous approximation, and nonsmooth output feedback stabilization of nonlinear systems. IEEE Transactions on Automatic Control, 2006, 51(9): 1457-1471
[9]	Li J, Qian C J, Ding S H. Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems. International Journal of Control, 2010, 83(11): 2241-2252
[10]	Åström K J, Wittenmark B. Computer-Controlled Systems: Theory and Design (3rd Edition). NJ: Prentice Hall, 1997
[11]	Nešić D, Teel A R, Kokotović P V. Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations. Systems and Control Letters, 1999, 38(4-5): 259-270
[12]	Nešić D, Teel A R, Carnevale D. Explicit computation of the sampling period in emulation of controllers for nonlinear sampled-data systems. IEEE Transactions on Automatic Control, 2009, 54(3): 619-624
[13]	Karafyllis I, Kravaris C. Global stability results for systems under sampled-data control. International Journal of Robust and Nonlinear Control, 2009, 19(10): 1105-1128
[14]	Dabroom A M, Khalil H K. Output feedback sampled-data control of nonlinear systems using high-gain observers. IEEE Transactions on Automatic Control, 2001, 46(11): 1712-1725
[15]	Khalil H K. Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems. IEEE Transactions on Automatic Control, 2004, 49(12): 2173-2184
[16]	Zhang Jian, Xu Hong-Bing, Zhang Hong-Bin. Observer-based sampled-data control for a class of continuous nonlinear systems. Acta Automatica Sinica, 2010, 36(12): 1780-1787 (张健, 徐红兵, 张洪斌. 基于观测器的一类连续非线性系统的采样控制. 自动化学报, 2010, 36(12): 1780-1787)
[17]	Qian C, Du H. Global output feedback stabilization of a class of nonlinear systems via linear sampled-data control. IEEE Transactions on Automatic Control, 2012, 57(11): 2934-2939
[18]	Hermes H. Homogeneous coordinates and continuous asymptotically stabilizing feedback controls. Differential Equations, Stability and Control, Lecture Notes in Pure and Applied Mathematics. Dekker: New York, 1991, 249-260
[19]	Bacciotti A, Roiser L. Liapunov Functions and Stability in Control Theory. Springer, 2005
[20]	Ding Shi-Hong, Li Shi-Hua. A survey for finite-time control problems. Control and Decision, 2011, 26(2): 161-169 (丁世宏, 李世华. 有限时间控制问题综述. 控制与决策, 2011, 26(2): 161-169)
[21]	Yu X H, Xu J X, Hong Y G, Yu S H. Analysis of a class of discrete-time systems with power rule. Automatica, 2007, 43(3): 562-566
[22]	Polendo J, Qian C J. An expanded method to robustly stabilize uncertain nonlinear systems. Communications in Information and Systems, 2008, 8(1): 55-70