连续非线性系统的滑模鲁棒正不变集控制

傅健; 吴庆宪; 姜长生; 王宇飞

doi:10.3724/SP.J.1004.2011.01395

连续非线性系统的滑模鲁棒正不变集控制

doi: 10.3724/SP.J.1004.2011.01395

1.
南京航空航天大学自动化学院南京 210016

详细信息

通讯作者:
傅健南京航空航天大学自动化学院博士研究生. 2007年获南京理工大学计算机系学士学位. 主要研究方向为滑模变结构控制和飞行控制.E-mail: fujian1986216@126.com

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出版历程
- 收稿日期: 2011-02-14
- 修回日期: 2011-06-05
- 刊出日期: 2011-11-20

Robust Sliding Mode Positively Invariant Set for Nonlinear Continuous System

1.
College of Automation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016

摘要

摘要: 针对一类具有控制和状态有界约束的连续非线性系统, 提出了一种基于单向辅助面滑模控制的正不变集设计方法. 该方法通过将约束条件引入单向辅助面的设计中, 利用单向辅助面构造系统状态的正不变集, 以保证系统状态和控制输入在整个过程中都能满足约束条件. 同时, 滑模控制器设计不再受到切换面的限制, 一些不稳定的超平面也可以作为单向辅助面以设计控制器. 随后给出该方法的稳定性分析以及正不变集的理论证明, 并且通过仿真验证了设计方法的有效性.
- 滑模 /
- 正不变集 /
- 单向辅助面滑模控制 /
- 状态和控制有界约束
Abstract: A sliding mode control with unidirectional auxiliary surfaces (UAS-SMC) method of positively invariant sets is proposed for a class of nonlinear continuous systems with states and control inputs constraints. These unidirectional auxiliary surfaces are designed by the state constraints and the feasible state region of the control input constraints. The constraints are guaranteed by using these surfaces to constitute the boundaries of positively invariant sets. As the controller of the system is constituted by unidirectional auxiliary surfaces, the positively invariant sets can be properly enlarged or shrunk with unchanged controller. Even the unstable hyperplanes can be used as unidirectional auxiliary surfaces to design a stable controller. The stability of the system and the positively invariant sets are proved in this paper. Simulation results show the effectiveness of this method.
- Sliding mode /
- positively invariant sets /
- sliding mode control with unidirectional auxiliary surfaces (UAS-SMC) /
- bounded states and control inputs

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参考文献(1)

[1]

Blanchini F. Set invariance in control. Automatica, 1999, 35(11): 1747-1767[2] Jiang Wei-Hua, Huang Lin, Chu Tian-Guang. Robust positively invariant sets of discrete-time nonlinear and time-variable convex polyhedral system family. Acta Automatica Sinica, 2001, 27(5): 631-636(蒋卫华, 黄琳, 楚天广. 离散非线性时变凸多面体系统族的鲁棒正不变集. 自动化学报, 2001, 27(5): 631-636)[3] Zhou B, Duan G R, Lin Z L. Approximation and monotonicity of the maximal invariant ellipsoid for discrete-time systems by bounded controls. IEEE Transactions on Automatic Control, 2010, 55(2): 440-446[4] Tu Z W, Jian J G. Estimating the ultimate bounds and positively invariant sets for a class of general Lorenz-type new chaotic systems. In: Proceedings of International Workshop on Chaos-Fractals Theories and Applications. Kunming, China: IEEE, 2010. 225-228[5] Wu M, Yan G F, Lin Z Y, Liu M Q. Characterization of backward reachable set and positive invariant set in polytopes. In: Proceedings of American Control Conference. St. Louis, USA: IEEE, 2009. 4351-4356[6] Borrelli F, Vecchio C D, Parisio A. Robust invariant set theory applied to networked buffer-level control. In: Proceedings of the 47th IEEE Conference on Decision and Control. Cancun, Mexico: IEEE, 2008. 2111-2116[7] Lee Y, Kouvaritakis B. Robust receding horizon predictive control for systems with uncertain dynamics and input saturation. Automatica, 2000, 36(10): 1497-1504[8] Davila J, Poznyak A. Attracting ellipsoid method application to designing of sliding mode controllers. In: Proceedings of the 11th International Workshop on Variable Structure Systems. Mexico City, Mexico: IEEE, 2010. 83-88[9] Zhang L, Zhang Y, Zhang S L, Heng P A. Activity invariant sets and exponentially stable attractors of linear threshold discrete-time recurrent neural networks. IEEE Transactions on Automatic Control, 2009, 54(6): 1341-1347[10] Masubuchi I. Analysis of positive invariance and almost regional attraction via density functions with converse results. IEEE Transactions on Automatic Control, 2007, 52(7): 1329-1333[11] Rakovic S V, Baric M. Parameterized robust control invariant sets for linear systems: theoretical advances and computational remarks. IEEE Transactions on Automatic Control, 2010, 55(7): 1599-1614

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