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一类非光滑优化及其在控制系统稳定化中的应用 被引量：3

A Class of Nonsmooth Optimizations and Its Applications to Stabilization for Control Systems
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摘要 研究一类来自控制系统稳定化中的非光滑优化问题.考虑Lyapunov函数是非光滑的,特别是有限个光滑函数的极大值函数.建立了相应的非光滑优化模型,进一步导出了这类非光滑优化的KKT系统,然后基于非线性互补函数将此KKT系统转化成一个非光滑方程组,最后分别用广义牛顿法和光滑化牛顿法求解此非光滑方程组,使得此类稳定化设计可以具体实现. A nonsmooth optimization problem, which arises from the stabilization for nonlinear control systems, is studied. Nonsmooth Lyapunov functions are obtained by maximizing finitely many smooth functions. First, a nonsmooth optimization model and its Karush-Kuhn-Tucker （KKT） system are proposed. Based on the nonlinear complementarity problem function, the KKT system is transformed into a system of nonsmooth equations. Finally, the generalized Newton method and the smoothing Newton method are applied to solving this system of nonsmooth equations.
作者 高岩
机构地区 上海理工大学管理学院
出处 《控制与决策》 EI CSCD 北大核心 2006年第1期118-120,共3页 Control and Decision
基金 教育部归国留学人员基金项目 上海市教委重点项目(04EA01) 上海市重点学科建设项目(T0502)
关键词 非光滑优化 非光滑方程组 稳定化 LYAPUNOV函数 牛顿法 Nonsmooth optimization Nonsmooth equations Stabilization Lyapunov function Newton method
分类号 O231.2 [理学—运筹学与控制论] TD350 [矿业工程—矿井建设]
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参考文献8

  • 1Quincampoix M, Seube N. Stabilization of Uncertain Control Systems Through Piecewise Constant Feedback[J]. J Mathematics Analysis and Applications, 1998,218(1): 240-255.
  • 2Gao Y, Lygeros J, Quineampoix M, et al.Approximate Stabilisation of Uncertain Hybrid Systems with Controllable Transitions [A]. Proc 36th IEEE Conf on Control and Decision[C]. Maui, Hawaii, 2003:1675-1680.
  • 3Gao Y, Lygeros J, Quincampoix M, et al.Approximate Control of Uncertain Hybrid Systems: Stabilisation and Controlled Invariance[J]. Int J of Control, 2004, 77(16): 1393-1407.
  • 4Clarke F H, Leda Yu S, Stern R J, et al. Nonsmooth Analysis and Control Theory[M]. New York: Springer-Verlag, 1998.
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  • 6Qi L, Sun J. A Nonsmooth Version of Newton's Method [J]. Mathematical Programming, 1993, 58(2):353-367.
  • 7Qi L, Sun D. Smoothing Functions and a Smoothing Newton Method for Complementarity and Variational Inequality Problems [J]. J Optimization Theory and Applications, 2002, 113(1): 121-147.
  • 8Gao Y. Newton Methods for Solving Nonsmooth Equations via a New Subdifferential [J]. Mathematical Methods of Operations Research, 2001, 54(2): 239-257.

同被引文献17

  • 1Decarlo R, Branicky M, Pettersson S, et al. Perspectives and Results on the Stability and Stabilizability of Hybrid Systems [J].Proceedings of the IEEE, 2000,88 (7):1 069- 1 082.
  • 2Hiskens I A, Pai M A. Trajectory Sensitivity Analysis of Hybrid Systems [J].IEEE Transaction on Circuits and Systems, 2000,47(2):204-220.
  • 3Lygeros J,Johansson K H, Simic S N, et al. Dynamical Properties of Hybrid Automata [J]. IEEE Transaction on Automatic Control, 2003,48 (1):2-17.
  • 4Aubin J P, Lygeros J, Quincampoix M, et al.Impulse Differential Inclusions:a Viability Approach to Hybrid System [J]. IEEE Transaction on Automatic Control, 2002,47(1):2-20.
  • 5Gao Y, Lygeros J ,Quincampoix M. On the Re Achability Problem of Uncertain Hybrid Systems[J]. IEEE Transactions on Automatic Control, 2007,52(9): 1 572-1 586.
  • 6Lou Z E, Gao Y . Approximate Stabilization of Switched Nonlinear Systems[J] .Journal of Information and Computing Science,2009,4(1):26-32.
  • 7Aubin J-P. Viability Theory[M]. Boston:Birkhauser,1991.
  • 8Gao Y, Lygeros J, Quincampoix M ,et al.On the Control of Uncertain Impulsive Systems: Approximate Stabilization and Controlled Invariance [J].Intemational Journal of Control ,2004,77(16):1 393-1 407.
  • 9Qi Li-qun, Sun Jie. A Nonsmooth Version of Newton's Method[J].Mathematical Programming, 1993,58:353-367.
  • 10Marc Quincampoix , Nicolas Seube. Stabilization of Uncertain Control Systems through Piecewise Constant Feedback [ J ]. Journal of Mathematical Analysis and Applications , 1998. 218,240- 255.

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控制与决策
2006年 第1期

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