| 一类非光滑优化及其在控制系统稳定化中的应用 |
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| 引用本文： | 高岩. 一类非光滑优化及其在控制系统稳定化中的应用[J]. 控制与决策, 2006, 21(1): 118-0120 |
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| 作者姓名： | 高岩 |
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| 作者单位： | 上海理工大学,管理学院,上海,200093 |
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| 基金项目： | 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）. |
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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．
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| 关 键 词： | 非光滑优化 非光滑方程组 稳定化 Lyapunov函数 牛顿法 |
| 文章编号： | 1001-0920（2006）01-0118-03 |
| 收稿时间： | 2004-11-30 |
| 修稿时间： | 2005-04-15 |
A Class of Nonsmooth Optimizations and Its Applications to Stabilization for Control Systems |
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| GAO Yan. A Class of Nonsmooth Optimizations and Its Applications to Stabilization for Control Systems[J]. Control and Decision, 2006, 21(1): 118-0120 |
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| Authors: | GAO Yan |
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| Affiliation: | School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China. |
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| Abstract: | 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. |
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| Keywords: | Nonsmooth optimization Nonsmooth equations Stabilization Lyapunov function Newton method |
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