| 引用本文: | 倪郁东,费树岷.临界状态下三维仿射控制系统的局部光滑镇定[J].控制理论与应用,2011,28(2):179~184.[点击复制] |
| NI Yu-dong,FEI Shu-min.Local smooth stabilization of 3-dimensional nonlinear affine control systems in critical cases[J].Control Theory and Technology,2011,28(2):179~184.[点击复制] |
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| 临界状态下三维仿射控制系统的局部光滑镇定 |
| Local smooth stabilization of 3-dimensional nonlinear affine control systems in critical cases |
| 摘要点击 1573 全文点击 894 投稿时间：2009-05-09 修订日期：2010-11-16 |
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| DOI编号 10.7641/j.issn.1000-8152.2011.2.CCTA090579 |
| 2011,28(2):179-184 |
| 中文关键词 非线性控制系统 临界状态 李雅普诺夫函数 局部光滑镇定 |
| 英文关键词 nonlinear control systems critical case Lyapunov function local smooth stabilization |
| 基金项目 国家自然科学基金重点资助项目(60835001). |
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| 中文摘要 |
| 讨论三维仿射非线性控制系统, 在具有零和一对共轭纯虚数特征值的临界状态下的局部光滑镇定性. 首先, 应用非奇异线性状态变换和时间尺度变换, 将系统转化成标准形式. 之后, 运用形式级数法的思想和扩展正则判别函数法, 构造多组线性方程组, 给出确定光滑控制律和闭环系统李雅普诺夫函数的一种方法, 从而得到该标准化系统局部光滑镇定的充分条件. 示例说明该方法是有效的. |
| 英文摘要 |
| This paper studies the local smooth stabilization of 3-dimensional nonlinear affine control systems with a null eigenvalue and a pair of conjugated imaginary eigenvalues. The system is converted to a standard form by employing a nonsingular linear transform and a time-scale transform; and then, sets of linear equations are formed by using the formal progression method and the extended canonical discriminant function. Furthermore, an approach is developed to determine the smooth control law and the Lyapunov function for the closed-loop system. Consequently, a sufficient condition of the local smooth stabilization for the standard system is obtained; the validity of which is shown by an example. |