| 引用本文: | 周燕茹,汪育成,付荣.一类具有凸多面体不确定性的非线性变参数系统鲁棒H∞控制[J].控制理论与应用,2023,40(6):995~1004.[点击复制] |
| ZHOU Yan-ru,WANG Yu-cheng,FU Rong.Robust H∞ control for a class of nonlinear parameter-varying systems with polytopic uncertainty[J].Control Theory and Technology,2023,40(6):995~1004.[点击复制] |
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| 一类具有凸多面体不确定性的非线性变参数系统鲁棒H∞控制 |
| Robust H∞ control for a class of nonlinear parameter-varying systems with polytopic uncertainty |
| 摘要点击 1653 全文点击 479 投稿时间：2022-02-14 修订日期：2023-06-19 |
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| DOI编号 10.7641/CTA.2022.20110 |
| 2023,40(6):995-1004 |
| 中文关键词 凸多面体不确定性 非线性变参数系统 鲁棒H∞控制 平方和 |
| 英文关键词 convex polytopic uncertainty nonlinear parameter-varying systems robust H∞ control sum of squares |
| 基金项目 福建省自然科学基金项目(2020J01284), 福建省中青年教师教育科研项目(JAT200495, JAT190675), 厦门市科技计划项目(3502Z20203066) |
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| 中文摘要 |
| 针对具凸多面体不确定性的非线性变参数(NPV)系统, 本文研究了其非线性鲁棒H∞控制问题. 基于Lyapunov稳定性理论和多项式平方和(SOS)方法, 对该系统设计了非线性鲁棒状态反馈镇定控制器. 在此基础上, 进一 步考虑存在外部扰动情形, 给出相应的非线性鲁棒H∞控制可解性条件. 该条件以状态和时变参数依赖的线性矩阵 不等式形式(LMIs)给出, 可借助凸优化工具进行有效检验. 最后, 通过数值仿真验证了所得方法的有效性和优势. |
| 英文摘要 |
| This paper focuses on the nonlinear robust H∞ control problem for a class of nonlinear parameter-varying (NPV) systems with convex polytopic uncertainties. A nonlinear robust state feedback stabilization controller is designed based on the Lyapunov stability theory and polynomial sum of squares (SOS) method. Furthermore, by taking into consideration the external disturbances, the corresponding solvability conditions of nonlinear robust H∞ control are presented in the form of state- and time-varying parameter-dependent linear matrix inequalities (LMIs), which can be effectively checked with the aid of convex optimization tools. Finally, two numerical examples are given to verify the effectiveness and advantages of the proposed approach. |