| 引用本文: | 李昇平.基于l∞范数和l1范数最小化的二自由度最优鲁棒跟踪控制[J].控制理论与应用,2001,18(4):519~524.[点击复制] |
| LI Sheng-ping.Two-Degree Optimal Robust Tracking Control Based on l∞ and l1 Norm Minimization[J].Control Theory and Technology,2001,18(4):519~524.[点击复制] |
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| 基于l∞范数和l1范数最小化的二自由度最优鲁棒跟踪控制 |
| Two-Degree Optimal Robust Tracking Control Based on l∞ and l1 Norm Minimization |
| 摘要点击 1509 全文点击 1553 投稿时间：2000-01-18 修订日期：2000-10-13 |
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| DOI编号 10.7641/j.issn.1000-8152.2001.4.010 |
| 2001,18(4):519-524 |
| 中文关键词 二自由度控制 最优鲁棒跟踪 l∞和l1范数最优化 |
| 英文关键词 two parameter compensator optimal robust tracking l∞ and l1 norm optimization |
| 基金项目 广东省自然科学基金(990795)资助项目. |
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| 中文摘要 |
| 研究了具有乘摄动模型不确定性并存在未知干扰系统的最优鲁棒跟踪控制问题. 采用二自由度控制器结构Youla参数化方法将最优鲁棒跟踪控制问题转化为两个相互独立的优化问题: 跟踪问题和鲁棒设计问题. 跟踪问题以l∞范数为性能指标通过极小化跟踪误差的最大幅值实现最优跟踪控制; 鲁棒性设计问题中, 将模型不确定性视为一种外界干扰, 通过极小化干扰到误差的灵敏度函数的l1范数使得干扰对跟踪误差的影响最小. 通过截断处理, 上述两种优化问题均可化为标准线性规划问题. 给出了截断阶数与逼近误差之间的关系. 仿真结果表明新方法的有效性. |
| 英文摘要 |
| We investigate the problem of optimal robust tracking control of plants with multiplicative perturbations and unknown disturbances.By making use of Youla parametrization of two parameter compensation scheme,the optimal robust tracking problem can be transformed into two independent problems that are called tracking problem and robustness design problem. The tracking performance is optimized by minimizing l∞ norm of tracking error; The robustness design ensures stability to multiplicative perturbations and minimizes the l1 norm of system's sensitivity from tracking error to various disturbances including that caused by model perturbations. These two optimizations are set up as linear program by truncation techniques. The relation between truncation degree and approximation error is provided. Simulations show that the new robust tracking control is effective. |