引用本文:郝　飞,楚天广,黄　琳.离散时间系统混合l1/H∞-控制问题[J].控制理论与应用,2002,19(5):667~672.[点击复制]
HAO Fei,CHU Tian-guang,HUANG Lin.Mixed l-one/H-infinity control problem for discrete-time systems[J].Control Theory and Technology,2002,19(5):667~672.[点击复制]
离散时间系统混合l1/H∞-控制问题
Mixed l-one/H-infinity control problem for discrete-time systems
摘要点击 1241  全文点击 1309  投稿时间：2001-05-31  修订日期：2001-12-30
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DOI编号  10.7641/j.issn.1000-8152.2002.5.003
  2002,19(5):667-672
中文关键词  离散时间系统  l1控制问题  H∞-控制  多目标优化
英文关键词  discrete-time systems  l-one-control  H-infinity-control  multiple objective
基金项目  国家重点基础研究基金(G1998020302); 国家自然科学基金(19872005,69925307)资助项目.
作者单位E-mail
郝　飞 北京大学 力学与工程科学系系统与控制研究中心, 北京 100871 fhao@mech.pku.edu.cn  
楚天广 北京大学 力学与工程科学系系统与控制研究中心, 北京 100871  
黄　琳 北京大学 力学与工程科学系系统与控制研究中心, 北京 100871  
中文摘要
      研究MIMO离散时间系统混合l1/H∞控制问题. 通过引入辅助优化问题, 证明了目标优化值关于约束H∞指标的连续依赖性及其辅助问题最优化解的存在性, 同时证明了辅助优化问题的截断序列问题解的收敛性, 且其极限为混合l1/H∞_控制优化的辅助问题的最优化解. 还给出了优化目标值的上下界逼近.
英文摘要
      This paper is concerned with mixed l-one/H-infinity-control problem of MIMO discrete_time systems where l-one-performance objective is minimized subject to an H-infinity constraint. By introducing an auxiliary optimal problem, we prove the continuous_dependence of optimal objective with respect to the constrainted H-infinity-performance objective. The existence of the solution of the auxiliary optimal problem is also proved. We present the convergence of the solutions of a series of the truncation problems of the auxiliary optimal problem, and show that its limit is the optimal solution of the auxiliary optimal problem. Particularly, we give an approach to obtain the converging lower and upper bounds of the mixed l-one/H-infinity-control problem. This approach gives a computationally efficient synthesis procedure which avoid the problem of zero-interpolation techniques. Finally, an example shows that the approach is feasible for designing suboptimal controller of the mixed control problem.