l1优化设计的连续性分析

Analysis of Continuity Property of l1 Optimization Design *

中文关键词  l1优化设计  连续性  次优解

英文关键词  l1 0ptimization design  continuity property  suboptimal solution

中文摘要

      本文研究l1优化设计在一般情形下的连续性，本文的结论是文[1]的推广. 首先，证明了l1优化设计在一般情形下次优解的存在性并给出了l1优化设计的统一算法. 然后，证明了l1优化设计在一般情形下的连续性. 这个结论是研究自适应l1控制理论的基础.

英文摘要

      In this paper we investigate the continuity property of l1 optimization design in ge-neral case，extending the main result in [1] where the continuity of l1 optimization design is proved under some restrictive assumption. At first，in the general case，the existence of suboptimal solu-tion of l1 optimization problem is proved and a unified l1 optimization design algorithm is presented. Then the continuity property of l1 optimization design in general case is proved. This conclusion is the basis of the development of adaptive l1 control theory.