Multiple solutions to the <i>l</i><SUP>1</SUP>-optimal control problem and its dual linear programming problem

作     者：Alpay, ME Shor, MH 

作者机构：Electrosci Ind Inc Porland OR 97229 USA Oregon State Univ Dept Elect & Comp Engn Corvallis OR 97331 USA 

出 版 物：《IEEE TRANSACTIONS ON AUTOMATIC CONTROL》 (IEEE Trans Autom Control)

年 卷 期：1999年第44卷第5期

页      面：1089-1093页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 

基　　金：National Science Foundation, NSF, (ECS-9309336) National Science Foundation, NSF 

主　　题：dual linear multiple solutions l(1)-optimal control programming problem 

摘      要：This paper explores the consequences for the l(1)-optimal controller of the dual linear programming problem having multiple solutions, for linear time-invariant single-input/single-output systems. When the dual problem has multiple solutions, all solutions yield the same set of optimal controllers. If these multiple solutions comprise an entire face of the constraint region, there is a single optimal controller. Thus, if the constraint region is two-dimensional, the primal and dual problems cannot both have multiple solutions. An example is given with a three-dimensional constraint region where both problems have multiple solutions.