文献类型：期刊文献

英文题名：ON THE GLOBAL OPTIMAL SOLUTION FOR LINEAR QUADRATIC PROBLEMS OF SWITCHED SYSTEM

作者：He, Jin Feng[1];Xu, Wei[2];Feng, Zhi Guo[1,3];Yang, Xinsong[1]

机构：[1]Chongqing Normal Univ, Coll Math Sci, Chongqing, Peoples R China;[2]Shanghai Univ, Sch Management, Shanghai, Peoples R China;[3]Guangdong Ocean Univ, Fac Math & Comp Sci, Zhanjiang, Guangdong, Peoples R China

年份：2019

卷号：15

期号：2

起止页码：817

外文期刊名：JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

收录：SCI-EXPANDED(收录号：WOS:000457104800022)、、Scopus(收录号：2-s2.0-85063721100)、WOS

基金：This paper is supported by the grant of National Natural Science Foundation of China (No. 61673078), the grant of Chongqing Science and Technology Commission (No. cstc2017jcyjAX0161), the grant of Chongqing Normal University (No. 17XLB010) and the graduate innovative research grant of Chongqing Normal University (No. YKC17016).

语种：英文

外文关键词：Global optimal solution; optimal switching problem; switching sequence; relaxation method

外文摘要：The global optimal solution for the optimal switching problem is considered in discrete time, where these subsystems are linear and the cost functional is quadratic. The optimal switching problem is a discrete optimization problem. Complete enumeration search is always required to find the global optimal solution, which is very expensive. Relaxation method is an effective method to transform the discrete optimization problem into the continuous optimization problem, while the optimal solution is always not the feasible solution of the discrete optimization problem. In this paper, we propose a special class of relaxation method to transform the optimal switching problem into a relaxed optimization problem. We prove that the optimal solution of this modified relaxed optimization problem is exactly that of the optimal switching problem. Then, the global optimal solution can be obtained by solving the continuous optimization problem easily. Numerical examples are demonstrated to show that the modified relaxation method is efficient and effective to obtain the global optimal solution.