Optimization method for solving bang-bang and singular control problems

作     者：Shurong LI Ruiyan ZHAO Qiang ZHANG Shurong LI;Ruiyan ZHAO;Qiang ZHANG

作者机构：College of Information and Control EngineeringChina University of Petroleum 

出 版 物：《控制理论与应用（英文版）》 (控制理论与应用)

年 卷 期：2012年第10卷第4期

页      面：559-564页

核心收录：

学科分类：0711[理学-系统科学] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：supported by the Natural Science Foundation of China(No.60974039) the National Science and Technology Major Project(No. 2008ZX05011) 

主　　题：Bang-bang control Singular control Multi-stage problem Nonlinear programming problem 

摘      要：In this paper we study optimal control problems with the control variable appearing linearly. A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented. This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem. The optimal control problem is partitioned as several stages, with each stage corresponding to a particular control arc. A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming （NLP） problem. The control profiles and stage lengths act as decision variables. Based on the Pontryagin maximal principle, a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers. Two examples are studied to demonstrate the effectiveness of this strategy.