An Adaptive Pseudospectral Method Combined With Homotopy Method for Solving Optimal Control Problems

被引：0
|
作者：
Qin T.-H. [1 ]
机构：
[1] School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing
来源：
Zidonghua Xuebao/Acta Automatica Sinica | 2019年 / 45卷 / 08期
关键词：
Adaptive pseudospectral method; Bang-Bang control; Homotopy method; Optimal control problem; Weakly discontinuous solution;
D O I：
10.16383/j.aas.2018.c170551
中图分类号：
学科分类号：
摘要：
Aiming at the weakly discontinuous and Bang-Bang optimal control problems, an adaptive pseudospectral method combined with the homotopy method is proposed. The Chebyshev pseudospectral method transforms the original problems into the resulting nonlinear programming problems. Based on the idea of homotopy method, the homotopic parameters change the bounds on path constraints to obtain a series of smoother optimal control problems. The nonsmooth original problems are solved by starting from the smoother problems. The convergence of numerical solutions is proved for the weakly discontinuous problems. With the help of the convergence and the homotopic parameters, an error indicator is able to capture the nonsmooth points. Several numerical examples are given to compare the proposed method with other methods. The comparison shows that the proposed method has obvious advantages in terms of accuracy and efficiency. Copyright © 2019 Acta Automatica Sinica. All rights reserved.
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页码：1579 / 1585
页数：6
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