用分块法求解最优控制问题

Samuel Adamu
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摘要

.使用前向-后向扫描方法来解决最优控制问题,该方法利用配置混合二阶导数块方法,利用pontryagin原理使用多项式近似解。块法是由离散线性多步方法形成的。还编写了正向算法、反向算法。分析并证明了分块法的稳定性是稳定的、收敛的,其阶数为6。该算法用编写的MATLAB代码实现,并求解了三个最优控制问题来检验该方法的准确性,数值算例表明,前向-后向扫描法和基于Pontryagin原理的分块法比用传统的经典龙格-库塔方法求解最优控制问题更准确。因此,本研究工作确定了块法可以与使用庞特里亚金原理的前向-后向扫描法相结合来解决最优控制问题,并且比使用传统的经典龙格-库塔方法产生更准确的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Numerical Solution of Optimal Control Problems using Block Method
. Forward-backward sweep approach is used to solve optimal control problems utilizing a collocation hybrid second derivative block method using polynomial approximate solution via pontryagin’s principle. The block method is formulated from the discrete linear multistep methods. Also, the forward algorithms, backward algorithm written. The stability properties of the block method are analyzed and proved to be stable, convergent and of order 6. The algorithm is implemented with a written MATLAB code, and three optimal control problems are solved to test the accuracy of the approach, which the numerical examples show that, forward-backward sweep methods together with block method via Pontryagin’s principle are more accurate than when solving optimal control problems with the traditional classical Runge-Kutta method. This research work therefore established that block method can be combined with forward backward sweep method using Pontryagin’s principle to solve optimal control problems and produce more accurate result than using the traditional classical Runge-Kutta method.
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