Stepwise Methods in Optimal Control Problems

TL;DR

This paper introduces a stepwise method for solving optimal control problems, addressing limitations of continuous control functions in PMP and demonstrating advantages in complex models and real-world applications.

Contribution

A novel stepwise approach to optimal control that improves practical implementation and handles complex cost functions better than traditional PMP.

Findings

The stepwise method effectively solves control problems with practical control change intervals.

It outperforms PMP in models with complicated cost functions or systems.

The method shows high performance in real-world applications.

Abstract

We introduce a new method, stepwise method for solving optimal con- trol problems. Our first motivation for new approach emanate from limi- tations on continuous time control functions in PMP. Practically in most of the real world models, we are not able to change control value for every time such as in drug dose calculation or in resourse allocation problems. But it is practical to change control value in some time section that lead to stepwise control function. We study some examples via classical Pontrya- gin Maximum Principle(PMP) and via stepwise method. The new method has some other advantages in comparison with PMP method in models with complicated cost function or systems. In real world applications, the new method has a high performance in implementation.