Iterative Switching Time Optimization for Mixed-integer Optimal Control Problems

TL;DR

This paper introduces an iterative Switching Time Optimization method for mixed-integer optimal control problems with switched dynamics, addressing issues with relaxed problem solutions and demonstrating improved efficiency through numerical examples.

Contribution

It presents a novel iterative algorithm combining Switching Time Optimization and sequence optimization for better solutions in mixed-integer control problems.

Findings

The proposed method outperforms traditional relaxed problem approaches.

Numerical examples demonstrate the efficiency of the iterative algorithm.

Discussion of advantages and disadvantages guides future research directions.

Abstract

This paper proposes an iterative method to solve Mixed-Integer Optimal Control Problems arising from systems with switched dynamics. The so-called relaxed problem plays a central role within this context. Through a numerical example, it is shown why relying on the relaxed problem can lead the solution astray. As an alternative, an iterative Switching Time Optimization method is proposed. The method consists of two components that iteratively interact: a Switching Time Optimization (STO) problem and a sequence optimization. Each component is explained in detail, and the numerical example is resolved, the results of which shows the efficiency of the proposed algorithm. Finally, the advantages and disadvantages of the method are discussed and future lines of research are sketched.