The time optimal control problem with control constraints of the rectangular type for a class of ODEs

TL;DR

This paper investigates a time optimal control problem with rectangular control constraints for linear time-varying ODEs, establishing conditions for optimality and developing an algorithm for finding optimal controls.

Contribution

It provides necessary and sufficient conditions for optimal time and controls, and introduces an algorithm to compute them for this class of problems.

Findings

Derived necessary and sufficient conditions for optimal control.

Developed an algorithm for computing optimal controls.

Applied results to specific linear time-varying systems.

Abstract

This paper studies a time optimal control problem with control constraints of the rectangular type for the linear multi-input time-varying ordinary differential equations. The aims of this study are to establish certain necessary and sufficient conditions for the optimal time and time optimal control, and to build up an algorithm for the optimal time and time optimal control.