Explicit bounds for solutions to optimal control problems

TL;DR

This paper derives explicit bounds for solutions to Lagrange optimal control problems without end-point constraints, using an approach based on equivalence to time-optimal differential inclusion problems.

Contribution

It introduces explicit bounds for Lagrange problems by leveraging Gamkrelidze's method and the equivalence to time-optimal differential inclusions, providing new analytical tools.

Findings

Derived explicit bounds for optimal control solutions.

Applied Gamkrelidze's approach to establish bounds.

Connected Lagrange problems to differential inclusions.

Abstract

In this paper we present explicit bounds for optimal control in a Lagrange problem without end-point constraints. The approach we use is due to Gamkrelidze and is based on the equivalence of the Lagrange problem and a time-optimal problem for diferential inclusions.