Optimal synthesis in the simplest time-optimal problem with a linear state constraint

TL;DR

This paper provides a complete synthesis of optimal trajectories for a double integrator system under linear state constraints using the Maximum Principle, offering insights into the structure of optimal controls.

Contribution

It introduces a comprehensive solution to the time-optimal control problem with linear state constraints for the double integrator system, employing the Maximum Principle.

Findings

Complete optimal trajectory synthesis derived

Qualitative analysis of Lagrange multipliers conducted

Insights into control structure under constraints obtained

Abstract

We consider the time-optimal problem for a classical system of "double integrator" under the presence of a linear state constraint. By using the Maximum Principle of Dubovitskii and Milyutin, we determine a complete synthesis of optimal trajectories and qualitatively analyze the corresponding Lagrange multipliers.