Analytic Solution of the Time-Optimal Control of a Double Integrator from an Arbitrary State to the State-space Origin

TL;DR

This paper provides a detailed, step-by-step analytical solution for the minimum-time control problem of a double integrator system from any initial state to the origin, serving as a didactical resource.

Contribution

It offers a comprehensive, detailed derivation of the time-optimal control law for the double integrator, enhancing understanding through a didactical approach.

Findings

Explicit analytical solution derived

Step-by-step procedure outlined

Applicable to arbitrary initial states

Abstract

This brief note presents known results about the minimum-time control of a double integrator system from an arbitrary initial state to the state-space origin (minimum-time regulation problem, or special problem). The main purpose of this note is didactical. Results are presented in all details and following a step by step procedure.