Energy Optimal Control of a Harmonic Oscillator with a State Inequality Constraint

TL;DR

This paper derives analytical solutions for the energy-optimal control of a harmonic oscillator with inequality constraints, considering various initial states and time horizons, revealing distinct control modes.

Contribution

It provides the first analytical solutions for energy-optimal control of a harmonic oscillator with inequality constraints, including multiple initial conditions and time durations.

Findings

Analytical solutions for small and large terminal times.

Identification of three control modes: wait-move, move-wait, move-wait-move.

Optimal control strategies depend on initial states and time horizon.

Abstract

In this article, the optimal control problem for a harmonic oscillator with an inequality constraint is considered. The applied energy of the oscillator during a fixed final time period is used as the performance criterion. The analytical solution with both small and large terminal time is found for a special case when the undriven oscillator system is initially at rest. For other initial states of the Harmonic oscillator, the optimal solution is found to have three modes: wait-move, move-wait, and move-wait-move given a longer terminal time.