How not to discretize the control

TL;DR

This paper investigates the discretization of higher order polynomial optimal control problems, providing conditions to ensure feasible limits and highlighting potential pitfalls of naive discretization methods.

Contribution

It introduces a necessary and sufficient condition for the feasibility of weak limits in discretized control problems with higher order polynomials.

Findings

Naive discretization can lead to non-feasible solutions.

The paper provides a criterion to guarantee feasible limits.

Counterexample demonstrates issues with higher order polynomial discretization.

Abstract

In this short note, we address the discretization of optimal control problems with higher order polynomials. We develop a necessary and sufficient condition to ensure that weak limits of discrete feasible controls are feasible for the original problem. We show by means of a simple counterexample that a naive discretization by higher order polynomials can lead to non-feasible limits of sequences of discrete solutions.