Optimal control of multiscale systems using reduced-order models

TL;DR

This paper investigates whether reducing multiscale systems before optimal control is feasible and effective, providing conditions, numerical examples, and discussing potential pitfalls of the 'first reduce, then control' strategy.

Contribution

It establishes theoretical conditions under which the reduction-before-control approach is valid and illustrates its application with numerical examples.

Findings

Conditions for valid reduction-before-control strategy

Numerical examples demonstrating the approach

Discussion of potential pitfalls and limitations

Abstract

We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal control computed from the reduced-order model to control the original, high-dimensional system? The strategy "first reduce, then optimize"--rather than "first optimize, then reduce"--is motivated by the fact that solving optimal control problems for high-dimensional multiscale systems is numerically challenging and often computationally prohibitive. We state sufficient and necessary conditions, under which the "first reduce, then control" strategy can be employed and discuss when it should be avoided. We further give numerical examples that illustrate the "first reduce, then optmize" approach and discuss possible pitfalls.