Linear Reduced Order Model Predictive Control

TL;DR

This paper introduces a reduced order model predictive control scheme for high-dimensional linear systems, enabling real-time control with guarantees on robustness and stability, demonstrated on complex CFD models.

Contribution

It proposes a projection-based ROMPC method that guarantees robust constraint satisfaction and stability for high-dimensional systems, addressing computational challenges in real-time control.

Findings

Successfully applied to an aircraft control problem with nearly one million dimensions.

Achieved computational efficiency enabling real-time control.

Provided theoretical guarantees on robustness and stability.

Abstract

Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless, high-dimensional models arise in many settings, for example discretization methods for generating finite-dimensional approximations to partial differential equations can result in models with thousands to millions of dimensions. In such cases, reduced order models (ROMs) can significantly reduce computational requirements, but model approximation error must be considered to guarantee controller performance. In this work, a reduced order model predictive control (ROMPC) scheme is proposed to solve robust, output feedback, constrained optimal control problems for high-dimensional linear systems. Computational efficiency is obtained by using projection-based ROMs, and guarantees on robust constraint satisfaction and stability are provided. Performance of the approach is demonstrated in simulation for several examples, including an aircraft control problem leveraging an inviscid computational fluid dynamics model with dimension 998,930.