Error Bounds for Reduced Order Model Predictive Control

TL;DR

This paper develops an offline method to compute error bounds for reduced order model predictive control, ensuring constraint satisfaction and stability in high-dimensional linear systems with disturbances.

Contribution

It introduces a novel offline approach to efficiently compute error bounds for ROMPC, enhancing safety guarantees for high-dimensional systems.

Findings

Provides a systematic way to compute error bounds for ROMPC

Guarantees constraint satisfaction despite model reduction errors

Applicable to linear systems with bounded disturbances

Abstract

Model predictive control is a powerful framework for enabling optimal control of constrained systems. However, for systems that are described by high-dimensional state spaces this framework can be too computationally demanding for real-time control. Reduced order model predictive control (ROMPC) frameworks address this issue by leveraging model reduction techniques to compress the state space model used in the online optimal control problem. While this can enable real-time control by decreasing the online computational requirements, these model reductions introduce approximation errors that must be accounted for to guarantee constraint satisfaction and closed-loop stability for the controlled high-dimensional system. In this work we propose an offline methodology for efficiently computing error bounds arising from model reduction, and show how they can be used to guarantee constraint satisfaction in a previously proposed ROMPC framework. This work considers linear, discrete, time-invariant systems that are compressed by Petrov-Galerkin projections, and considers output-feedback settings where the system is also subject to bounded disturbances.