Robust reduced-order model predictive control using peak-to-peak analysis of filtered signals

TL;DR

This paper introduces a robust reduced-order model predictive control method that guarantees constraint satisfaction for large-scale linear systems by bounding errors using peak-to-peak analysis of filtered signals.

Contribution

It presents a novel approach to obtain guaranteed bounds on full-system outputs using peak-to-peak analysis, enhancing robustness and reducing conservatism in ROM-based MPC.

Findings

Achieved over four orders of magnitude reduction in conservatism.

Successfully applied to a 100-dimensional mass-spring-damper system.

Guaranteed constraint satisfaction in large-scale systems.

Abstract

We address the design of a model predictive control (MPC) scheme for large-scale linear systems using reduced-order models (ROMs). Our approach uses a ROM, leverages tools from robust control, and integrates them into an MPC framework to achieve computational tractability with robust constraint satisfaction. Our key contribution is a method to obtain guaranteed bounds on the predicted outputs of the full-order system by predicting a (scalar) error-bounding system alongside the ROM. This bound is then used to formulate a robust ROM-based MPC that guarantees constraint satisfaction and robust performance. Our method is developed step-by-step by (i) analysing the error, (ii) bounding the peak-to-peak gain, an (iii) using filtered signals. We demonstrate our method on a 100-dimensional mass-spring-damper system, achieving over four orders of magnitude reduction in conservatism relative to existing approaches.