Guaranteed Cost Approach to Robust Model Predictive Control of Uncertain Linear Systems

TL;DR

This paper introduces a guaranteed cost robust model predictive controller for uncertain discrete systems, offering a computationally efficient alternative to traditional methods by using QCQP optimization.

Contribution

It presents a novel guaranteed cost approach that handles quadratically bounded uncertainties efficiently without relying on polytopic approximations.

Findings

Achieves robustness against quadratic uncertainties

Reduces computational complexity compared to SDP-based methods

Uses QCQP optimization for practical implementation

Abstract

In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect to quadratically bound uncertainties. Such a class of problems is currently intractable by Min-Max Robust Model Predictive Controllers without polytopic approximations of the uncertainties. The proposed technique is computationally more efficient then an enumeration-based approach and requires only a Quadratically Constrained Quadratic Problem (QCQP) optimization, whereas LMI-based GCMPC approaches require a Semi-Definite Programming (SDP) optimization.