Computationally Efficient Robust Model Predictive Control for Uncertain System Using Causal State-Feedback Parameterization

TL;DR

This paper introduces a computationally efficient robust model predictive control method for uncertain linear systems, linearizing the problem via semidefinite relaxation to enable real-time implementation with minimal conservatism.

Contribution

A novel linearization approach for RMPC using semidefinite relaxation that reduces computational complexity while maintaining control performance.

Findings

Significantly reduced online computational burden compared to existing methods.

Maintains tracking performance with minimal conservatism.

Effective offline feasibility strategy enhances real-time applicability.

Abstract

This paper investigates the problem of robust model predictive control (RMPC) of linear-time-invariant (LTI) discrete-time systems subject to structured uncertainty and bounded disturbances. Typically, the constrained RMPC problem with state-feedback parameterizations is nonlinear (and nonconvex) with a prohibitively high computational burden for online implementation. To remedy this, a novel approach is proposed to linearize the state-feedback RMPC problem, with minimal conservatism, through the use of semidefinite relaxation techniques. The proposed algorithm computes the state-feedback gain and perturbation online by solving a linear matrix inequality (LMI) optimization that, in comparison to other schemes in the literature is shown to have a substantially reduced computational burden without adversely affecting the tracking performance of the controller. Additionally, an offline strategy that provides initial feasibility on the RMPC problem is presented. The effectiveness of the proposed scheme is demonstrated through numerical examples from the literature.