Homothetic tube model predictive control with multi-step predictors

TL;DR

This paper introduces a robust MPC framework using multi-step predictors and homothetic tubes to reduce conservatism and computational complexity in controlling linear systems with uncertainties.

Contribution

It integrates multi-step predictors into homothetic tube MPC, providing less conservative bounds and a multi-rate formulation for improved robustness and efficiency.

Findings

Reduced conservatism compared to standard MPC

Guarantees recursive feasibility and stability

Lower computational complexity in simulations

Abstract

We present a robust model predictive control (MPC) framework for linear systems facing bounded parametric uncertainty and bounded disturbances. Our approach deviates from standard MPC formulations by integrating multi-step predictors, which provide reduced error bounds. These bounds, derived from multi-step predictors, are utilized in a homothetic tube formulation to mitigate conservatism. Lastly, a multi-rate formulation is adopted to handle the incompatibilities of multi-step predictors. We provide a theoretical analysis, guaranteeing robust recursive feasibility, constraint satisfaction, and (practical) stability of the desired setpoint. We use a simulation example to compare it to existing literature and demonstrate advantages in terms of conservatism and computational complexity.