Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version

TL;DR

This paper introduces a computationally efficient robust adaptive MPC scheme for linear systems with parametric uncertainty and disturbances, balancing reduced conservatism, stability guarantees, and fixed complexity via online parameter adaptation.

Contribution

It presents a novel fixed-complexity adaptive MPC method with theoretical guarantees and reduced conservatism, using online parameter set identification and tube-based robust control.

Findings

Achieves constraint satisfaction and stability with fixed computational complexity.

Demonstrates improved performance and reduced conservatism through online adaptation.

Provides a numerical example illustrating the trade-off between conservatism and complexity.

Abstract

In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with theoretical guarantees (constraint satisfaction and stability), while allowing for reduced conservatism and improved performance due to online parameter adaptation. A moving window parameter set identification is used to compute a fixed complexity parameter set based on past data. Robust constraint satisfaction is achieved by using a computationally efficient tube based robust MPC method. The predicted cost function is based on a least mean squares point estimate, which ensures finite-gain $\mathcal{L}_2$ stability of the closed loop. The overall algorithm has a fixed (user specified) computational complexity. We illustrate the applicability of the approach and the trade-off between conservatism and computational complexity using a numerical example. This paper is an extended version of~[1], and contains additional details regarding the theoretical proof of Theorem~1, the numerical example, and the offline computations in Appendix~A--B.