Self-Tuning Tube-based Model Predictive Control

TL;DR

This paper introduces a self-tuning, adaptive robust control algorithm for uncertain linear systems that guarantees constraint satisfaction and stability using a least-squares estimator and polytopic tubes, with proven confidence bounds.

Contribution

The paper proposes a novel self-tuning MPC method that adaptively bounds system uncertainty and ensures robustness without increasing computational complexity.

Findings

Guarantees robust constraint satisfaction with confidence bounds.

Ensures recursive feasibility and input-to-state stability.

Demonstrates effective performance through numerical experiments.

Abstract

We present Self-Tuning Tube-based Model Predictive Control (STT-MPC), an adaptive robust control algorithm for uncertain linear systems with additive disturbances based on the least-squares estimator and polytopic tubes. Our algorithm leverages concentration results to bound the system uncertainty set with prescribed confidence, and guarantees robust constraint satisfaction for this set, along with recursive feasibility and input-to-state stability. Persistence of excitation is ensured without compromising the algorithm's asymptotic performance or increasing its computational complexity. We demonstrate the performance of our algorithm using numerical experiments.