Robust Adaptive Model Predictive Control with Worst-Case Cost

TL;DR

This paper introduces a robust adaptive MPC algorithm for linear systems with unknown dynamics, using set-membership identification and worst-case cost optimization to ensure constraint satisfaction under uncertainty.

Contribution

It proposes a novel robust adaptive MPC scheme that minimizes worst-case cost considering model uncertainties and enforces constraints for all feasible models.

Findings

Outperforms existing adaptive MPC in simulations.

Ensures constraint satisfaction under bounded uncertainties.

Effective in reducing uncertainty through set-membership identification.

Abstract

A robust adaptive model predictive control (MPC) algorithm is presented for linear, time invariant systems with unknown dynamics and subject to bounded measurement noise. The system is characterized by an impulse response model, which is assumed to lie within a bounded set called the feasible system set. Online set-membership identification is used to reduce uncertainty in the impulse response. In the MPC scheme, robust constraints are enforced to ensure constraint satisfaction for all the models in the feasible set. The performance objective is formulated as a worst-case cost with respect to the modeling uncertainties. That is, at each time step an optimization problem is solved in which the control input is optimized for the worst-case plant in the uncertainty set. The performance of the proposed algorithm is compared to an adaptive MPC algorithm from the literature using Monte-Carlo simulations.