Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty

TL;DR

This paper introduces a learning-based robust predictive control method for discrete-time linear systems with unknown nonlinear dynamics, enhancing safety and performance under large uncertainties by leveraging online learning and statistical safety guarantees.

Contribution

It presents a novel adaptive robust MPC framework that exploits learned structure in unknown dynamics and extends to constrained systems with probabilistic safety certification.

Findings

Handles larger uncertainties than existing methods

Guarantees safety with high probability

Improves performance through learned nonlinear feedback policies

Abstract

We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems commonly model the nonlinear effects of an unknown environment on a nominal system. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws pioneered in classical adaptive control to achieve significant performance improvements in the presence of uncertainties of large magnitude, a setting in which existing learning-based predictive control algorithms often struggle to guarantee safety. In contrast to previous work in robust adaptive MPC, our approach allows us to take advantage of structure (i.e., the numerical predictions) in the a priori unknown dynamics learned online through function approximation. Our approach also extends typical nonlinear adaptive control methods to systems with state and input constraints even when we cannot directly cancel the additive uncertain function from the dynamics. Moreover, we apply contemporary statistical estimation techniques to certify the system's safety through persistent constraint satisfaction with high probability. Finally, we show in simulation that our method can accommodate more significant unknown dynamics terms than existing methods.