Dual MPC for Active Learning of Nonparametric Uncertainties

TL;DR

This paper introduces a dual model predictive control approach leveraging Gaussian processes to actively learn nonparametric uncertainties while maintaining control performance, demonstrated on a nonlinear system.

Contribution

It proposes a novel dual MPC framework that uses GP posterior covariance for active learning, balancing system identification and control in a unified approach.

Findings

Successfully balances exploration and exploitation in control tasks.

Ensures robust constraint satisfaction through contingency planning.

Demonstrates effectiveness on a nonlinear system with nonparametric uncertainties.

Abstract

This manuscript presents a dual model predictive controller (MPC) that balances the two objectives of dual control, namely, system identification and control. In particular, we propose a Gaussian process (GP)-based MPC that uses the posterior GP covariance for active learning. The dual MPC can steer the system towards states with high covariance, or to the setpoint, thereby balancing system identification and control performance (exploration vs. exploitation). We establish robust constraint satisfaction of the novel dual MPC through a contingency plan. We demonstrate the dual MPC in a numerical study of a nonlinear system with nonparametric uncertainties.