Multi‐Objective Bayesian Co‐Optimization of Parameterized Moving Horizon Estimation and Model Predictive Control

ABSTRACT This paper proposes a Machine Learning (ML)‐enabled estimator‐controller design framework, in which a parameterized Model Predictive Controller (MPC) and a parameterized Moving Horizon Estimator (MHE) are jointly refined using Bayesian Optimization (BO). We show how to modify the MHE cost functional to achieve accurate state estimations even when an imperfect model of the real system is adopted. Since the parameterized control policy depends on the estimated state delivered by the parametric MHE, it inherently represents a policy derived from the combined MHE‐MPC and is influenced by both the MHE and MPC parameters. This coupling leads to two conflicting performance objectives: refining the entire parameterized MHE‐MPC scheme for optimal closed‐loop performance may alter the MHE parameters in a way that degrades the estimation performance, and conversely, improving estimation performance may come at the expense of closed‐loop control performance. To address this issue, we propose leveraging Multi‐objective Bayesian Optimization (MOBO) to update the MHE parameters, while employing a stability‐aware BO approach for refining the MPC parameters. Simulation results demonstrate the efficacy of the proposed approach in achieving sample‐efficient, stable, and high performance learning for combined estimation and control design purposes.