Learning Dynamics from Infrequent Output Measurements for Uncertainty-Aware Optimal Control

TL;DR

This paper introduces a Bayesian framework with scenario-based optimal control for nonlinear systems with unknown dynamics and infrequent noisy measurements, validated on a diabetes model.

Contribution

It develops a novel method combining Bayesian inference and scenario-based control to handle limited sensing in nonlinear systems.

Findings

Effective uncertainty quantification in control decisions.

Successful application to glucose regulation model.

Robust control performance despite sparse data.

Abstract

Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior over the continuous-time dynamics and latent state trajectory in state-space form and updating it through a targeted Metropolis-Hastings sampler equipped with a numerical ODE integrator. The resulting posterior samples are used to formulate a scenario-based optimal control problem that accounts for the uncertainty in the dynamics and latent state and is solved using standard nonlinear programming methods. The approach is validated in a numerical case study on glucose regulation using a Type 1 diabetes model.