Safe Learning-Based Optimization of Model Predictive Control: Application to Battery Fast-Charging

TL;DR

The paper addresses optimizing long-term closed-loop performance of nonlinear systems under substantial model-plant mismatch while enforcing safety constraints, a scenario where traditional MPC can be overly conservative. It proposes a Safe Bayesian Optimization framework that tunes an MPC whose stage cost is parameterized by a radial-basis-function (RBF) network, learning only the weights of 16 RBFs with short-horizon MPC to enable real-time operation. Gaussian Process surrogates model the relationship between the RBF weights and both performance and safety metrics, while a log-barrier acquisition ensures probabilistic constraint satisfaction during learning with a specified confidence level $1-\delta$. The method is validated on a battery fast-charging case study with model-plant mismatch up to 50%, showing substantial reductions in charging time compared to conventional MPC and significantly fewer constraint violations when learning is performed safely, highlighting the approach’s potential for safety-critical, data-efficient optimization in real-time control contexts.

Abstract

Model predictive control (MPC) is a powerful tool for controlling complex nonlinear systems under constraints, but often struggles with model uncertainties and the design of suitable cost functions. To address these challenges, we discuss an approach that integrates MPC with safe Bayesian optimization to optimize long-term closed-loop performance despite significant model-plant mismatches. By parameterizing the MPC stage cost function using a radial basis function network, we employ Bayesian optimization as a multi-episode learning strategy to tune the controller without relying on precise system models. This method mitigates conservativeness introduced by overly cautious soft constraints in the MPC cost function and provides probabilistic safety guarantees during learning, ensuring that safety-critical constraints are met with high probability. As a practical application, we apply our approach to fast charging of lithium-ion batteries, a challenging task due to the complicated battery dynamics and strict safety requirements, subject to the requirement to be implementable in real time. Simulation results demonstrate that, in the context of model-plant mismatch, our method reduces charging times compared to traditional MPC methods while maintaining safety. This work extends previous research by emphasizing closed-loop constraint satisfaction and offers a promising solution for enhancing performance in systems where model uncertainties and safety are critical concerns.

Figures (4)

• Figure 1: R-RC battery ECM with parameters depending on the SOC $z_k$.
• Figure 2: Reduction in charging time to 80% SOC using unconstrained BO.
• Figure 3: Reduction in charging time to 80% SOC using safe BO.
• Figure 4: Terminal voltage $V_T$ (top) and temperature $T$ (bottom) trajectories for all sampled charging cycles during the safe learning procedure, using a confidence scaling parameter of $\beta = 1$. Constraints are shown in dashed red and unsafe trajectories are shown in orange.