Learning Model Predictive Control Parameters via Bayesian Optimization for Battery Fast Charging

TL;DR

This work tackles the problem of tuning MPC parameters under substantial model–plant mismatch for battery fast charging. It introduces a hierarchical framework that uses Bayesian Optimization to tune global parameters $\theta$ to optimize a long-horizon objective $G(\theta)$, while the MPC handles short-horizon control with predictions $\hat{f}_\theta$ and constraints. Two key contributions are demonstrated: learning a constraint backoff to prevent voltage violations and directly tuning the MPC prediction-model parameters (e.g., the $R_1$ spline) to improve closed-loop performance, even when the nominal model is deliberately mismatched. The results show that the approach can achieve safe operation and faster charging times, with the BO process offering sample-efficient, potentially online adaptation in a battery charging context. This framework enables practical, data-driven improvement of MPC in safety-critical, time-constrained systems using simple nominal models.

Abstract

Tuning parameters in model predictive control (MPC) presents significant challenges, particularly when there is a notable discrepancy between the controller's predictions and the actual behavior of the closed-loop plant. This mismatch may stem from factors like substantial model-plant differences, limited prediction horizons that do not cover the entire time of interest, or unforeseen system disturbances. Such mismatches can jeopardize both performance and safety, including constraint satisfaction. Traditional methods address this issue by modifying the finite horizon cost function to better reflect the overall operational cost, learning parts of the prediction model from data, or implementing robust MPC strategies, which might be either computationally intensive or overly cautious. As an alternative, directly optimizing or learning the controller parameters to enhance closed-loop performance has been proposed. We apply Bayesian optimization for efficient learning of unknown model parameters and parameterized constraint backoff terms, aiming to improve closed-loop performance of battery fast charging. This approach establishes a hierarchical control framework where Bayesian optimization directly fine-tunes closed-loop behavior towards a global and long-term objective, while MPC handles lower-level, short-term control tasks. For lithium-ion battery fast charging, we show that the learning approach not only ensures safe operation but also maximizes closed-loop performance. This includes maintaining the battery's operation below its maximum terminal voltage and reducing charging times, all achieved using a standard nominal MPC model with a short horizon and notable initial model-plant mismatch.

Figures (5)

• Figure 1: R-RC battery model with parameters depending on the $z_k$.
• Figure 2: First case study: Learning constraint backoff. Initial closed-loop solution in blue, trials in gray, and optimized closed-loop result in orange. a) SOC trajectories, b) Current trajectories, c) Voltage trajectories with voltage constraint, $V_{T, \text{max}}$, red dashes.
• Figure 3: Spline interpolation and tuned grid points of the backed-off constraint (green) and OCV (red).
• Figure 4: Second case study: Learning prediction model parameters. Initial closed-loop solution in blue, trials in gray, and optimized closed-loop result in orange. a) SOC trajectories, b) Current trajectories, c) Voltage trajectories with voltage constraint, $V_{T, \text{max}}$, red dashes.
• Figure 5: Spline interpolation and tuned grid points for $R_1$ in the prediction . Plant parameter (red), initial prediction parameter (purple), and tuned prediction parameter (green).