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Model-free fast charging of lithium-ion batteries by online gradient descent

Hamed Taghavian, Malin Andersson, Mikael Johansson

TL;DR

The paper tackles fast charging of lithium-ion batteries under safety and aging constraints by proposing a model-free controller that drives the system toward bang-ride charging without requiring a battery model or full training. It casts the problem as online convex optimization with a fixed-structure controller updated via online gradient descent, yielding sublinear regret $\mathcal{R}_{t_f}=O(t_f^{\mu^{*}})$ and convergence to the bang-ride protocol under mild conditions. The approach is validated on SPMeT, ECM, and large ECM-pack simulations, showing accurate tracking of ideal bang-ride profiles and robustness to model perturbations, even when only measured outputs are available. The method offers a data-efficient alternative to model identification and training-based policies, enabling real-time, constraint-satisfying fast charging in uncertain dynamics.

Abstract

A data-driven solution is provided for the fast-charging problem of lithium-ion batteries with multiple safety and aging constraints. The proposed method optimizes the charging current based on the observed history of measurable battery quantities, such as the input current, terminal voltage, and temperature. The proposed method does not need any detailed battery model or full-charging training episodes. The theoretical convergence is proven under mild conditions and is validated numerically on several linear and nonlinear battery models, including single-particle and equivalent-circuit models.

Model-free fast charging of lithium-ion batteries by online gradient descent

TL;DR

The paper tackles fast charging of lithium-ion batteries under safety and aging constraints by proposing a model-free controller that drives the system toward bang-ride charging without requiring a battery model or full training. It casts the problem as online convex optimization with a fixed-structure controller updated via online gradient descent, yielding sublinear regret and convergence to the bang-ride protocol under mild conditions. The approach is validated on SPMeT, ECM, and large ECM-pack simulations, showing accurate tracking of ideal bang-ride profiles and robustness to model perturbations, even when only measured outputs are available. The method offers a data-efficient alternative to model identification and training-based policies, enabling real-time, constraint-satisfying fast charging in uncertain dynamics.

Abstract

A data-driven solution is provided for the fast-charging problem of lithium-ion batteries with multiple safety and aging constraints. The proposed method optimizes the charging current based on the observed history of measurable battery quantities, such as the input current, terminal voltage, and temperature. The proposed method does not need any detailed battery model or full-charging training episodes. The theoretical convergence is proven under mild conditions and is validated numerically on several linear and nonlinear battery models, including single-particle and equivalent-circuit models.
Paper Structure (11 sections, 1 theorem, 50 equations, 4 figures, 1 algorithm)

This paper contains 11 sections, 1 theorem, 50 equations, 4 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. FAST CHARGING AND BANG-RIDE PROTOCOLS
  3. MODEL-FREE CHARGING
  4. Active constraint switching
  5. Active constraint riding
  6. Convergence analysis
  7. NUMERICAL EXPERIMENTS
  8. SPMeT cell
  9. ECM cell
  10. ECM pack
  11. CONCLUSION

Key Result

Theorem 1

Assume $\Theta\subseteq \mathbb{R}^m$ is a bounded set, $\theta_0\in\Theta$, $J_t(\theta)$ is convex in $\theta$, $\varepsilon_t=\Vert\theta^{\star}_{t+1}-\theta^{\star}_{t}\Vert=O(t^{-\mu_2})$, and that Assumption ass:h holds. Let the step size be where $\mu_1\in(0,1)$ and $\mu_1<\mu_2$. Let $\Vert g_t\Vert,\vert c_t\vert\leq G$ for some $G>0$ and assume that the sequence $c_{t+1}/\alpha_{t+1}-c

Figures (4)

  • Figure 1: The data-driven control scheme: The thick lines represent vector signals in $\mathbb{R}^p$ and $\Gamma=\textnormal{diag}(\gamma)$ is a non-negative diagonal matrix used to adjust the loop gains if necessary. The loop is only connected in one component at a time, which corresponds to the active constraint.
  • Figure 2: The battery is charged with the maximum current until the terminal voltage constraint in (\ref{['eqn:constr_SPMet']}) is activated at $t=1561$, after which, the battery is charged with a constant voltage in Example \ref{['ex:SPMeT']}.
  • Figure 3: The active constraint changes three times in Example \ref{['ex:ECM1']}. In the beginning, the current constraint ($y_{1,t}= u_{\rm max}$) is active to charge with the maximum current until $t=421.3$, when the current constraint is switched to the voltage constraint. The voltage constraint is active until $t=820.7$ before the active constraint is switched to the temperature constraint. Finally, the active constraint is switched back to the voltage constraint at $t=1289$ which remains active until the end of the experiment.
  • Figure 4: Under the ideal bang-ride charging approach in Example \ref{['ex:ECM2']}, the battery is charged with the maximum current $u_t=u_{\rm max}$ until $t=3.8$ when a cell voltage constraint is activated. After that, the active voltage constraint is exchanged several times among different cells in the pack until $t=992.7$ when it is handed over to a temperature difference constraint. The last activated constraint maintains a difference of $\Delta T_{\rm max}$ between the cells' temperatures in the pack.

Theorems & Definitions (2)

  • Theorem 1
  • proof