发表机构
Mohammed VI Polytechnic University; Université Côte d’Azur（穆罕默德六世理工大学; 蔚蓝海岸大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对全固态电池快速充电中的正极输运约束，提出最小时间边界控制方法，证明最优策略的最大可行性结构，并开发离线-在线计算策略及非线性校正，兼顾效率与鲁棒性。
AI 中文摘要
全固态电池的快速充电受到正极中固态输运的限制，在激进充电条件下可能产生显著的浓度不均匀性。我们将快速充电问题表述为一维阴极扩散模型的最小时间边界控制问题，并受到终端平均浓度目标以及体相到表面浓度差的路径约束。对于恒定扩散系数，我们证明了全局极小值的存在性，并表明每个最小时间策略都是最大可行的：充电速率保持在其上界，直到输运约束变为活跃，随后遵循活跃边界。这一结构启发了离线-在线策略，其中预计算的PDE响应通过低维代数运算进行组合，避免了重复的PDE约束优化。数值细化与扰动研究验证了所预测的控制结构和约束满足性。我们进一步研究了浓度依赖的扩散系数，量化了恒定扩散系数策略在模型迁移下的鲁棒性，并引入了一种分块非线性校正，当迁移策略违反输运约束时恢复其可行性。
英文摘要
Fast charging of all-solid-state batteries is limited by solid-state transport in the positive electrode, which can generate substantial concentration nonuniformity under aggressive charging. We formulate fast charging as a minimum-time boundary-control problem for a one-dimensional cathode diffusion model, subject to a terminal average-concentration target and a path constraint on the bulk-to-surface concentration difference. For constant diffusivity, we prove existence of a global minimizer and show that every minimum-time policy is maximal-feasible: the charging rate remains at its upper bound until the transport constraint becomes active and subsequently follows the active boundary. This structure motivates an offline-online strategy in which precomputed PDE responses are combined through low-dimensional algebraic operations, avoiding repeated PDE-constrained optimization. Numerical refinement and perturbation studies verify the predicted control structure and constraint satisfaction. We further investigate concentration-dependent diffusivity, quantify the robustness of the constant-diffusivity policy under model transfer, and introduce a blockwise nonlinear correction that restores admissibility when the transferred policy violates the transport constraint.
Comments21 pages, 7 figures, 3 tables. Code and numerical data available at Zenodo
