用神经基函数实现最优控制零样本迁移，高效适配新任务。
Zero-Shot Transferable Solution Method for Parametric Optimal Control Problems
- 通过离线学习通用基函数，在线仅需轻量系数估计。
- 跨任务泛化性能接近最优，计算开销极低。
- 适合需要实时反馈的复杂系统控制场景。
本文提出一种可迁移的最优控制求解方法，采用函数编码器（FE）策略应对目标变化。传统基于优化的方法在目标变更时需重新求解，计算成本高昂，难以支持频繁评估与自适应。所提方法通过离线模仿学习一次性构建一组覆盖控制策略空间的神经基函数，使新任务可通过数据投影或直接映射从问题描述中实现零样本适应。核心思想是离线-在线解耦：基函数仅需离线训练，而在线适应仅需轻量级系数估计。在多种动力学、维度和代价结构下的数值实验表明，该方法在跨任务泛化时达到近最优性能，开销极小，可生成适用于实时部署的半全局反馈策略。
原文摘要 · Abstract (English)
This paper presents a transferable solution method for optimal control problems with varying objectives using function encoder (FE) policies. Traditional optimization-based approaches must be re-solved whenever objectives change, resulting in prohibitive computational costs for applications requiring frequent evaluation and adaptation. The proposed method learns a reusable set of neural basis functions that spans the control policy space, enabling efficient zero-shot adaptation to new tasks through either projection from data or direct mapping from problem specifications. The key idea is an offline-online decomposition: basis functions are learned once during offline imitation learning, while online adaptation requires only lightweight coefficient estimation. Numerical experiments across diverse dynamics, dimensions, and cost structures show our method delivers near-optimal performance with minimal overhead when generalizing across tasks, enabling semi-global feedback policies suitable for real-time deployment.
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