SD-DPC：稀疏字典可微预测控制
SD-DPC: Sparse Dictionary Differentiable Predictive Control
- Concordia University（康考迪亚大学）
- Johns Hopkins University（约翰斯·霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
SD-DPC提出一种从数据学习稀疏可解释反馈策略的框架，结合SINDy识别与可微预测控制，以闭环性能选择字典项，在基准问题中满足约束且大幅降低计算开销。
AI中文摘要：
我们提出了稀疏字典可微预测控制（SD-DPC），这是一个从数据中学习非线性系统的稀疏、可解释反馈策略的框架。首先，通过基于滚动（rollout）的稀疏非线性动力学识别（SINDy）方法，结合基于梯度和多步的公式，识别出预测模型。然后，策略被参数化为字典函数的稀疏组合，并通过该模型对受约束的有限时域预测控制目标进行微分来训练，从而根据闭环性能选择其项，而非模仿先前训练的控制器。其结果是仅包含少量项的显式反馈律。在三个基准控制问题中，SD-DPC在所有测试场景下均满足约束，其性能比蒸馏到相同项的策略高出一个数量级，并且相比优化基准，所需内存和在线计算量减少了几个数量级，同时允许显式的灵敏度界限。
英文摘要：
We present sparse dictionary differentiable predictive control (SD-DPC), a framework for learning sparse, interpretable feedback policies for nonlinear systems from data. A prediction model is first identified by rollout-based sparse identification of nonlinear dynamics (SINDy), building on gradient-based and multistep formulations. The policy is then parameterized as a sparse combination of dictionary functions and trained by differentiating a constrained finite-horizon predictive-control objective through this model, so that its terms are selected by closed-loop performance rather than by imitating a previously trained controller. The result is an explicit feedback law with only a handful of terms. Across three benchmark control problems, SD-DPC satisfies the constraints in all test scenarios, outperforms a policy distilled onto the same terms by up to an order of magnitude, and requires orders of magnitude less memory and online computation than an optimization benchmark, while admitting explicit sensitivity bounds.
