用数据驱动方法让非线性模型预测控制更透明、更快，还能看懂它为啥这样算。
ExAMPC: the Data-Driven Explainable and Approximate NMPC with Physical Insights
- 用低阶样条嵌入降维超95%，结合可解释AI技术逼近原控制算法。
- 预测轨迹违规减少93%，且能提前预判计算耗时和最坏情况。
- 适合需要透明、可靠控制的工业场景，如自动驾驶泊车与竞速。
随着人工智能在控制领域的广泛应用，基于模型的经典控制方法因其透明性和确定性仍具吸引力。然而，尽管非线性模型预测控制（NMPC）性能优异，其高计算复杂度及在复杂系统中不可预测的闭环表现阻碍了实际应用。本文提出ExAMPC，通过引入数据驱动的物理洞察，将经典控制与可解释人工智能（XAI）融合，提升NMPC的可信度，并揭示优化解与闭环性能对物理变量和参数的敏感性。采用低阶样条嵌入，将开环轨迹维度降低超过95%，并结合SHAP与符号回归实现近似NMPC，使优化过程具备直观的物理可解释性。通过引入受物理启发的连续时间约束惩罚，近似NMPC的预测精度显著提升，连续轨迹违规减少93%。此外，ExAMPC可准确预测NMPC的计算需求，并提供最坏情形的可解释分析。在自动代客泊车与自主竞速（含圈速优化）的实验验证中，展示了该方法在真实场景中的有效性。
原文摘要 · Abstract (English)
Amidst the surge in the use of Artificial Intelligence (AI) for control purposes, classical and model-based control methods maintain their popularity due to their transparency and deterministic nature. However, advanced controllers like Nonlinear Model Predictive Control (NMPC), despite proven capabilities, face adoption challenges due to their computational complexity and unpredictable closed-loop performance in complex validation systems. This paper introduces ExAMPC, a methodology bridging classical control and explainable AI by augmenting the NMPC with data-driven insights to improve the trustworthiness and reveal the optimization solution and closed-loop performance's sensitivities to physical variables and system parameters. By employing a low-order spline embedding, we reduce the open-loop trajectory dimensionality by over 95%, and integrate it with SHAP and Symbolic Regression from eXplainable AI (XAI) for an approximate NMPC, enabling intuitive physical insights into the NMPC's optimization routine. The prediction accuracy of the approximate NMPC is enhanced through physics-inspired continuous-time constraints penalties, reducing the predicted continuous trajectory violations by 93%. ExAMPC also enables accurate forecasting of the NMPC's computational requirements with explainable insights on worst-case scenarios. Experimental validation on automated valet parking and autonomous racing with lap-time optimization, demonstrates the methodology's practical effectiveness for potential real-world applications.
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