提出高效计算非线性模型预测控制敏感度的新方法，提升学习增强型控制的效率。
Differentiable Nonlinear Model Predictive Control
- 基于隐函数定理与内点法，用SQP框架求解非线性规划的灵敏度。
- 在acados中实现，对一般最优控制问题支持前向与反向敏感度，速度超现有工具3倍以上。
- 适合需要快速梯度更新的强化学习与优化控制研究者使用。
学习增强型非线性模型预测控制（MPC）中，参数解的灵敏度高效计算是一个关键挑战，因为其对许多学习算法至关重要。本文利用隐函数定理（IFT）和内点法（IPM）处理的平滑最优性条件，讨论了通用非线性规划（NLP）解灵敏度的计算方法。详细介绍了在序列二次规划（SQP）框架中，采用内点法求解二次子问题时的灵敏度计算过程。此前机器学习领域的研究多局限于凸或无约束问题，或缺乏高效的灵敏度评估实现。本文配套发布了基于acados框架的开源实现，支持一般最优控制问题的前向与反向灵敏度计算，在速度上超越当前主流求解器mpc.pytorch和cvxpygen超过3倍。
原文摘要 · Abstract (English)
The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control (MPC), as their availability is crucial for many learning algorithms. This paper discusses the computation of solution sensitivities of general nonlinear programs (NLPs) using the implicit function theorem (IFT) and smoothed optimality conditions treated in interior-point methods (IPM). We detail sensitivity computation within a sequential quadratic programming (SQP) method which employs an IPM for the quadratic subproblems. Previous works presented in the machine learning community are limited to convex or unconstrained formulations, or lack an implementation for efficient sensitivity evaluation. The publication is accompanied by an efficient open-source implementation within the acados framework, providing both forward and adjoint sensitivities for general optimal control problems, achieving speedups exceeding 3x over the state-of-the-art solvers mpc.pytorch and cvxpygen.
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