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.

翻译：参数化解灵敏度的有效计算是将学习增强方法与非线性模型预测控制（MPC）相结合的关键挑战，因为其可用性对许多学习算法至关重要。本文讨论了使用隐函数定理（IFT）以及内点法（IPM）中处理的平滑最优性条件来计算一般非线性规划（NLP）的解灵敏度。我们详细阐述了在采用IPM求解二次子问题的序列二次规划（SQP）方法中的灵敏度计算。机器学习领域先前的工作仅限于凸优化或无约束的表述，或者缺乏用于高效灵敏度评估的实现。本出版物附带在acados框架内实现的一个高效开源实现，为一般最优控制问题提供前向和伴随灵敏度，其加速效果超过最先进的求解器mpc.pytorch和cvxpygen三倍以上。