可微分非线性模型预测控制
Differentiable Nonlinear Model Predictive Control
Jonathan Frey, Katrin Baumgärtner, Gianluca Frison, Dirk Reinhardt, Jasper Hoffmann, Leonard Fichtner, Sebastien Gros, Moritz Diehl
AI 速读 基于摘要
提出在内点法平滑最优性条件下用隐函数定理计算一般非线性规划的解灵敏度，并以序列障碍二次规划（SBQP）统一推广 SQP，配套 acados 开源实现。
math.OC · cs.AI · cs.LG
查看原文摘要
The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control, as their availability is crucial for many learning algorithms. This paper discusses the computation of solution sensitivities of general nonlinear programs using the implicit function theorem and smoothed optimality conditions treated in interior-point methods (IPM). We introduce sequential barrier quadratic programming (SBQP), which generalizes SQP with an IPM quadratic programming (QP) solver by allowing the barrier parameter to approach a prescribed nonnegative target value, recovering classical SQP when this target is zero. Previous works 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`.