Differentiable Nonlinear Model Predictive Control
This work addresses a key bottleneck for researchers and practitioners in control systems and machine learning by enabling more efficient learning-enhanced MPC, though it is incremental as it builds on existing sensitivity computation techniques.
The paper tackles the challenge of computing parametric solution sensitivities for integrating learning methods with nonlinear model predictive control (MPC), by developing a method using the implicit function theorem and interior-point methods within a sequential quadratic programming framework, achieving speedups over 3x compared to the state-of-the-art solver mpc.pytorch.
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. While approaches presented in the machine learning community are limited to convex or unconstrained formulations, 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. The publication is accompanied by an efficient open-source implementation within the framework, providing both forward and adjoint sensitivities for general optimal control problems, achieving speedups exceeding 3x over the state-of-the-art solver mpc.pytorch.