Differentiable Nonlinear Model Predictive Control

TL;DR

This paper presents a method for efficiently computing solution sensitivities in nonlinear model predictive control using implicit function theorem and interior-point methods, with an open-source implementation that significantly outperforms existing solvers.

Contribution

It introduces a novel sensitivity computation approach for general nonlinear programs within NMPC, implemented efficiently in the acados framework.

Findings

Achieves over 3x speedup compared to existing solvers.

Provides both forward and adjoint sensitivities for general optimal control problems.

Extends sensitivity computation to non-convex and constrained NLPs in NMPC.

Abstract

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.