# Gauss-Newton Runge-Kutta Integration for Efficient Discretization of Optimal Control Problems with Long Horizons and Least-Squares Costs

arXiv: https://arxiv.org/abs/2310.20390 · HTML: https://mlsanity.com/paper/2310.20390/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2023.

## Built on by (most cited first, 1 of 1)

- [Differentiable Nonlinear Model Predictive Control](https://mlsanity.com/paper/2505.01353/) (2025)

## Abstract (arXiv)

This work proposes an efficient treatment of continuous-time optimal control problem (OCP) with long horizons and nonlinear least-squares costs. The Gauss-Newton Runge-Kutta (GNRK) integrator is presented which provides a high-order cost integration. Crucially, the Hessian of the cost terms required within an SQP-type algorithm is approximated with a Gauss-Newton Hessian. Moreover, L2 penalty formulations for constraints are shown to be particularly effective for optimization with GNRK. An efficient implementation of GNRK is provided in the open-source software framework acados. We demonstrate the effectiveness of the proposed approach and its implementation on an illustrative example showing a reduction of relative suboptimality by a factor greater than 10 while increasing the runtime by only 10 %.