# NOSNOC: A Software Package for Numerical Optimal Control of Nonsmooth Systems

arXiv: https://arxiv.org/abs/2203.11516 · HTML: https://mlsanity.com/paper/2203.11516/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2022.

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

- [A Model-Free Optimal Control Method With Fixed Terminal States and Delay](https://mlsanity.com/paper/2409.10722/) (2024)

## Abstract (arXiv)

This letter introduces the NOnSmooth Numerical Optimal Control (NOSNOC) open-source software package. It is a modular MATLAB tool based on CasADi and IPOPT for numerically solving Optimal Control Problems (OCP) with piecewise smooth systems (PSS). The tool supports: 1) automatic reformulation of systems with state jumps into PSS (via the time-freezing reformulation [Nurkanovi'c et al., 2021]) and of PSS into computationally more convenient forms, 2) automatic discretization of the OCP via, e.g., the recently introduced Finite Elements with Switch Detection [Nurkanovi'c et al., 2022] which enables high accuracy optimal control and simulation of PSS, 3) solution methods for the resulting discrete-time OCP. The nonsmooth discrete-time OCP are solved with techniques of continuous optimization in a homotopy procedure, without the use of integer variables. This enables the treatment of a broad class of nonsmooth systems in a unified way. Two tutorial examples are given. A benchmark shows that NOSNOC provides both faster and more accurate solutions than conventional approaches, including mixed-integer formulations.