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

TL;DR

NOSNOC is an open-source MATLAB software for solving optimal control problems involving nonsmooth and piecewise smooth systems, offering automatic reformulation, discretization, and efficient solution methods that outperform traditional approaches.

Contribution

The paper introduces NOSNOC, a novel software package that automates reformulation, discretization, and solution of nonsmooth optimal control problems without integer variables.

Findings

NOSNOC achieves faster solutions than conventional methods.

It provides more accurate results in optimal control of nonsmooth systems.

The software supports high-accuracy simulation and control of PSS.

Abstract

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.