`nosnoc`

nosnoc is an open-source MATLAB software package for NOnSmooth Numerical Optimal Control. The Python package nosnoc_py with similar functionality is available as well.

Documnetation is avilable here.
A detailed overview of the theory and methods behind nosnoc can be found in the course material of the Summer School on Direct Methods for Optimal Control of Nonsmooth Systems.

General

nosnoc is a tool for numerically solving optimal control problems with nonsmooth dynamical systems that have switches and/or state jumps. It supports:

Automatic discretization via the FESD method:
- High accuracy and correct sensitivities.
- Classical time-stepping methods only have first-order accuracy and incorrect sensitivities, even when they appear to be differentiable.
Automatic reformulations of systems with state jumps:
- For example, contact problems via time-freezing into Filippov systems/Piecewise Smooth Systems (PSS).
- This enables high accuracy even for systems with state jumps.
Solving nonsmooth nonlinear programs via homotopy methods:
- Supports numerous relaxation-based algorithms for solving mathematical programs with complementarity constraints (MPCCs).
- Enables the use of off-the-shelf solvers like IPOPT and SNOPT.

With nosnoc, one can solve optimal control problems subject to several classes of hybrid and nonsmooth systems:

Switched systems
Piecewise affine, piecewise smooth systems
Filippov systems
Systems with logical Heaviside step functions
Relay systems
Projected dynamical systems
First-order Sweeping processes
Rigid body models with impacts and friction
Hybrid systems with hysteresis

Users may directly provide a DCS or the problem in a standard form which is automatically reformulated into a DCS. nosnoc discretizes a Dynamic Complementarity System (DCS) with the FESD method and solves the resulting MPCCs.

Installation

nosnoc requires CasADi version 3.5.5 and Matlab version R2021b or later.

Installation for MATLAB

Install CasADi and make sure it is added to your MATLAB path. For CasADi installation instructions follow visit: https://web.casadi.org/get/

Clone this repository

git clone --recursive https://github.com/nurkanovic/nosnoc.git

Open the nosnoc folder in Matlab and run the install_nosnoc script
```
>> install_nosnoc
```

Note that IPOPT is shipped with CasADi. More information including detailed documentation can be found on its homepage

Installation for python

Go to the nosnoc_py repository for more info.

Using nosnoc

The interface of nosnoc is based on the symbolic modeling framework CasADi. User inputs should be provided as CasADi expressions.

To get started, we recommend you look into our example libraries for:

Literature - theory and algorithms

FESD

Finite Elements with Switch Detection for Direct Optimal Control of Nonsmooth Systems \ A.Nurkanović, M. Sperl, S. Albrecht, M. Diehl \ Numerische Mathematik (2024): 1-48

@article{Nurkanovic2024,
  title={Finite elements with switch detection for direct optimal control of nonsmooth systems},
  author={Nurkanovi{\'c}, Armin and Sperl, Mario and Albrecht, Sebastian and Diehl, Moritz},
  journal={Numerische Mathematik},
  pages={1--48},
  year={2024},
  publisher={Springer}
}

Finite Elements with Switch Detection for numerical optimal control of nonsmooth dynamical systems with set-valued heaviside step functions \ A. Nurkanović, A. Pozharskiy, J. Frey, M. Diehl\ Nonlinear Analysis: Hybrid Systems 54, 101518

@article{Nurkanovic2024a,
  title={Finite Elements with Switch Detection for numerical optimal control of nonsmooth dynamical systems with set-valued heaviside step functions},
  author={Nurkanovi{\'c}, Armin and Pozharskiy, Anton and Frey, Jonathan and Diehl, Moritz},
  journal={Nonlinear Analysis: Hybrid Systems},
  volume={54},
  pages={101518},
  year={2024},
  publisher={Elsevier}
}

Time-Freezing

A Time-Freezing Approach for Numerical Optimal Control of Nonsmooth Differential Equations with State Jumps \ A. Nurkanović, T. Sartor, S. Albrecht, M. Diehl \ IEEE Control Systems Letters 2021

The Time-Freezing Reformulation for Numerical Optimal Control of Complementarity Lagrangian Systems with State Jumps \ A. Nurkanović, S. Albrecht, B. Brogliato, M. Diehl \ Automatica 158 (2023): 111295.

Continuous Optimization for Control of Hybrid Systems with Hysteresis via Time-Freezing \ A.Nurkanović , M. Diehl \ IEEE Control Systems Letters 2022

Literature - Software

nosnoc

nosnoc: A Software Package for Numerical Optimal Control of Nonsmooth Systems \ A.Nurkanović , M. Diehl \ IEEE Control Systems Letters 2022

@article{Nurkanovic2022,
  title={nosnoc: A software package for numerical optimal control of nonsmooth systems},
  author={Nurkanovi{\'c}, Armin and Diehl, Moritz},
  journal={IEEE Control Systems Letters},
  volume={6},
  pages={3110--3115},
  year={2022},
  publisher={IEEE}
}

CasADi

CasADi - A software framework for nonlinear optimization and optimal control \ J.A.E. Andersson, J. Gillis, G. Horn, J.B. Rawlings, M. Diehl \ Mathematical Programming Computation, 2019

IPOPT

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming \ A. Wächter, L. T. Biegler Mathematical programming, 2006

Contact

If you have questions, remarks, or comments, you are strongly encouraged to report them by creating a new issue on this Github page.

Feel free to contact one of the main developers directly: Armin Nurkanović (armin.nurkanovic@imtek.uni-freiburg.de), Anton Pozharskiy (anton.pozharskiy@imtek.uni-freiburg.de), Jonathan Frey (jonathan.frey@imtek.uni-freiburg.de).

Success stories and source code contributions are very welcome.

nurkanovic / nosnoc

readme