Copyright (C) 2009-2025 Victor M. Becerra
This is the PSOPT library, a software tool for computational optimal control
PSOPT is an open source optimal control package written in C++ that uses direct collocation methods. These methods solve optimal control problems by approximating the time-dependent variables using global or local polynomials. This allows to discretize the differential equations and continuous constraints over a grid of nodes, and to compute any integrals associated with the problem using well known quadrature formulas. Nonlinear programming then is used to find local optimal solutions. PSOPT is able to deal with problems with the following characteristics:
- Single or multiphase problems
- Continuous time nonlinear dynamics
- General endpoint constraints
- Nonlinear path constraints (equalities or inequalities) on states and/or control variables
- Integral constraints
- Interior point constraints
- Bounds on controls and state variables
- General cost function with Lagrange and Mayer terms.
- Free or fixed initial and final conditions
- Linear or nonlinear linkages between phases
- Fixed or free initial time
- Fixed or free final time
- Optimisation of static parameters
- Parameter estimation problems with sampled measurements • Differential equations with delayed variables.
The implementation has the following features:
- Choice between Legendre, Chebyshev, trapezoidal, or Hermite-Simpson based collocation
- Automatic scaling
- Automatic first and second derivatives using the ADOL-C library
- Numerical differentiation by using sparse finite differences
- Automatic mesh refinement
- Automatic identification of the Jacobian and Hessian sparsity.
- DAE formulation, so that differential and algebraic constraints can be implemented in the same C++ function.
The PSOPT interface uses both Eigen3 (a linear algebra template library) and ADOL-C (an automatic differentiation library).
The first release of PSOPT was published in 2009. This is release 5 of PSOPT.
The PSOPT website is http://www.psopt.net.
This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA, or visit http://www.gnu.org/licenses/
Author: Professor Victor M. Becerra
Address:
University of Portsmouth
School of Electrical and Mechanical Engineering
Portsmouth PO1 3DJ
United Kingdom
e-mail: v.m.becerra@ieee.org
Please consult the PSOPT PDF documentation for further details on the software functionality and how to use it.
PSOPT relies on three main software packages to perform a number of tasks: IPOPT, ADOL-C and EIGEN3. Some of these packages have their own dependencies.
IPOPT
IPOPT is an open-source C++ package for large-scale nonlinear optimization, which uses an interior point method. It is the default nonlinear programming algorithm used by PSOPT. IPOPT can be easily installed using a package manager in some, but not all, Linux distributions.
• IPOPT repository:
https://github.com/coin-or/Ipopt
• Version 3.12.12 is tested, but other versions may work.
https://www.coin-or.org/download/source/Ipopt/
• Installation guide:
https://coin-or.github.io/Ipopt/INSTALL.html
ADOL-C
ADOL-C is a library for automatic differentiation of C++ code. It computes gradients and sparse Jacobians required by PSOPT.
A suitable version of ADOL-C can be easily installed using a package manager in some, but not all, Linux distributions. In some platforms, it may be necessary to manually install Adol-c and ColPack. The following commands should allow to perform a manual installation on various platforms:
$ wget --continue archive.ubuntu.com/ubuntu/pool/universe/a/adolc/adolc_2.7.2.orig.tar.xz
$ tar -xf adolc_2.7.2.orig.tar.xz
$ cd ADOL-C-2.7.2
$ mkdir ./ThirdParty
$ cd ./ThirdParty
$ wget --continue http://archive.ubuntu.com/ubuntu/pool/universe/c/colpack/colpack_1.0.10.orig.tar.gz
$ tar zxvf colpack_1.0.10.orig.tar.gz
$ mv ColPack-1.0.10 ColPack
$ cd ColPack
$ autoreconf -fi
$ ./configure --prefix=/usr/local
$ make
$ sudo make install
$ cd ../..
$ autoreconf -fi
$ ./configure --prefix=/usr/local --enable-sparse --with-colpack=/usr/local
$ make
$ sudo make install
EIGEN3
Eigen is a lightweight, powerful linear algebra package for C++. Eigen is available on most major Linux distributions.
If necessary, Eigen can also be installed using CMake:
$ wget --continue https://gitlab.com/libeigen/eigen/-/archive/3.3.7/eigen-3.3.7.tar.gz
$ tar zxvf eigen-3.3.7.tar.gz
$ cd eigen-3.3.7
$ mkdir build
$ cd build
$ cmake ..
$ sudo make install
The following optional libraries can be employed for additional functionality.
SNOPT
SNOPT is an optimization algorithm for large-scale nonlinearly constrained problems based on sequential quadratic programming.
GNUplot
GNUplot is a portable, interactive data and function plotting utility. GNU plot is available on most Linux distributions. PSOPT includes a number of functions that allow to easily plot results using GNUplot.
Building PSOPT
PSOPT relies on CMake and 'pkg-config' for configuring builds, and on 'make' for managing compilation and linking.
CMake is an open-source tool for managing software builds. PSOPT requires CMake 3.12 or later.
pkg-config is a helper tool used to provide the necessary details for compiling and linking a program to a library. It ensures that PSOPT’s dependencies are found correctly. pkg-config is available on most major Linux distributions. In particular, the build process expects to see pkg-config configuration files for IPOPT, ColPack and ADOL-C. These configuration files are usually installed under /usr/local/lib/pkgconfig or /usr/lib/pkgconfig. If these configuration files are not created during the build process for the above libraries, they can be created manually and be placed at the correct folder. If the pkg-config configuration files are being created manually, the contents of these files on the authors' computer are provided below as examples. Please note that the paths that are given in these files depend on the actual location where the different libraries have been installed.
For IPOPT (filename: ipopt.pc):
prefix=/usr/local
exec_prefix=${prefix}
libdir=${exec_prefix}/lib
includedir=${prefix}/include/coin-or
Name: IPOPT
Description: Interior Point Optimizer
URL: https://github.com/coin-or/Ipopt
Version: 3.13.2
Cflags: -I${includedir}
Libs: -L${libdir} -lipopt
Requires.private: coinhsl coinmumps
For ColPack (filename: ColPack.pc):
prefix=/usr/local
exec_prefix=${prefix}
libdir=${exec_prefix}/lib
includedir=${prefix}/include/ColPack
Name: ColPack
Version: 1.0.10
Description: Graph Coloring Library
Requires:
Libs: -L${libdir} -lColPack -Wl,-rpath,${libdir} -Wl,-rpath,${libdir}
Cflags: -I${includedir}
For ADOL-C (filename: adolc.pc):
prefix=/usr/local
exec_prefix=${prefix}
libdir=${exec_prefix}/lib
includedir=${prefix}/include
Name: adolc
Version: 2.6.3
Description: Algorithmic Differentiation Library for C/C++
Requires:
Libs: -L${libdir} -ladolc -Wl,-rpath,${libdir} -lColPack -Wl,-rpath,${libdir}
Cflags: -I${includedir}
\end{verbatim}
For EIGEN3 (filename: eigen3.pc):
prefix=/usr/local
exec_prefix=${prefix}
libdir=${exec_prefix}/lib
includedir=${prefix}/include
Name: Eigen3
Version: 3.3.77
Description: Numerical linear algebra library for C++
Requires:
Libs: -Wl,-rpath,${libdir} -L$${libdir}
Cflags: -I${includedir} -std=c++11
For SNOPT (filename: snopt7.pc):
prefix=/usr/local
exec_prefix=${prefix}
libdir=${exec_prefix}/lib
includedir=${prefix}/include/snopt7
Name: SNOPT7
Version: 7
Description: SNOPT NONLINEAR PROGRAMMING LIBRARY
Requires:
Libs: -L${libdir} -lsnopt7_cpp -Wl,-rpath,${libdir} -Wl,-rpath,${libdir}
Cflags: -I${includedir}
Tested Platforms
PSOPT has been successfully compiled on:
• Ubuntu Linux 24.04 LTS
• OpenSUSE Linux 15.5 Leap and Tumbleweed
• Arch Linux (latest versions as of 2025)
• Manjaro Linux (latest versions as of 2025)
• MacOS Sequoia (MacPorts on Intel CPU)
Installing Dependencies
For Ubuntu 24.04:
$ sudo apt-get install git cmake gfortran g++ libboost-dev libboost-system-dev \
coinor-libipopt-dev gnuplot libeigen3-dev libblas-dev liblapack-dev
Note that Adol-c and ColPack needs to be manually installed on the latest version of Ubuntu (version 24.04). See the instructions above.
For Debian 12.9.0:
$ su
$ apt-get install git cmake gfortran g++ libboost-dev libboost-system-dev \
coinor-libipopt-dev gnuplot libeigen3-dev libblas-dev liblapack-dev
Note that Adol-c and ColPack needs to be manually installed on the latest version of Debian (version 11.9). See the instructions above.
For OpenSUSE Leap 15.5 and Tumbleweed:
$ sudo zypper install git gnuplot libboost_system1_66_0-devel eigen3-devel ColPack-devel \
adolc-devel blas-devel lapack-devel Ipopt-devel cmake gcc-c++
For Arch Linux / Manjaro:
$ sudo pacman -Syu
$ sudo pacman -S git base-devel cmake gnuplot eigen boost blas lapack yay
$ yay -S coin-or-ipopt colpack adol-c
The use of the tool yay requires AUR support to be enabled on the package manager. On ARM64, it may be necessary to install Anaconda, which provides gklib and IPOPT, as the installation script for IPOPT provided by AUR currently fails to build using yay.
For MacOS
It is also possible to build PSOPT on some versions of MacOS. This can be done by using MacPorts, which is an is an open-source system for compiling, installing, and upgrading open-source software on MacOS.
To use MacPorts, download and install MacPorts from:
https://www.macports.org/install.php
To install the PSOPT dependencies, issue the following commands from a terminal window:
sudo port install cmake
sudo port install eigen3
sudo port install git
sudo port install ipopt
sudo port install ADOL-C
sudo port install gnuplot
The above is working with MacOS Sequoia with an Intel processor (date: 16 Feb 2025). Currently, there are issues with the ARM64 (M1 and above) processors that have MacOS Sequoia. The installation might work with previous versions of MacOS on ARM64.
Building and Installing PSOPT
Once all dependencies are installed, PSOPT can be downloaded from GitHub, and built using CMake using the following commands.
$ git clone https://github.com/PSOPT/psopt.git
$ cd psopt
$ mkdir build
$ cd build
$ cmake -DBUILD_EXAMPLES=ON ..
$ make
$ sudo make install
If using SNOPT:
$ cmake -DBUILD_EXAMPLES=ON -DWITH_SNOPT_INTERFACE=ON ..
For debugging:
$ cmake -DBUILD_EXAMPLES=ON -DCMAKE_BUILD_TYPE=Debug ..
After installation, run at least one example to check that the build is working correctly:
$ cd build/examples/launch
$ ./launch
- PSOPT Documentation with information about the functionality and use of the software, background theory, and more.
- Issue tracking system: If you believe you found a bug in the code, please use the issue tracking system. Please include as much information as possible, and if possible some example code so that we can reproduce the error.
- Mailing list: subscribe to receive notifications about updates and to post questions and comments about PSOPT.
This software is provided for free in the hope that it may be useful to others, and we would very much like to hear about your experience with it. If you find PSOPT helpful for your work or research, please emai the author at v.m.becerra@ieee.org to incorporate a feature on the PSOPT web page.
Given that a great deal of time and effort has gone into PSOPT's development, please cite the following publication if you are using PSOPT for your own research:
- Becerra, V.M. (2010). Solving complex optimal control problems at no cost with PSOPT. Proc. IEEE Multi-conference on Systems and Control, Yokohama, Japan, September 7-10, 2010, pp. 1391-1396.
BibTex entry:
@INPROCEEDINGS{5612676,
author={V. M. Becerra},
booktitle={2010 IEEE International Symposium on Computer-Aided Control System Design},
title={Solving complex optimal control problems at no cost with PSOPT},
year={2010},
pages={1391-1396},
doi={10.1109/CACSD.2010.5612676}}
