NOS-NOC is open source software package for NOnSmooth Numerical Optimal Control.

It is a modular tool for numerically solving optimal control problems with piecewise smooth systems (PSS). It relies on the recently introduced Finite Elements with Switch Detection (FESD) which enables high accuracy optimal control of PSS. The time-freezing reformulation, which transforms several classes of systems with state jumps into PSS is supported as well. It enables the treatment of a broad class of nonsmooth systems in a unified way. The user manual can be found here.

NOS-NOC requires CasADi version 3.5.5.

Currently, a MATLAB version is avilable. Versions to come will support a python interface as well.

1. Install CasADi and make sure it is added to your MATLAB path.

   For CasADi installation instructions follow this link.

2. Clone this repository and add it to your MATLAB path:

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

Note that IPOPT is shipped with CasADi, but more information including a detailed documentation can be found on its homepage

A python version is currently under development.

The interface of NOS-NOC is based on the symbolic modeling framework CasADi.
User inputs should be given as CasADi expressions Function objects.

Minimal code example

import casadi.*
% Call this function to have an overview of all options.
[settings] = default_settings_fesd();  
% Highlight that the problem is treated with time-freezing reformulation and change the number of IRK stages
settings.time_freezing = 1; 
settings.n_s = 3; 
% Discretization data
model.T = 5; 
model.N_stages = 15; 
model.N_finite_elements = 3;
% Define states, controls and inital values
q = MX.sym('q',2); v = MX.sym('v',2); t = MX.sym('t');
model.x = [q;v;t];
model.x0 = [0;0.5;0;0;0];
u = MX.sym('u',2); 
model.u = u;
% Define regions of the PSS
model.S = [1; -1];
model.c = q(2); 
% Define modes of PSS 
f_1 = [v;u(1);u(2)-9.81;1];
 f_2 = [0;v(2);0;-10*(q(2))-0.211989*v(2);0];
model.F = [f_1 f_2];
% Stage and terminal costs
model.f_q = u'*u; model.f_q_T = 10*v'*v;
% Path and terminal constraints
model.g_ineq = u'*u-7^2;
model.g_terminal = q-[4;0.25];
% Solve OCP with MPCC homotopy and plot results
[solver,solver_initalization, model,settings] = create_nlp_fesd(model,settings);
[results,stats] = homotopy_solver(solver,model,settings,solver_initalization);
plot_result_ball(model,settings,results,stats)

More details can be found in the user manual.

Finite Elements with Switch Detection for Direct Optimal Control of Nonsmooth Systems
A.Nurkanović, M. Sperl, S. Albrecht, M. Diehl
arXiv preprint 2022

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
arXiv preprint 2021

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

NOS-NOC: An Software Package for Numerical Optimal Control of Nonsmooth Systems
A.Nurkanović , M. Diehl
arXiv preprint 2022

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

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

Feel free to contact the main developer directly: Armin Nurkanović, [email protected] If you have got questions, remarks or comments, you are strongly encouraged to report them by creating a new issue on this github page. Success stories and source code contributions are very welcome.