NOSNOC is an open source software package for NOnSmooth Numerical Optimal Control.
It is a modular tool for numerically solving nonsmooth optimal control problems with Piecewise Smooth/Filippov Systems (PSS). It supports:
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Automatic discretization via the FESD method - high accuracy and correct sensitivities. (Note that standard time-stepping methods have only first order accuracy and wrong sensitivities even when they appear to be differentiable!)
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Automatic reformulations of systems with state jumps (e.g. contact problems) via time-freezing into Filippov systems/PSS. (enables high accuracy even for system with state jumps, check out the example library)
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Solving the nonsmooth nonlinear programs via homotopy methods. Enables the use of off-the-shelf solvers like IPOPT.
NOSNOC relies on the recently introduced Finite Elements with Switch Detection (FESD) which enables high accuracy optimal control of PSS. It enables the treatment of a broad class of nonsmooth systems in a unified way. The user manual can be found here.
NOSNOC requires CasADi version 3.5.5.
Currently, a MATLAB version is avilable. Versions to come will support a python interface as well.
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Install 8000
CasADiand make sure it is added to yourMATLABpath.For
CasADiinstallation instructions follow this link. -
Clone this repository and add it to your
MATLABpath: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 NOSNOC is based on the symbolic modeling framework CasADi.
User inputs should be given as CasADi expressions.
Minimal code example for time-optimal problem for a car with two modes of opration.
import casadi.*
% Call this function to have an overview of all options.
[settings] = default_settings_nosnoc();
% Choosing the Runge - Kutta Method and number of stages
settings.irk_scheme = 'Lobatto-IIIA';
settings.n_s = 2;
% Time-settings - Solve an time optimal control problem
settings.time_optimal_problem = 1;
% Model - define all problem functions and
% Discretization parameters
model.N_stages = 10; % number of control intervals
model.N_finite_elements = 6; % number of finite element on every control intevral (optionally a vector might be passed)
model.T = 15; % Time horizon
% Symbolic variables and bounds
q = SX.sym('q'); v = SX.sym('v');
model.x = [q;v]; % add all important data to the struct model,
model.x0 = [0;0]; % inital value
% bounds on states
model.lbx = [-inf;-20];
model.ubx = [inf;20];
% control
u = SX.sym('u'); model.u = u;
model.lbu = -5; model.ubu = 5;
% Dyanmics and the regions
f_1 = [v;u]; % mode 1 - nominal
f_2 = [v;3*u]; % mode 2 - turbo
model.S = [-1;1];
model.F = [f_1 f_2];
model.c = v-10;
% Add terminal constraint
model.g_terminal = [q-200;v-0];
% Solve OCP
[results,stats,model,settings] = nosnoc_solver(model,settings);
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
IEEE Control Systems Letters 2022
NOSNOC: A Software Package for Numerical Optimal Control of Nonsmooth Systems
A.Nurkanović , M. Diehl
IEEE Control Systems Letters 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, armin.nurkanovic@imtek.uni-freiburg.de 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.