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CORA v2025.1.0
- contDynamics/nrOfDims: added, renamed from nrOfStates - contDynamics/printSystem: bug fix, function handles not printed correctly - contSet/contains: major improvements, now also provides a certificate on its result - contSet/plot: bug fix, better handling of (partially) transparent colors - ellipsoid/zonotope: bug fix for 'inner:norm', returned zonotope now always has the desired number of generators - neuralNetwork/computePGDAttack: bug fix, no upper and lower bound is set per default (apart from the epsilon radius) - nonlinearSys/reach: fixes for special approximative reachability - global/codingConventions: harmonized code writing throughout CORA - global/macros/CORAGITBRANCH: added, returns the current git branch name - global/printMatrix: bug fix, clearline flag was ignored if matrix has all zeros - polygon/compact: bugfix for Douglas Peuker algorithm - polyZonotope/exponentMatrix/id: improved merging of redundant exponents and ids - polyZonotope/polyMap: bug fix, E with all-zero columns - zonotope/reduce: added order reduction method from the Sadraddini-Tedrake paper
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‎README.md‎

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<img src="./app/images/coraLogo_readme.svg" alt="CORA"/>
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A Tool for COntinuous Reachability Analysis.
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<a href='https://cora.in.tum.de' target='_blank'>cora.in.tum.de</a> - <a href='https://cora.in.tum.de/manual' target='_blank'>Manual</a>
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![TUMcps - CORA](https://img.shields.io/static/v1?label=TUMcps&message=CORA&color=4596FF&logo=github&link=https://github.com/TUMcps/CORA)
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![CORA version](https://img.shields.io/github/tag/TUMcps/CORA?include_prereleases=&sort=semver&color=4596FF&link=https://github.com/TUMcps/CORA/tags/)
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![CORA CI:passing](https://img.shields.io/static/v1?label=CI&message=passing&color=78C57F)
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<hr style="height: 1px;">
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The COntinuous Reachability Analyzer (CORA) is a collection of MATLAB classes for the formal verification of cyber-physical systems using reachability analysis. CORA integrates various vector and matrix set representations and operations on them as well as reachability algorithms of various dynamic system classes. The software is designed such that set representations can be exchanged without having to modify the code for reachability analysis. CORA is designed using the object-oriented paradigm, such that users can safely use methods without concerning themselves with detailed information hidden inside the objects. Since the toolbox is written in MATLAB, the installation and use is platform independent. From Release 2018 on, the direct import of SpaceEx models into CORA is also supported. The following points summarize the main capabilities of the CORA toolbox:
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### Reachability Analysis for Continuous Systems
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CORA computes reachable sets for linear systems, nonlinear systems as well as for systems with constraints. Continuous as well as discrete-time models are supported. Uncertainty in the system inputs as well as uncertainty in the model parameters can be explicitly considered. In addition, CORA also provides capabilities for the simulation of dynamical models.
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### Reachability Analysis for Hybrid Systems
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The toolbox is also capable of computing the reachable sets for hybrid systems. All implemented dynamic system classes can be used to describe the different continuous flows for the discrete system states. Furthermore, various methods for the calculation of the intersections with guard sets are implemented in CORA.
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### Geometric Sets
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CORA has a modular design, making it possible to use the capabilities of the various set representations for other purposes besides reachability analysis. The toolbox implements vector set representation, e.g., zonotopes, Taylor models and intervals, as well as matrix set representations such as matrix zonotope and interval matrices.
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### Installation
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Please check Section 1.3 in the <a target='_blank' href="https://cora.in.tum.de/manual">CORA manual</a>.
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Furthermore, if you clone CORA using git, please also install git lfs (large file storage) and run the command `git lfs pull` to ensure all data files are downloaded correctly.
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### Folder Structure
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| Folder | Description |
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|---|---|
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|`./app` | CORA app, graphical user interface |
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| `./contDynamics`| continuous dynamics classes |
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| `./contSet`| continuous set classes and operations |
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| `./converter`| converter from various formats to CORA |
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| `./discrDynamics`| discrete dynamics |
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| `./examples`| examples demonstrating the capabilities of CORA |
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| `./global`| global classes, functions, and macros |
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| `./hybridDynamics`| hybrid dynamics classes |
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| `./matrixSet`| matrix set classes |
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| `./models`| model files |
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| `./nn`| neural network verification and robust training |
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| `./specification`| specification classes for verification |
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| `./unitTests`| unit tests |
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<hr style="height: 1px;">
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<img src="./app/images/coraLogo_readme.svg" alt="CORA"/>
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A Tool for COntinuous Reachability Analysis.
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<a href='https://cora.in.tum.de' target='_blank'>cora.in.tum.de</a> - <a href='https://cora.in.tum.de/manual' target='_blank'>Manual</a>
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![TUMcps - CORA](https://img.shields.io/static/v1?label=TUMcps&message=CORA&color=4596FF&logo=github&link=https://github.com/TUMcps/CORA)
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![CORA version](https://img.shields.io/github/tag/TUMcps/CORA?include_prereleases=&sort=semver&color=4596FF&link=https://github.com/TUMcps/CORA/tags/)
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![CORA CI:passing](https://img.shields.io/static/v1?label=CI&message=passing&color=78C57F)
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<hr style="height: 1px;">
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The COntinuous Reachability Analyzer (CORA) is a collection of MATLAB classes for the formal verification of cyber-physical systems using reachability analysis. CORA integrates various vector and matrix set representations and operations on them as well as reachability algorithms of various dynamic system classes. The software is designed such that set representations can be exchanged without having to modify the code for reachability analysis. CORA is designed using the object-oriented paradigm, such that users can safely use methods without concerning themselves with detailed information hidden inside the objects. Since the toolbox is written in MATLAB, the installation and use is platform independent. From Release 2018 on, the direct import of SpaceEx models into CORA is also supported. The following points summarize the main capabilities of the CORA toolbox:
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### Reachability Analysis for Continuous Systems
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CORA computes reachable sets for linear systems, nonlinear systems as well as for systems with constraints. Continuous as well as discrete-time models are supported. Uncertainty in the system inputs as well as uncertainty in the model parameters can be explicitly considered. In addition, CORA also provides capabilities for the simulation of dynamical models.
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### Reachability Analysis for Hybrid Systems
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The toolbox is also capable of computing the reachable sets for hybrid systems. All implemented dynamic system classes can be used to describe the different continuous flows for the discrete system states. Furthermore, various methods for the calculation of the intersections with guard sets are implemented in CORA.
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### Geometric Sets
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CORA has a modular design, making it possible to use the capabilities of the various set representations for other purposes besides reachability analysis. The toolbox implements vector set representation, e.g., zonotopes, Taylor models and intervals, as well as matrix set representations such as matrix zonotope and interval matrices.
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### Installation
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Please check Section 1.3 in the <a target='_blank' href="https://cora.in.tum.de/manual">CORA manual</a>.
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Furthermore, if you clone CORA using git, please also install git lfs (large file storage) and run the command `git lfs pull` to ensure all data files are downloaded correctly.
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### Folder Structure
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| Folder | Description |
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|---|---|
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|`./app` | CORA app, graphical user interface |
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| `./contDynamics`| continuous dynamics classes |
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| `./contSet`| continuous set classes and operations |
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| `./converter`| converter from various formats to CORA |
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| `./discrDynamics`| discrete dynamics |
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| `./examples`| examples demonstrating the capabilities of CORA |
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| `./global`| global classes, functions, and macros |
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| `./hybridDynamics`| hybrid dynamics classes |
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| `./matrixSet`| matrix set classes |
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| `./models`| model files |
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| `./nn`| neural network verification and robust training |
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| `./specification`| specification classes for verification |
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| `./unitTests`| unit tests |
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<hr style="height: 1px;">
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<img src="./app/images/coraLogo_readme.svg"/>

‎app/README.md‎

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coraApp
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in the MATLAB console to start defining your dynamic graphically.
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Check Section 8 in the <a target='_blank' href="https://tumcps.github.io/CORA/manual">CORA manual</a> for more information.
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Check Section 8 in the <a target='_blank' href="https://cora.in.tum.de/manual">CORA manual</a> for more information.
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<hr style="height: 1px;">

‎app/auxiliary/dynamics_equation_nonlinear‎

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‎app/auxiliary/dynamics_equation_nonlinear.m‎

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‎app/auxiliary/infoBox.m‎

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function varargout = infoBox(varargin)
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% GUI to display information to inform the user with a picture
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% ------------------------------------------------------------------
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% infoBox - GUI to display information to inform the user with a picture
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%
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% This file is part of the MORLAB_GUI, a Model Order Reduction and
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% System Analysis Toolbox developed at the
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% Institute of Automatic Control, Technische Universitaet Muenchen
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% For updates and further information please visit www.rt.mw.tum.de
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% ------------------------------------------------------------------
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% Input Argument: Cell array with one cell containing the path to
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% the picture that should be displayed on the
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% Info Box
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% ------------------------------------------------------------------
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% Authors: Niklas Kochdumper
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% Last Change: 13 Feb 2015
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% ------------------------------------------------------------------
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%
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% Syntax:
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% varargout = infoBox(varargin)
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%
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% Inputs:
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% varargin - Cell array with one cell containing the path to
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% the picture that should be displayed on the Info Box
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%
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% Outputs:
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% varargout - ???
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%
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% Other m-files required: none
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% Subfunctions: none
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% MAT-files required: none
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%
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% See also: -
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% Authors: Niklas Kochdumper
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% Written: ???
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% Last update: 13-February-2015
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% Last revision: ---
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% ------------------------------ BEGIN CODE -------------------------------
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% Begin initialization code - DO NOT EDIT
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gui_Singleton = 1;
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gui_State = struct('gui_Name', mfilename, ...
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'gui_Singleton', gui_Singleton, ...
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'gui_OpeningFcn', @infoBox_OpeningFcn, ...
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'gui_OutputFcn', @infoBox_OutputFcn, ...
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'gui_OpeningFcn', @aux_infoBox_OpeningFcn, ...
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'gui_OutputFcn', @aux_infoBox_OutputFcn, ...
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'gui_LayoutFcn', [] , ...
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'gui_Callback', []);
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% End initialization code - DO NOT EDIT
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function infoBox_OpeningFcn(hObject, eventdata, handles, varargin)
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% Auxiliary functions -----------------------------------------------------
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function aux_infoBox_OpeningFcn(hObject, eventdata, handles, varargin)
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% Choose default command line output for infoBox
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handles.output = hObject;
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errordlg('Wrong number of input arguments','Error Dialog','modal');
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path = cell2mat(varargin{1,1});
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h = imread(path);
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% position ok panel
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set(handles.ok_panel,'Units','pixels');
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ok_panel_pos = get(handles.ok_panel, 'Position');
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set(hObject,'Units','pixels');
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pos = get(hObject,'Position');
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% position image
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path = cell2mat(varargin{1,1});
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h = imread(path);
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% set axes ok panel
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set(handles.axes,'Units','characters');
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set(handles.ok_panel,'Position',ok_panel_pos);
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set(handles.ok_panel,'Units','characters');
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% set axes pb
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set(handles.pb,'Units','pixels');
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posPb = get(handles.pb,'Position');
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imshow(h);
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set(handles.axes,'XTick',[]);
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set(handles.axes,'YTick',[]);
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function varargout = infoBox_OutputFcn(hObject, eventdata, handles)
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function varargout = aux_infoBox_OutputFcn(hObject, eventdata, handles)
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% output function
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function pb_Callback(hObject, eventdata, handles)
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function aux_pb_Callback(hObject, eventdata, handles)
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delete(handles.infoBox)
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% --- Executes on slider movement.
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function slider1_Callback(hObject, eventdata, handles)
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function aux_slider1_Callback(hObject, eventdata, handles)
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% hObject handle to slider1 (see GCBO)
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% --- Executes during object creation, after setting all properties.
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function slider1_CreateFcn(hObject, eventdata, handles)
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function aux_slider1_CreateFcn(hObject, eventdata, handles)
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% hObject handle to slider1 (see GCBO)
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end
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% ------------------------------ END OF CODE ------------------------------

‎app/auxiliary/inputArgsLength_app.m‎

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function [count,out] = inputArgsLength_app(f,varargin)
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% inputArgsLength_app - computes the number of inputs of a function handle
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%
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% Syntax:
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% Syntax:
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% [count,out] = inputArgsLength_app(f)
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% [count,out] = inputArgsLength_app(f,inpArgs)
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%
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%
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% See also: nonlinearSys
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% Author: Victor Gassmann
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% Written: 11-September-2020
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% Last update: ---
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% Last revision:---
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% Authors: Victor Gassmann
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% Written: 11-September-2020
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% Last update: ---
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% Last revision: ---
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%------------- BEGIN CODE --------------
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% ------------------------------ BEGIN CODE -------------------------------
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% parse input arguments: number of input arguments to function handle
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narginf = setDefaultValues({nargin(f)},varargin);
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maxVal = maxVal + 3;
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end
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%------------- END OF CODE --------------
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% ------------------------------ END OF CODE ------------------------------

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