This package contains code and appendix.

Appendix to the paper

Containing proofs and benchmark details.

See file appendix.PDF

Dependencies:

The code uses the CMake compilation system. It has been tested on a MAC OSX machine.

To compile, you will need to install the libraries

• C++ BOOST library
• GNU MPFR library for multi precision floating point
• MPFI library
• glpk library

You will also need parser generator and lexical analyzers

• Flex
• Bison

These are installed from packages on homebrew (MAC OSX) or apt (Linux/Ubuntu).

$ apt-get install -y cmake libmpfr-dev libmpfi-dev flex bison libglpk

Compile:

Type

$ cmake ./CMakeLists.txt
$ make

If your system has libraries installed at non-standard locations, you will need to edit the files in the directory cmake-includes. Specifically the files FindMPFR.cmake and FindMPFI.cmake specify where to search for these libraries.

Running to reproduce table entries

First go to the test directory

$ cd ./tests

Rimless Wheel Model (run using polynomial form API functions)

../polynomialFormUncertaintyPropagation -n 2000 -t -d 2 -w 4

2D Robot model (run using polynomial form API functions)

../polynomialFormUncertaintyPropagation  -n 100 -d 2 -r

Cartpole model (run using polynomial form API functions)

../polynomialFormUncertaintyPropagation  -n 8 -d 2 -c 

Ebola model (run from model file)

$ cat ebola-model.sys
$ ../polynomialFormUncertaintyPropagation -d 6 -n 25 -4 ebola-model.sys 

Honeybee model (run from model file)

$ cat honeybee.sys
$ ../polynomialFormUncertaintyPropagation -n 25 -d 4 -4 honeybee.sys 

Coupled Vanderpol oscillator

$ cat coupledVanderpol-3.sys
$ ../polynomialFormUncertaintyPropagation -n 15 -d 2  coupledVanderPolOscillators-3.sys 

Laub Loomis Model

$ cat laub-loomis.sys
$ ../polynomialFormUncertaintyPropagation -n 25 -d 4 laub-loomis.sys 

Lattice 10x1 Model

$ cat 1d-lattice-10.sys
$ ../polynomialFormUncertaintyPropagation -n 15 -d 4 1d-lattice-10.sys 

Reproducing Affine Arithmetic Results

NOTE: Code requested and provided as is by Bouissou et al. Used as a library inside our tool. Rimless wheel, 2D robot and Cartpole model results reported directly from Bouissou et al.

Ebola model (run from model file)

$ cat ebola-model.sys
$ ../polynomialFormUncertaintyPropagation  -n 25 -a ebola-model.sys 

Honeybee model (run from model file)

$ cat honeybee.sys
$ ../polynomialFormUncertaintyPropagation -n 25 -a honeybee.sys 

Coupled Vanderpol oscillator

$ cat coupledVanderpol-3.sys
$ ../polynomialFormUncertaintyPropagation -n 15 -a coupledVanderPolOscillators-3.sys 

Laub Loomis Model

$ cat laub-loomis.sys
$ ../polynomialFormUncertaintyPropagation -n 25 -a laub-loomis.sys 

Lattice 10x1 Model

$ cat 1d-lattice-10.sys
$ ../polynomialFormUncertaintyPropagation -n 15 -a  1d-lattice-10.sys 

Running Simulations

cd ../python-simulation

Each python file corresponds to the model of the same name

python3 rimlessWheel.py
python3 roboticArm.py
python3 cartpole.py
python3 ebola-model.py
python3 honeybee.py
python3 coupledVanderPolOscillators-3.py
python3 laub-loomis.py
python3 1d-lattice-10.py