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Automatic Control and System Dynamics
PoCET Toolbox

PoCET (Polynomial Chaos Expansion Toolbox)

Overview

PoCET is a free and open-scource Polynomial Chaos Expansion Toolbox for MATLAB®. Its main contribution is the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic parameters or initial conditions. PoCET features

  • a simple syntax and usability,
  • built-in handling of Gaussian, uniform, and beta probability density functions,
  • projection and collocation-based calculation of PCE coefficients,
  • routines for the calculation of stochastic moments from PCE coefficients,
  • several routines for system simulation and visualization of results,
  • as well as a variety of introductory and instructive examples.
Efficient algorithms for the involved computations have been designed in order to increase its applicability. Therefore, PoCET's possible use-cases include (but are not limited to)
  • uncertainty analysis
  • parameter estimation
  • state estimation and prediction
  • optimal experimental design
  • (active) fault diagnosis
  • stochastic nonlinear MPC

PoCET was officially released and introduced on the 21st IFAC World Congress 2020. A preprint of the corresponding paper, which includes more detailed information about its usage and features, is available here.

 

Download and Installation

System Requirements

PoCET requires MATLAB® R2010b or later as well as the Symbolic Math Toolbox for parsing.

 

Copyright, License, and Citation Information

Copyright (c) 2020 Stefan Streif, stefan.streif@etit.tu-chemnitz.de

PoCET is licensed under the EUPL-1.2-or-later.

When publishing results gained by using PoCET use the following citation:
F. Petzke, A. Mesbah, and S. Streif. PoCET: a Polynomial Chaos Expansion Toolbox for Matlab. In Proc. 21st IFAC World Congress, 2020. (download bib)

 

Download and Installation

The latest version of PoCET is available for download on GitHub. For installation simply run the installation script (installPoCET.m).

An introduction to PoCET is available here.

Contact

If you have any questions or comments, please feel free to send us an e-mail ( stefan.streif@...).

Related Publications

Release on IFAC 2020

  • Petzke, F.; Mesbah, A.; Streif. S.: PoCET: a Polynomial Chaos Expansion Toolbox for Matlab. In Proc. 21st IFAC World Congress, 2020.

Stochastic model predictive control

  • Streif, S.; Karl, M.; Mesbah, A.: Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints. [URL]
  • Paulson, J.A.; Streif, S.; Mesbah, A.: Stability for Receding-horizon Stochastic Model Predictive Control with Chance Constraints. In Proc. American Control Conference (ACC). Chicago, IL. July 2015. In press..
  • Mesbah, A.; Streif, S.; Findeisen, R.; Braatz, R.D.: Stochastic Nonlinear Model Predictive Control with Probabilistic Constraints. In Proc. American Control Conference (ACC), pp. 2413-2419. Portland, Oregon. June 2014. [URL]
  • Paulson, J.A.; Mesbah, A.; Streif, S.; Findeisen, R.; Braatz, R.D.: Fast Stochastic Model Predictive Control of High-dimensional Systems. In Proc. 53rd IEEE Conference on Decision and Control (CDC), pp. 2802-2809. Los Angeles, CA. December 2014.

Active fault fiagnosis

  • Mesbah, A.; Streif, S.; Findeisen, R.; Braatz, R.D.: Active Fault Diagnosis for Nonlinear Systems with Probabilistic Uncertainties. In Proc. 19th IFAC World Congress, pp. 7079-7084. Cape Town, South Africa. August 2014. [URL]
  • Paulson, J.A.; Raimondo, D.M.; Braatz, R.D.; Findeisen, R.; Streif, S.: Guaranteed Active Fault Diagnosis for Uncertain Nonlinear Systems. In Proc. European Control Conference (ECC), pp. 926-931. Strasbourg, France. June 2014. [URL]
  • Streif, S.; Hast, D.; Braatz, R.D.; Findeisen, R.: Certifying robustness of separating inputs and outputs in active fault diagnosis for uncertain nonlinear systems. In Proc. 10th IFAC International Symposium on Dynamics and Control of Process Systems (DyCoPS), pp. 837-842. Mumbai, India. December 2013. [URL]

Experimental design

  • Mesbah, A.; Streif, S.: A Probabilistic Approach to Robust Optimal Experiment Design with Chance Constraints. In International Symposium on Advanced Control of Chemical Processes (ADCHEM). Whistler, British Columbia, Canada. June 2015. In press.. [URL]
  • Streif, S.; Petzke, F.; Mesbah, A.; Findeisen, R.; Braatz, R.D.: Optimal Experimental Design for Probabilistic Model Discrimination Using Polynomial Chaos. In Proc. 19th IFAC World Congress, pp. 4103-4109. Cape Town, South Africa. August 2014. [URL]