The PAROC Platform

On this page we present the software components of the PAROC framework. In general, any high-fidelity action is performed in PSE's gPROMS ModelBuilder, while all other tasks are executed in MATLAB ®. Our software solutions are tailored to work with these two programs and to allow for the application of PAROC. The key components are thereby:

Based on the approximate model, formulate the corresponding multi-parametric programming problem
Solve the multi-parametric programming problem
Make the solution of the multi-parametric programming problem available to gPROMS®.

Each of these tasks can be treated separately, and especially in the case of the solution of the multi-parametric programming problem, yields a stand-alone software for the solution of multi-parametric programming problems. Note: the versions which are available here will always be the ones which are up to date. If you are interested in an older version of the software, please contact us.

The POP Toolbox

The core of PAROC is its ability to solve multi-parametric programming problems. To this end, we have developed POP, the Parametric Optimization toolbox which allows for the efficient solution of multi-parametric programming problems. It features:

Algorithms for multi-parametric linear and quadratic programming (mp-LP/mp-QP) problems, namely:
- A geometrical algorithm, based on 'Baotic, M. (2002) An efficient algorithm for multiparametric quadratic programming. Technical Report, ETH Zurich.'
- A combinatorial algorithm, based on 'Gupta, A.; Bhartiya, S.; Nataraj, P.S.V. (2011) A novel approach to multiparametric quadratic programming. Automatica, 47(9), 2112-2117'.
- A connected graph approach, based on 'Oberdieck, R.; Diangelakis, N.A.; Pistikopoulos, E.N. (2016) Explicit Model Predictive Control: A connected-graph approach. Automatica, submitted.'
An algorithm for the solution of multi-parametric mixed-integer linear and quadratic programming (mp-MILP/mp-MIQP) problems, featuring implementations of a decomposition-based strategy including:
- All comparison procedures presented in the open literature, i.e.
  - No comparison: 'Dua, V.; Bozinis, N.A.; Pistikopoulos, E.N. (2002) A multiparametric programming approach for mixed-integer quadratic engineering problems. Computers & Chemical Engineering, 26(4-5), 715-733.'
  - MinMax comparison: 'Axehill, D.; Besselmann, T.; Raimondo, D.M.; Morari, M. (2014) A parametric branch and bound approach to suboptimal explicit hybrid MPC. Automatica, 50(1), 240-246.'
  - Affine comparison: 'Oberdieck, R.; Wittmann-Hohlbein, M.; Pistikopoulos, E.N. (2014) A branch and bound method for the solution of multiparametric mixed integer linear programming problems. Journal of Global Optimization, 59(2-3), 527-543.'
  - Exact solution: 'Oberdieck, R.; Pistikopoulos, E.N. (2015) Explicit hybrid model-predictive control: The exact solution. Automatica, 58, 152-159.'
- Handling the integer variables using global optimization or exhaustive enumeration

Additionally to its solver capabilities, it also features a problem library as well as a problem generator, which allows for its use beyond PAROC and as a general toolbox for multi-parametric programming problems.

POP comes fully equipped with a suite of test set problems, which allow for benchmarking of algorithms and as an idea of the type and scale of problem, multi-parametric programming is currently able to solve. The latest version of POP, together with the test sets 'POP_mpLP1', 'POP_mpQP1', 'POP_mpMILP1' and 'POP_mpMIQP1' can be found here:

In order to facilitate the use of the POP toolbox, below you can find several tutorial videos related to the use of the POP toolbox:

Welcome
The Solver
The Library
The Generator
The Controller Design

Closing the loop - mpMPC.dll

Once the solution of the multi-parametric programming problem has been obtained, its solution needs to be passed on to gPROMS, where the obtained controller is validated against a high-fidelity model. Currently, this procedure is performed via gO:MATLAB, the in-build link of gPROMS with MATLAB ®.

PAROC App - A Demo version

This material is based upon work supported by the National Science Foundation under Grant Number 1705423. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Here we present a complete prototype software package for the PAROC Framework, developed in the MATLAB environment. The software allows the user to derive a custom-made mpMPC for their system of interest. The user can (i) derive approximate models based on the high fidelity model dynamics, (ii) design and tune mpMPC schemes based on the approximate model, and (iii) test the closed-loop performance of the control schemes on the high fidelity model. The PAROC App requires the POP Toolbox to solve multi-parametric programming problems, and the YALMIP toolbox to reformulate the MPC problems into multi-parametric programming problems.

The PAROC App comes with a user manual and a benchmark nonisothermal CSTR example for the interested user to test. For any feedback about the software, please feel free to contact us.

Download the PAROC App