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OCMat

OCMat - Software

OCMat is a collection of MATLAB files developed to analyze optimal control models.

With the help of OCMat it is possible to

  • Analyze (non-)autonomous optimal control models of (in)finite time horizon.
  • Deal adequately with constraints on control and/or state variables.
  • Locate steady states and limit cycles.
  • Find solution paths by solving a BVP.
  • Locate Skiba points and continue Skiba curves (manifolds).
  • Easy storing and plotting of (numerical) results.
  • and much more...

We invite the user to visit this site every now and then to follow the actual stage of development.

 

Acknowledgement

The development of OCMat2.0 was financially supported by the Austrian Science Fund (FWF) under grant No. P23084-N13 (A MATLAB Package for Analyzing Optimal Control Problems).

 

 

Download

Find here the most current version of the toolbox.

     OCMat2.0 Version 25.06.2014: Download

System Requirements

  • MATLAB V. 7 or higher together with: Symbolic-toolbox (required to derive necessary optimality conditions automatically) and Optimization-toolbox (in default settings used).
  • MatCont toolbox (optional) for bifurcation related calculations.

Installation Guide (Version 2.0)

  1. Make sure you have correctly installed MATLAB and the necessary toolboxes.
  2. Download the OCMat-toolbox and unzip it into any directory.
  3. Change to the directory in the MATLAB command window and type 'init'. This adds the necessary OCMat folders to the MATLAB path.

 

Find here an old version of the toolbox.

     OCMat1.0 Version 09.03.2011: Download

 

Documentation

Manual

You can find the OCMat-toolbox manual here: View

We also want to refer the reader to the book 'Optimal Control of Nonlinear Processes - With Applications in Drugs, Corruption and Terror', where the reader can learn about the mathematical background used in this toolbox and see some examples (graphics and numerical computations) presenting some of the capabilities of the toolbox.

Demos (Version 1.0)

For a demonstration about what currently can be done with the OCMat-toolbox, you can find some demo files together with the toolbox.

By invoking these demo files with ochivdemo and occademo, some explanatory text is provided. The in MATLAB experienced user is also advised to go through the commented MATLAB files and find the answers and explanations of several questions. Further support will be provided here.

Seminar (Version 1.0)

In the following you can find the slides of an introductory seminar about the toolbox

  1. December 6th, 2010: First steps: Implementation and a simple model
  2. December 13th, 2010: Basic numerical methods
  3. December 20th, 2010: Higher dimensional models and constraints
  4. January 10th, 2011: Multiple solutions and heteroclinic bifurcations
  5. January 17th, 2011: Limit cycles and a MatCont interface


Handouts (for printing)

  1. December 6th, 2010: one-sided, two-sided
  2. December 13th, 2010: one-sided, two-sided
  3. December 20th, 2010: one-sided, two-sided
  4. January 10th, 2011: one-sided, two-sided
  5. January 17th, 2011: one-sided, two-sided

Links

Related Sites

  • Matlab is a high-level language and interactive environment for numerical computation, visualization, and programming.
  • MatCont is a Matlab software project for the numerical continuation and bifurcation study of continuous and discrete parameterized dynamical systems.
  • pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs.
  • Scilab is a free and open source software for numerical computation providing a powerful computing environment for engineering and scientific applications.

 

Literature

D. Grass, J.P. Caulkins, G. Feichtinger, G. Tragler, D.A. Behrens, Optimal Control of Nonlinear Processes - With Applications in Drugs, Corruption and Terror, Springer, 2008

D. Grass, Numerical computation of the optimal vector field in a fishery model, Journal of Economic Dynamics and Control, 36(10):1626-1658, 2012.

Animations

For a talk held at the workshop "The Economics of Complex Systems workshop", April 28-29 (2014) at the Beijer Institute of Ecological Economics, some results, based on a coral-reef model, were animated using the open source software Synfig Studio, Blender, Inkscape and ImageMagick. The two main issues were

  1. Present the outcome of the numerical analysis to interested persons without loosing information.
  2. Remove the underlying mathematics completely from the presentation.