name = PROPT
developer = [http://tomopt.com/ Tomlab Optimization Inc.]
latest_release_version = 6.1
latest_release_date = release date|2008|06|11
operating_system = [http://tomopt.com/tomlab/about/ TOMLAB® - OS Support]
genre = Technical computing
license = Proprietary
website = [http://tomdyn.com/ PROPT product page]
The PROPT [cite book | title = PROPT - Matlab Optimal Control Software | first = Per | last = Rutquist | coauthors = M. M. Edvall | date = June 2008 | url = http://tomopt.com/docs/TOMLAB_PROPT.pdf | location = 1260 SE Bishop Blvd Ste E, Pullman, WA 99163, USA | publisher = Tomlab Optimization Inc.]
MATLABOptimal Control Software is a new generation platform for solving applied optimal control (with ODE or DAE formulation) and parameters estimation problems.
The platform was developed by MATLAB Programming Contest Winner, [http://www.mathworks.com/contest/golf_1.cgi/winners.html Per Rutquist] in
PROPT is a combined modeling, compilation and solver engine for generation of highly complex optimal control problems. PROPT uses a pseudospectral collocation method for solving optimal control problems. This means that the solution takes the form of a polynomial, and this polynomial satisfies the DAE and the path constraints at the collocation points.
In general PROPT has five main functions:
* Text manipulation to turn user-supplied expressions into MATLAB code for the cost function and constraint function that are passed to a nonlinear programming solver in
TOMLAB, ensuring that the code is compatible with [http://matlabad.com/ MAD] (TOMLAB package for automatic differentiationto achieve floating point precision for derivatives).
* Functionality for plotting and computing a variety of information for the solution to the problem.
* Partial automatic linearization for the following scenarios:
** Minimal (or maximal) time problem
** Problems with a linear objective (pure feasibility problems are also handled)
** Linear systems with a fixed end time
* Integrated support for non-smooth [cite journal | title = Dynamic optimization of bioprocesses: efficient and robust numerical strategies | first = J. R. | last = Banga | coauthors = Balsa-Canto, E. and Moles, C. G. and Alonso, A. A. | date = 2003 | publisher = Journal of Biotechnology] (hybrid) optimal control problems.
The PROPT system uses equations and expressions to model optimal control problems. It is possible to define independent variables, dependent functions, scalars and constant parameters:
States and Controls
States and controls only differ in the sense that controls need be continuous between phases.
Boundary, path, event and integral constraints
A variety of boundary, path, event and integral constraints are shown below:
Single Phase Optimal Control Example
Van der Pol Oscillator [ [http://tomdyn.com/examples/vanDerPol.html "Van Der Pol Oscillator - Matlab Solution", "PROPT Home Page"] June, 2008.]
To solve the problem with PROPT the following code can be used (with 60 collocation points):
Multi Phase Optimal Control Example
One-dimensional rocket [ [http://tomdyn.com/examples/onedimRocket.html "One Dimensional Rocket Launch (2 Free Time)", "PROPT Home Page"] June, 2008.] with free end time and undetermined phase shift
The problem is solved with PROPT by creating two phases and connecting them:
Parameter Estimation Example
Parameter Estimation Problem [ [http://tomdyn.com/examples/parameterEstimation.html "Matlab Dynamic Parameter Estimation with PROPT", "PROPT Home Page"] June, 2008.]
In the code below the problem is solved with a fine grid (10 collocation points). This solution is subsequently fine-tuned using 40 collocation points:
Optimal Control Problems Supported
* Aerodynamic trajectory control [cite journal | title = SOCS Release 6.5.0 | first = J. | last = Betts | date = 2007 | publisher = THE BOEING COMPANY]
Bang-bang control[cite journal | title = Solving Tough Optimal Control Problems by Network Enabled Optimization Server (NEOS) | first = J. | last = Liang | coauthors = Meng, M. and Chen, Y. and Fullmer, R. | date = 2003 | publisher = School of Engineering, Utah State University USA, Chinene University of Hong Kong China]
Chemical engineering[cite journal | title = A HYBRID METHOD FOR THE OPTIMAL CONTROL OF CHEMICAL PROCESSES | first = E. F. | last = Carrasco | coauthors = Banga, J. R. | date = September 1998 | location = University of Wales, Swansea, UK | publisher = UKACC International Conference on CONTROL 98]
* Dynamic systems [cite journal | title = Second-order sensitivities of general dynamic systems with application to optimal control problems | first = V. S. | last = Vassiliadis | coauthors = Banga, J. R. and Balsa-Canto, E. | date = 1999 | publisher = Chemical Engineering Science | volume = 54 | pages = 3851-3860]
* General optimal control
* Large-scale linear control [cite book | title = Iterative dynamic programming | first = R. | last = Luus | date = 2002 | publisher = Chapman and Hall/CRC]
* Multi-phase system control [cite journal | title = A Java Application for the Solution of Optimal Control Problems | first = B. C. | last = Fabien | date = 1998 | location = Stevens Way, Box 352600 Seattle, WA 98195, USA | publisher = Mechanical Engineering, University of Washington]
Mechanical engineeringdesign [cite journal | title = MISER3: Optimal Control Toolbox User Manual, Matlab Beta Version 2.0 | first = L. S. | last = Jennings | coauthors = Fisher, M. E. | date = 2002 | location = Nedlands, WA 6907, Australia | publisher = Department of Mathematics, The University of Western Australia]
* Nondifferentiable control [citation | title = Global Optimization of Chemical Processes using Stochastic Algorithms - State of the Art in Global Optimization: Computational Methods and Applications | first = J. R. | last = Banga | coauthors = Seider, W. D. | editor-last = Floudas | editor-first = C. A. | editor2-last = Pardalos | editor2-first = P. M.
date = 1996 | location = Dordrecht, The Netherlands | publisher = Kluwer Academic Publishers | isbn = 0-7923-3838-3 | pages = 563-583]
* Parameters estimation for dynamic systems [cite journal | title = Benchmarking Optimization Software with COPS | first = E. D. | last = Dolan | coauthors = More, J. J. | date = January 2001 | location = 9700 South Cass Avenue, Argonne, Illinois 60439 | publisher = ARGONNE NATIONAL LABORATORY]
* [http://tomopt.com/ TOMLAB] - Developer and distributor of the software.
* [http://matlabad.com/ MAD] - Automatic differentiation package used in software.
* [http://tomdyn.com/ PROPT] - Home page for PROPT.
* [http://tomopt.com/tomlab/products/snopt/solvers/SNOPT.php SNOPT] - Default solver used in PROPT.
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