The PROPT MATLAB Optimal 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, Per Rutquist in 2008.
PROPT is a combined modeling
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:
- Computation of the constant matrices used for the differentiation and integration of the polynomials used to approximate the solution to the trajectory optimization problem.
- 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 MAD (TOMLAB package for automatic differentiation to 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 (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
To solve the problem with PROPT the following code can be used (with 60 collocation points):
Multi Phase Optimal Control Example
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
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
- TOMLAB - Developer and distributor of the software.
- MAD - Automatic differentiation package used in software.
- PROPT - Home page for PROPT.
- SNOPT - Default solver used in PROPT.