PROPT

From NEOS

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.

Contents 1 Description 2 Modeling 3 Optimal Control Examples 4 Optimal Control Problems Supported 5 External links

Description

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:

• 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 f and constraint function c 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.

Modeling

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 only differ in the sense that controls need be continuous between phases. A variety of boundary, path, event and integral constraints can be defined.

Optimal Control Examples

• Van der Pol Oscillator
• One-dimensional rocket
• Parameter Estimation Problem

Optimal Control Problems Supported

• Aerodynamic trajectory control
• Bang-bang control
• Chemical engineering
• Dynamic systems
• General optimal control
• Large-scale linear control
• Multi-phase system control
• Mechanical engineering design
• Nondifferentiable control
• Parameters estimation for dynamic systems
• Singular control

External links

• TOMLAB - Developer and distributor of the software.
• MAD - Automatic differentiation package used in software.
• PROPT - Home page for PROPT.
• TomSym - Page about source transformation used in PROPT.
• SNOPT - Default solver used in PROPT.