England, Roland; Gómez, Susana and Lamour, René
PDF (Not Set)
- Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
|DOI (Digital Object Identifier) Link:||http://doi.org/10.1016/j.apnum.2009.04.003|
|Google Scholar:||Look up in Google Scholar|
This paper outlines a procedure for transforming a general optimal control problem to a system of Differential-Algebraic Equations (DAEs). The Kuhn-Tucker conditions consist of differential equations, complementarity conditions and corresponding inequalities. These latter are converted to equalities by the addition of a new variable combining the slack variable and the corresponding Lagrange multipliers. The sign of this variable indicates whether the constraint is active or not.
The concept of the tractability index is introduced as a general purpose tool for determining the index of a system of DAEs by checking for the nonsingularity of the elements of the matrix chain. This is helpful in determining the well-conditioning of the problem, and an appropriate method for solving it numerically.
In the examples used here, the solution of all the differential equations could be performed analytically. The given examples are tested by the numerical determination of the tractability index chain, and the results confirm the previously known properties of the examples.
|Item Type:||Journal Article|
|Copyright Holders:||2009 IMACS|
|Keywords:||optimal control; differential-algebraic equations; tractability index; differentiation index; Kuhn-Tucker conditions|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
|Depositing User:||Roland England|
|Date Deposited:||23 Jun 2006|
|Last Modified:||23 Feb 2016 22:00|
|Share this page:|
Download history for this item
These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.