optimal control problem
DAE
tractability index
The properties of differentialalgebraic equations representing optimal control problems
Roland England
England
Roland
Susana Go'mez
Go'mez
Susana
René Lamour
Lamour
René
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976),
The properties of differentialalgebraic equations representing optimal control problems
Roland England
,
Susana Go'mez
,
René Lamour
Preprint series:
Institut für Mathematik, HumboldtUniversität zu Berlin (ISSN 08630976),
MSC 2000
 49K15 Problems involving ordinary differential equations

65L80 Methods for differentialalgebraic equations
Abstract
This paper outlines a procedure for transforming a general optimal control problem to
a system of DifferentialAlgebraic Equations (DAEs). The KuhnTucker 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 wellconditioning 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.
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