A necessary optimality condition for the linear-quadratic DAE control problem

André Backes

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

49K15 Problems involving ordinary differential equations

49N10 Linear-quadratic problems

Abstract
We consider the linear-quadratic optimal control problem for a controlled differential algebraic equation (DAE). Under minimal assumptions on the DAE concerning index and regularity it will be possible to prove that the sufficient optimality condition given in papers of G.Kurina and R.März is also a necessary condition. This condition includes the solution of an appropriate boundary value problem and, in the special case of an explicit ordinary differential equation, the condition is equal to the well known necessary and sufficient condition of the classical linear-quadratic optimal control problem.