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Preprint 10-2011

Formal adjoints of linear DAE operators and their role in optimal control

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Author(s) : Peter Kunkel , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2011

MSC 2000

93C10 Nonlinear systems
93C15 Systems governed by ordinary differential equations

Abstract :
For regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze the properties of the formal adjoints and their implications in solving linear-quadratic optimal control problems with DAE constraints.

Keywords : Differential-algebraic equation, adjoint operator, adjoint pair, formal adjoint pair, optimal control, necessary optimality condition, formal necessary optimality condition

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