Author(s) :
Volker Mehrmann
,
Lena Scholz
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 26-2012
MSC 2000
- 93C05 Linear systems
-
93C55 Discrete-time systems
-
93C15 Systems governed by ordinary differential equations
-
65L80 Methods for differential-algebraic equations
-
49K15 Problems involving ordinary differential equations
-
34H05 Control problems
Abstract :
We analyze the structure of the linear differential and difference operators associated with the necessary optimality conditions of optimal control problems for descriptor systems in continuous- and discrete-time.
It has previously been shown that in continuous-time the associated optimality system is a self-conjugate operator associated with a self-adjoint pair of coefficient matrices and we show that the same is true in the discrete-time setting.
We also extend these results to the case of higher order systems. Finally, we discuss how to turn higher order systems with this structure into first order systems with the same structure.
Keywords :
Differential-algebraic equation, self-conjugate difference operator, self-adjoint pair, discrete-time optimal control, necessary optimality condition, congruence transformation, higher order systems.