### Radoslaw Pytlak (Military University of Technology, Warsaw)

#### Numerical methods for optimal control of higher index differential-algebraic equations

*Wednesday 10 December 2003 at 15.30, JCMB 5215*

##### Abstract

The commonly used definition of the index of DAE's (differential-algebraic
equations) indicates how many times some algebraic equations have to be
differentiated in order to transform a set of DAE's to a set of implicit ODE's.
The differentiation can introduce higher-order derivatives of control variables
and impulse responses of the system. In this paper we introduce a class of
optimal control problems described by DAE's that can be optimized under the
assumption that control variables are essentially bounded measurable functions.
We show how to define adjoint equations for DAE's describing these problems.
Finally, we propose algorithms which find controls satisfying optimality
conditions in terms of the weak maximum principle.

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