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Numerical methods for parameter identification and optimal control

Methods for the solution of optimal control problems are the recently developed and implemented direct collocation and direct shooting methods (cf. [3], [6], [13], [14]). These methods have shown to be efficient, reliable and robust in solving real-life problems. If very high accuraccy is required then the indirect multiple shooting method is the choice [4]. A survey of efficient methods is given in [11].
Efficient methods for the solution of the mentioned parameter identification problems are based on multiple shooting in combination with generalized Gauss-Newton- or adapted SQP-methods (cf. [2], [7]). These identification algorithms only require some functions of the states and no derivatives to be measured in order to identify the unknown parameters p. In other widely used approaches it is necessary to measure not only the first but also the second time derivatives of the state variables . As this is often not practicable, artifical measurements of time derivatives have to be constructed.
The proposed methods for identification and optimal control use the same dynamic model. They can therefore be conviently used in combination.

Acknowledgement. This research has been supported in part by the Deutsche Forschungsgemeinschaft (DFG), the Bundesministerium für Forschung und Technologie (BMFT) and the Bayerische Forschungsstiftung within the Bayerischer Forschungsverbund für technisch-wissenschaftliches Hochleistungsrechnen (FORTWIHR).

Oskar von Stryk
Thu May 2 20:47:39 MET DST 1996