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IMA Journal of Mathematical Control and Information 2004 21(1):33-47; doi:10.1093/imamci/21.1.33
© 2004 by Institute of Mathematics and its Applications
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Computation of the observer gain for extended Luenberger observers using automatic differentiation

Klaus Röbenack1

1 Institut für Regelungs- und Steuerungstheorie, Fakultät Elektrotechnik und Informationstechnik, Technische Universität Dresden, Mommsenstr. 13, D-01062 Dresden, Germany

For a given nonlinear system, the extended Luenberger observer provides nearly exact error dynamics. In contrast to the normal form observer, the extended Luenberger observer exists even if the associated integrability condition is violated. Up to now, Lie derivatives and Lie brackets required by the design procedure have been computed symbolically. Even for systems with moderate size and complexity, one usually obtains extremely large expressions for the observer gain. The design of an extended Luenberger observer based on symbolic differentiation is not feasible for complicated or large-scale systems. In this paper we discuss a new approach to compute the observer gain. Our approach is based on a computation method for derivatives called automatic differentiation. In contrast to numeric differentiation by means of divided differences, automatic differentiation incurs no truncation errors.

Keywords: nonlinear observer design; error linearization; automatic differentiation; Taylor arithmetic; scientific computing.

Received 19 March 2003. Revised


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