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A set-valued filter for discrete time polynomial systems using sum of squares programming

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2 Author(s)
Christoph Maier ; Institute for Systems Theory and Automatic Control (IST), University of Stuttgart, Germany ; Frank Allgöwer

In this paper, we propose a novel approach for robust state reconstruction of multi-output discrete-time systems with polynomial nonlinear dynamics and measurements in presence of unknown but bounded disturbances corrupting both the state and measurement equations. The proposed recursive algorithm is based on ellipsoidal state bounding techniques and consists of a two-step prediction-correction procedure, with each step requiring the solution of a convex optimization problem under sum of squares rather than linear matrix inequality constraints. The presented approach reduces the conservatism in the calculation of the state bounding ellipsoid when compared to existing robust filtering approaches. The applicability and effectiveness of the new algorithm is exemplarily shown in numerical simulations of a benchmark system.

Published in:

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Date of Conference:

15-18 Dec. 2009