# American Institute of Mathematical Sciences

January  2007, 7(1): 53-76. doi: 10.3934/dcdsb.2007.7.53

## Galerkin method and approximate tracking in a non-minimum phase bilinear system

 1 Institute of Industrial and Control Engineering, Technical University of Catalonia, Avda. Diagonal 647, Pl. 11, 08028 Barcelona, Spain 2 Department of Automatic Control and Computer Engineering, Technical University of Catalonia, Avda. Diagonal 647, Pl. 2, 08028 Barcelona, Spain

Received  April 2005 Revised  August 2006 Published  October 2006

The tracking control of non-minimum phase systems is nowadays an open and challenging field, because a general theory is still not available. This article proposes an indirect control strategy in which a key role is played by the inverse problem that arises and their approximate solutions. These are obtained with the Galerkin method, a standard functional analysis tool. A detailed study of the effect on the output caused by the use of an approximate input is performed. Error bounds are also provided. The technique is motivated through its implementation in basic, DC-to-DC nonlinear power converters that are intended to be used as DC-to-AC voltage sources.
Citation: E. Fossas, J. M. Olm. Galerkin method and approximate tracking in a non-minimum phase bilinear system. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 53-76. doi: 10.3934/dcdsb.2007.7.53
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