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Bilinear Observer/Kalman Filter Identification

Vicario, Francesco; Phan, Minh Q.; Betti, Raimondo; Longman, Richard W.

Bilinear systems are important per se since several phenomena in engineering and other fields are inherently bilinear. Even more interestingly, bilinear systems can approximate more general nonlinear systems, providing a promising approach to handle various nonlinear identification and control problems, such as satellite attitude control. This paper develops and demonstrates via numerical examples a method for discrete-time state-space model identification for bilinear systems in the presence of noise in the process and in the measurements. The formulation relies on a bilinear observer which is proven to have properties similar to the linear Kalman filter under the sole additional assumption of stationary white excitation input, and on a novel approach to system identification based on the estimation of the observer residuals. The latter are used to construct a new, noise-free identification problem, in which the observer is identified and the matrices of the system state-space model are recovered. The resulting method represents the bilinear counterpart of the Observer/Kalman filter Identification (OKID) approach for linear systems, originally developed for the identification of lightly-damped structures and distributed by NASA.

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Also Published In

Title
Spaceflight mechanics 2014 : proceedings of the 24th AAS/AIAA Space Flight Mechanics Meeting
Publisher
Univelt

More About This Work

Academic Units
Mechanical Engineering
Published Here
January 5, 2016

Notes

This work was presented at the 24th AAS/AIAA Space Flight Mechanics Meeting, Santa Fe, NM, January 2014. The paper (identified as paper AAS 14-307) was then published as part of the conference proceedings in the Advances in the Astronautical Sciences, Vol. 150, 2014, pp. 1056-1076 (published by Univelt).

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