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Linear State Representations for Identification of Bilinear Discrete-Time Models by Interaction Matrices

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

Bilinear systems can be viewed as a bridge between linear and nonlinear systems, providing a promising approach to handle various nonlinear identification and control problems. This paper provides a formal justification for the extension of interaction matrices to bilinear systems and uses them to express the bilinear state as a linear function of input-output data. Multiple representations of this kind are derived, making it possible to develop an intersection subspace algorithm for the identification of discrete-time bilinear models. The technique first recovers the bilinear state by intersecting two vector spaces that are defined solely in terms of input-output data. The new input-output-to-state relationships are also used to extend the Equivalent Linear Model method for bilinear system identification. Among the benefits of the proposed approach, it does not require data from multiple experiments, and it does not impose specific restrictions on the form of input excitation.

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More About This Work

Academic Units
Mechanical Engineering
Published Here
August 13, 2015

Notes

This work was presented as a CONFERENCE PAPER at the 23rd AAS/AIAA Spaceflight Mechanics Meeting, February 10-14, 2013, Kauai, HI, 2013. Citation: Vicario, F., Phan, M.Q., Betti, R., Longman, R.W., "Linear State Representations for Identification of Bilinear Discrete-Time Models by Interaction Matrices," Advances in the Astronautical Sciences, vol. 148, 2013, pp. 2039–2058. This work was subsequently published as a JOURNAL ARTICLE in Nonlinear Dynamics - An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems. Citation: Vicario, F., Phan, M.Q., Betti, R., Longman, R.W., "Linear State Representations for Identification of Bilinear Discrete-Time Models by Interaction Matrices," Nonlinear Dynamics, vol. 77, 2014, pp. 1561-1576. DOI 10.1007/s11071-014-1399-9

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