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Observers for Bilinear State-Space Models by Interaction Matrices

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

This paper formulates a bilinear observer for a bilinear state-space model. Relationship between the bilinear observer gains and the interaction matrices are established and used in the design of such observer gains from input-output data. In the absence of noise, the question of whether a deadbeat bilinear observer exists that would cause the state estimation error to converge to zero identically in a finite number of time steps is addressed. In the presence of noise, an optimal bilinear observer that minimizes the state estimation error in the same manner that a Kalman filter does for a linear system is presented. Numerical results illustrate both the theoretical and computational aspects of the proposed algorithms.

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More About This Work

Academic Units
Mechanical Engineering
Published Here
August 21, 2015

Notes

This work was presented at the 16th Yale Workshop on Adaptive and Learning Systems, New Haven, CT, 2013. Citation: Minh Q. Phan, Francesco Vicario, Richard W. Longman, and Raimondo Betti, "Observers for Bilinear State-Space Models by Interaction Matrices," 16th Yale Workshop on Adaptive and Learning Systems, New Haven, CT, 2013. This work was later expanded and published as a journal paper. Citation: Minh Q. Phan, Francesco Vicario, Richard W. Longman, and Raimondo Betti, "Optimal bilinear observers for bilinear state-space models by interaction matrices," International Journal of Control, vol. 88, no. 8, 2015, pp. 1504-1522. DOI:10.1080/00207179.2015.1007530 http://www.tandfonline.com/doi/abs/10.1080/00207179.2015.1007530

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