Abstract
A strategy to Fuzzy Kalman Filter identification, is proposed. A mathematical formulation applied to fuzzy Takagi-Sugeno structure is presented: the algorithm FCM estimates the antecedent parameters; from the input and output data of dynamic system, the ERA/DC algorithm based on FCM clustering algorithm, is applied to obtain the state matrix, input influence matrix, output influence matrix, and direct transmission matrix (the matrices A, B, C, and D, respectively) to each rule of the consequent parameters. The Fuzzy Kalman Filter is applied to estimate states and output of a dynamic system with partial knowledge of states and the efficiency of the proposed methodology is shown in computational results, once that the Fuzzy Kalman Filter follows the dynamic behavior related to output and states of the dynamic system.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Wu, C.Y., Tsai, J.S.H., Guo, S.M., Shieh, L.S., Canelon, J.I., Ebrahimzadeh, F., Wang, L.: A novel on-line observer Kalman filter identification method and its application to input-constrained active fault-tolerance tracker design for unknown stochastic systems. J. Franklin Inst. 352, 1119–1151 (2015)
Juang, J.N.: Applied System Identification. Prentice Hall, United States (1994)
Kordik, V.: Kalman Filter. InTech (2010)
Huo, Y., Cai, Z., Gong, W., Liu, Q.: A new adaptive kalman filter by combining evolutionary algorithm and fuzzy inference system. In: China: IEEE Congress on Evolutionary Computation (CEC), pp. 2893–2899 (2014)
Lima, D.P., Kato, E.R.R., Tsunaki, R.H.: A new comparison of Kalman filtering methods for chaotic series. In: California: IEEE International Conference on Systems, Man and Cybernetics (SMC), pp. 3531–3536 (2014)
Inoue, R.S., Terra, M.H., Cerri, J.P.: Extended robust Kalman filter for attitude estimation. IET Control Theory Appl. 10, 162–172 (2016)
Serra, G.L.O.: Frontiers in Advanced Control Systems. InTech, Croatia (2012)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Grigorie, T.L.: Fuzzy Controllers, Theory and Applications. InTech, Croatia (2011)
Babuska, R., Schutter, B.D., Lendek, Z., Guerra, T.M.: Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models. Springer Publishing Company, Incorporated (2010)
Juang, J.N., Pappa, R.S.: An eigensystem realization algorithm for modal parameter identification and model reduction. J. Guidance Control Dyn. 8(5), 620–627 (1985)
Zhang, J., Shi, P., Qiu, J., Nguang, S.K.: A novel observer-based output feedback controller design for discrete-time fuzzy systems. IEEE Trans. Fuzzy Syst. 23(1), 223–229 (2015)
Acknowledgments
This work was encouraged by FAPEMA and by Ph.D. Program in Electrical Engineering of Federal University of Maranhão (PPGEE/UFMA).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Pires, D.S., de Oliveira Serra, G.L. (2017). Fuzzy Kalman Filter Black Box Modeling Approach for Dynamic System with Partial Knowledge of States. In: Garrido, P., Soares, F., Moreira, A. (eds) CONTROLO 2016. Lecture Notes in Electrical Engineering, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-319-43671-5_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-43671-5_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-43670-8
Online ISBN: 978-3-319-43671-5
eBook Packages: EngineeringEngineering (R0)