Abstract
The problem of continuation of an input-output mapping to a right invertible mapping is solved. The proposed solution is based on transforming the system to a normal form and solving the problem for such systems. The well-known Singh inversion algorithm is modified to calculate the normal forms. It is proved that each step of the modified algorithm can be realized and the result of the algorithm application is a normal form. A new approach to the parameter identification problem based on the inversion of the input-output mapping is proposed to illustrate the application of the results.
Similar content being viewed by others
References
Fliess, M., A note on invertibility of nonlinear input-output differential systems, Syst. Control Lett., 1986, vol. 8, no. 2, pp. 147–151.
Di Benedetto, M.D., Grizzle, J.W., and Moog, C.H., Rank invariants of nonlinear systems, SIAM J. Control Optim., 1989, vol. 27, no. 3, pp. 658–672
Conte, G., Moog, C.H., and Perdon, A.M., Algebraic Methods for Nonlinear Control Systems, London: Springer, 2007.
Il’in, A.V., Korovin, S.K., and Fomichev, V.V., Metody robastnogo obrashcheniya dinamicheskikh sistem (Methods of Robust Inversion of Dynamical Systems), Moscow: Fizmatlit, 2009.
Singh, S.N., A modified algorithm for invertibility in nonlinear systems, IEEE Trans. Automat. Control, 1981, vol. 26, no. 2, pp. 595–598.
Silverman, L., Inversion of multivariable linear systems, IEEE Trans. Automat. Control, 1969, vol. 14, no. 3, pp. 270–276.
Hirschorn, R.M., Invertibility of multivariable nonlinear systems, IEEE Trans. Automat. Control, 1979, vol. 24, no. 6, pp. 855–865.
Schenkendorf, R. and Mangold, M., Parameter identification for ordinary and delay differential equations by using flat inputs, Theor. Found. Chem. Eng., 2014, vol. 48, no. 5, pp. 594–607.
Fliess, M., Lévine, J., Martin, Ph., and Rouchon, P., A Lie–Bäcklund approach to equivalence and flatness of nonlinear systems, IEEE Trans. Automat. Control, 1999, vol. 44, no. 5, pp. 922–937.
Wald, S. and Zeitz, M., Flat inputs in the MIMO case, IFAC Proc. Volumes, 2010, vol. 43, no. 14, pp. 695–700.
Kalitkin, N.N., Chislennye metody (Numerical Methods), Moscow: Nauka, 1978.
Mboup, M., Join, C., and Fliess, M., A revised look at numerical differentiation with an application to nonlinear feedback control, in Proc. of the 15th IEEE Mediterranean Conf. on Control and Automation. Athens, 2007, pp. 1–6.
Mboup, M., Join, C., and Fliess, M., Numerical differentiation with annihilators in noisy environment, Numer. Algorithms, 2009, vol. 50, no. 4, pp. 439–467.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.N. Chetverikov, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 11, pp. 1547–1556.
Rights and permissions
About this article
Cite this article
Chetverikov, V.N. Construction of Invertible Input-Output Mappings and Parameter Identification. Diff Equat 54, 1524–1534 (2018). https://doi.org/10.1134/S0012266118110137
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266118110137