Yu. E. Danik Stabilizing Regulator for Nonlinear Systems Based on Fuzzy Matrix Padé Approximation
Yu. E. Danik Stabilizing Regulator for Nonlinear Systems Based on Fuzzy Matrix Padé Approximation

In this paper an approach for the construction of a stabilizing regulator for a nonlinear control system based on an approximate solution of the state dependent Riccati equation (SDRE) and the use of a fuzzy matrix Padé approximation is proposed. A fuzzy matrix Padé approximation of order[3/3] is constructed on the basis of fuzzy singleton membership functions. Numerical experiments where the constructed regulator is compared with the SDRE regulator are presented.


fuzzy matrix Padé approximation, Riccati equation, parameter, nonlinear control systems, fuzzy singleton membership function.

PP. 42-49.

DOI 10.14357/20718632210105

1. Baker, G.A., Graves-Morris, P. 1986. Approksimacii Pade: Osnovy teorii. Obobshhenija i prilozhenija [Pade approximation: Foundations of the theory. Generalizations and applications]. Moscow: Mir, 1986.
2. Berdyshev, V.I., Subbotin, Yu.N. 1979. Chislennye metody priblizhenija funkcij [Numerical methods for approximating functions]. Sverdlovsk: Middle Ural Book Publishing House, 1979. 119 p. (in Russian).
3. Belyaeva N.P., Dmitriev M.G., Komarova E.V. Pade-Approximation as a "Bridge" Between Two Parametric Boundary Asymptotics // IFAC Proceedings Volumes. 2001. № 6. С. 605-609.
4. Danik Yu., Dmitriev M. The construction of stabilizing regulators sets for nonlinear control systems with the help of Padé approximations // Nonlinear Dynamics of Discrete and Continuous Systems. Springer International. 2021. P. 45-62. DOI: 10.1007/978-3-030-53006-8
5. Abedinnasab M.H., Yoon Y.J., Saeedi-Hosseiny M.S. High performance fuzzy-Padé controllers: introduction and comparison to fuzzy controllers // Nonlinear Dynam-ics. 2013. №. 1-2. P. 141-157.
6. Fujita K., Mizumoto M. Fuzzy controls of parallel inverted-pendulum under fuzzy singleton-type reasoning method using genetic algorithm // Proc. 11th Fuzzy System Symp. 1995. P. 267–292.
7. Zhang S.Y. et al. A new fuzzy controller for stabilization of double inverted pendulum system // 2010 International Conference on Computer and Communication Technolo-gies in Agriculture Engineering. IEEE. 2010. P. 300-303.
8. Yi J., Yubazaki N., Hirota K. A new fuzzy controller for stabilization of parallel-type double inverted pendulum system // Fuzzy Sets and Systems. 2002. №. 1. P. 105-119.
9. Abdollahi T. et al. Simplified fuzzy-Padé controller for attitude control of quadrotor helicopters // IET Control Theory & Applications. 2017. №. 2. P. 310-317.
10. Danik Yu.E., Dmitriev M.G. Construction of Parametric Regulators for Nonlinear Control Systems Based on the Pade Approximations of the Matrix Riccati Equation Solu-tion // IFAC-PapersOnLine. 2018. Issue 32. P. 815-820. DOI: 10.1016/j.ifacol.2018.11.445.

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