Geodesic
An algorithm for constructing regulators for nonlinear systems with the formal small parameter
Informacionnye tehnologii i vyčislitelnye sistemy, no. 4 (2015), pp. 35-44.

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In this paper the problem of designing a stabilizing nonlinear controller for discrete and continuous time nonlinear control systems is considered. The method based on the formal Riccati equation with state-dependent coefficients (SDRE) is used for the construction of a nonlinear stabilizing regulator. Several numerical experiments were carried out to demonstrate the effectiveness of the proposed nonlinear regulator in comparison with the corresponding linear regulator.
Keywords: nonlinear discrete and continuous time systems, nonlinear stabilizing regulator, criteria construction, riccati equations with state-dependent coefficients, inverted pendulum model. 
@article{ITVS_2015_4_a4,
     author = {Y. E. Danik and M. G. Dmitriev and D. A. Makarov},
     title = {An algorithm for constructing regulators for nonlinear systems with the formal small parameter},
     journal = {Informacionnye tehnologii i vy\v{c}islitelnye sistemy},
     pages = {35--44},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ITVS_2015_4_a4/}
}
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Y. E. Danik; M. G. Dmitriev; D. A. Makarov. An algorithm for constructing regulators for nonlinear systems with the formal small parameter. Informacionnye tehnologii i vyčislitelnye sistemy, no. 4 (2015), pp. 35-44. http://geodesic.mathdoc.fr/item/ITVS_2015_4_a4/