Abstract
A numerical-analytical algorithm for designing nonlinear stabilizing regulators for the class of nonlinear discrete-time control systems is proposed that significantly reduces computational costs. The resulting regulator is suboptimal with respect to the constructed quadratic functional with state-dependent coefficients. The conditions for the stability of the closed-loop system are established, and a stability result is stated. Numerical results are presented showing that the nonlinear regulator designed is superior to the linear one with respect to both nonlinear and standard time-invariant cost functionals. An example demonstrates that the closed-loop system is uniformly asymptotically stable.
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References
S. V. Emel’yanov and S. K. Korovin, New Types of Feedback: Control under Uncertainty (Nauka, Moscow, 1997) [in Russian].
V. N. Afanas’ev, Control of Uncertain Dynamic Systems (Fizmatlit, Moscow, 2008) [in Russian].
I. Chang and J. Bentsman, “Constrained discrete-time state-dependent Riccati equation technique: A model predictive control approach,” The 52nd IEEE Conference on Decision and Control, December 10–13, 2013, Florence (2013), pp. 5125–5130.
A. S. Dutka, A. W. Ordys, and M. J. Grimble, “Optimized discrete-time state dependent Riccati equation regulator,” Proceedings of the American Control Conference (ACC 2005) (Baltimore, MD, 2005), pp. 2293–2298.
Y. Zhang, D. S. Naidu, C. X. Cai, and Y. Zou, Int. J. Syst. Sci. (2015); http://dxdoiorg/10.1080/00207721.2015.1006710.
M. G. Dmitriev and D. A. Makarov, Tr. Inst. Sist. Anal. Ross. Akad. Nauk 64 4, 53–58 (2014).
G. V. Demidenko, Matrix Equations (Novosib. Gos. Univ., Novosibirsk, 2009) [in Russian].
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Original Russian Text © S.V. Emel’yanov, Yu.E. Danik, M.G. Dmitriev, D.A. Makarov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 466, No. 3, pp. 282–284.
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Emel’yanov, S.V., Danik, Y.E., Dmitriev, M.G. et al. Stabilization of nonlinear discrete-time dynamic control systems with a parameter and state-dependent coefficients. Dokl. Math. 93, 121–123 (2016). https://doi.org/10.1134/S1064562416010142
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DOI: https://doi.org/10.1134/S1064562416010142