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.
DOI: https://link.springer.com/article/10.1134/S1064562416010142
Danik Yu. E., Dmitriev M. G., Makarov D. A., Yemelyanov S. V. Stabilization of nonlinear discrete-time dynamic control systems with a parameter and state-dependent coefficients // Reports of the Academy of Sciences. Vol. 466. No. 3. P. 282–284. 2016