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.
Bokovoy A. V., Yakovlev K. S. Stabilization of nonlinear discrete dynamic systems with a parameter and with state-dependent coefficients // Proceedings of the conference IEEE Intelligent Systems IS'16. - Sofia, Bulgaria, ss. 160-166. 2016