Optimal control of a particular class of singularly perturbed nonlinear discrete-time systems

Abstract

This note studies a class of discrete-time nonlinear systems which depend on a small parameter. Using the singular perturbation theory in a systematic way, we give a trajectory approximation result based on the decomposition of the model into reduced and boundary layer models. This decomposition is used to analyze optimal control via maximum principle of such systems. As a result, significant order reduction of optimal control problems is achieved.

Nonlinear Model Predictive Control for regulation of a class of Nonlinear Singularly Perturbed discrete-time systems

“…holds only on an interval excluding 0, for k ∈ {k 1 , k 1 + 1, · · ·} [14], where k 1 > 0. Thus, according to [1], [2], [14], it is said that system (1) is the singularly perturbed form and the boundary layer occurs at k = 0.…”

“…Thus, according to [1], [2], [14], it is said that system (1) is the singularly perturbed form and the boundary layer occurs at k = 0.…”

“…To investigate this initial value problem, we introduce the discrete boundary layer method from [1], [14] which assumes that the variables x and y can be written in the form of a ε-power series as…”

“…Compared with the continuous-time NSPSs, there are just a few results [13], [14], [15], [16] on discrete-time NSPSs. In [13], the authors have studied a class of nonlinear singularly perturbed discrete systems, proposed the trajectory approximation result based on the decomposition of the original system and developed a stabilizing feedback controller design method.…”

“…In [13], the authors have studied a class of nonlinear singularly perturbed discrete systems, proposed the trajectory approximation result based on the decomposition of the original system and developed a stabilizing feedback controller design method. In [14], composite optimal controller is designed based on the results from [13]. In [15], stability of nonstandard discretetime NSPSs is analyzed based on the decomposition into two standard NSPSs.…”