Adaptive set-point regulation of discrete-time nonlinear systems

TL;DR

This paper introduces an indirect adaptive control method for discrete-time nonlinear systems with parametric uncertainties, which does not rely on Lyapunov functions and uses excitation signals for parameter estimation.

Contribution

It presents a novel adaptive set-point regulation controller that calculates control inputs directly, expanding the design approach without Lyapunov functions.

Findings

Successfully regulates systems with parametric uncertainties

Uses excitation signals for parameter estimation

Does not require Lyapunov functions in controller design

Abstract

In this paper, adaptive set-point regulation controllers for discrete-time nonlinear systems are constructed. The system to be controlled is assumed to have a parametric uncertainty, and an excitation signal is used in order to obtain the parameter estimate. The proposed controller belongs to the category of indirect adaptive controllers, and its construction is based on the policy of calculating the control input rather than that of obtaining a control law. The proposed method solves the adaptive set-point regulation problem under the (possibly minimal) assumption that the target state is reachable provided that the parameter is known. Additional feature of the proposed method is that Lyapunov-like functions have not been used in the construction of the controllers.