An adaptive observer design approach for discrete-time nonlinear systems

TL;DR

This paper presents a novel adaptive observer design for discrete-time nonlinear systems by transforming them into a T-S form and employing Lyapunov methods for joint state and parameter estimation.

Contribution

It introduces a new discrete-time adaptive observer framework for nonlinear systems with unmeasured premise variables, extending continuous-time strategies.

Findings

Error bounded by $\\mathbb{L}_2$ gain

Applicable to systems with unmeasured premise variables

Transforms nonlinear systems into T-S form for observer design

Abstract

We discuss a design approach for nonlinear discrete-time adaptive observer. This involves transforming a nonlinear system into a quasi-LPV (Linear Parameter Varying) polytopic model in Takagi-Sugeno (T-S) form using nonlinear embedding and sector nonlinearity (SNL) transformation. We then develop a discrete-time counterpart for a joint state and parameter estimation, based on design strategies developed for continuous time models in the existing literature. The design uses a Lyapunov approach and provides an error bounded by $\mathbb{L}_2$ gain. Based on this strategy, we propose a design for adaptive observers for nonlinear systems whose T-S form can have unmeasured premise variables.