Data-Driven Model-Free Adaptive Control with Prescribed Performance: a rigorous Sliding-Mode based approach

Abstract

In this paper, the data-driven control approach known as Model-Free Adaptive Control technique is applied to the control of a class of general discrete-time Single-Input Single-Output nonlinear systems, making use of model obtained adopting a dynamic linearization technique based on pseudo-partial derivatives. The present study is inspired by the very recent paper [Liu and Yang, 2019], where a data-driven adaptive sliding mode controller has been proposed able to account also for prescribed performance constraints. In particular, a rigorous stability analysis is here proposed, achieved modifying the forms of the sliding surface and of the control law but still retaining the main setup presented in the source paper. The careful analysis of the closed loop system here provided is shown to lead to the definition of suitable constraints on the gain of the sliding-mode based control term. A comparative study, by simulation, is also provided, performed using a test taken from the literature. Results show a remarkable improvement of control accuracy.