2,312 publications from this institution
In this paper we present a systematic study of shadowing properties with average error in tracing such as (asymptotic) average shadowing, $\underline{d}$-shadowing, $\overline{d}$-shadowing and almost specification. As the main tools we provide a few equivalent characterizations of the average shadowing property, which also partly apply to other notions of shadowing. We prove that almost specification on the whole space induces this property on the measure center. Next, we show that always (e.g. without assumption that the map is onto) almost specification implies asymptotic average shadowing, which in turn implies the average shadowing property and consequently also $\underline{d}$-shadowing and $\overline{d}$-shadowing. Finally, we study connections among sensitivity, transitivity, equicontinuity and (average) shadowing.
The improved fuzzy controller designed is based on an existing fuzzy PI controller, which can control an uncertain flexible-joint robot arm to produce satisfactory tracking results. The improved fuzzy PI controller not only can control (stable and unstable) conventional linear systems, performing as well as the conventional PI controller, but also is capable of controlling many nonlinear systems such as the flexible-joint robot arm under investigation which contains uncertainties within ten percent tolerance of all the nominal system-parameter values. In this improved fuzzy PI controller, we used only three simple membership functions plus six simple fuzzy logic control rules. In this paper, we briefly describe the design principle of this improved fuzzy PI controller and its tracking performance in handling the nonlinearity, flexibilities and uncertainties of the flexible-joint robot arm system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
