Open AccessDiscrete-Time Feedback Error Learning and Nonlinear Adaptive Controller
Author(s) -
Sirisak Wongsura,
Waree Kongprawech,
members
Publication year - 2007
Publication title -
ecti transactions on electrical eng. / electronics and communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.148
H-Index - 7
ISSN - 1685-9545
DOI - 10.37936/ecti-eec.200862.171769
Subject(s) - control theory (sociology) , feedback linearization , nonlinear system , adaptive control , tracking error , controller (irrigation) , discrete time and continuous time , stability (learning theory) , linearization , mathematics , lyapunov function , exponential stability , lyapunov stability , computer science , control (management) , artificial intelligence , statistics , physics , quantum mechanics , machine learning , agronomy , biology
In this study, the technique of Discrete-Time Feedback Error Learning (DTFEL) is investigated from the viewpoint of adaptive control. First, the relationship between DTFEL and nonlinear discrete-time adaptive control with adaptive feedback linearization is discussed. It shows that DTFEL can be interpreted as a form of nonlinear adaptive control. Second, Lyapunov analysis of the controlled system is presented. It suggests that the condition of strictly positive realness (s.p.r.) associated with the tracking error dynamics is a sufficient condition for asymptotic stability of the closed-loop dynamics. Specifically, for a class of second order SISO systems, it is shown that the control problems is reduced to select the feedback gain that satisfies the s.p.r. Finally, numerical simulations is presented to illustrate the stability properties of DTFEL obtained from mathematical analysis.