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A Model‐Free Stability‐Based Adaptive Control Method for Unknown Nonlinear Systems
Author(s) -
Shen Xi,
Söffker Dirk
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310228
Subject(s) - control theory (sociology) , inverted pendulum , nonlinear system , computer science , artificial neural network , interval (graph theory) , stability (learning theory) , controller (irrigation) , quadratic equation , set (abstract data type) , adaptive control , control (management) , mathematical optimization , mathematics , artificial intelligence , machine learning , physics , geometry , quantum mechanics , combinatorics , agronomy , biology , programming language
This contribution considers an adaptive control method based on a cognition‐based framework to stabilize unknown nonlinear systems online. This method requires only the system outputs, which are assumed as measurable. The structure of the framework consists of three parts. The first part is based on a dynamic recurrent neural network (DRNN) to be used for local identification, analysis and multi‐step‐ahead prediction of the system. In the second part, a set of given input values will be calculated numerically with a geometrical criterion based on a suitable definition of quadratic stability. In the third part, the most suitable control input value is chosen for the next predefined time interval according to a suitable cost function. The proposed controller is able to gain useful local knowledge and define autonomously suitable local control input according to the stability criterion. Numerical examples using inverted pendulum system and Lorenz system are shown to demonstrate the successful application and performance of the method. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)