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Stable control of nonlinear systems using neural networks
Author(s) -
TzirkelHancock E.,
Fallside F.
Publication year - 1992
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4590020105
Subject(s) - control theory (sociology) , controller (irrigation) , artificial neural network , tracking error , linearization , convergence (economics) , nonlinear system , stability (learning theory) , computer science , range (aeronautics) , feedback linearization , exponential stability , approximation error , control engineering , control (management) , engineering , artificial intelligence , algorithm , machine learning , physics , quantum mechanics , aerospace engineering , agronomy , economics , biology , economic growth
A neural‐network‐based direct control architecture is presented that achieves output tracking for a class of continuous‐time nonlinear plants, for which the nonlinearities are unknown. The controller employs neural networks to perform approximate input/output plant linearization. The network parameters are adapted according to a stability principle. The architecture is based on a modification of a method previously proposed by the authors, where the modification comprises adding a sliding control term to the controller. This modification serves two purposes: first, as suggested by Sanner and Slotine, 1 sliding control compensates for plant uncertainties outside the state region where the networks are used, thus providing global stability; second, the sliding control compensates for inherent network approximation errors, hence improving tracking performance. A complete stability and tracking error convergence proof is given and the setting of the controller parameters is discussed. It is demonstrated that as a result of using sliding control, better use of the network's approximation ability can be achieved, and the asymptotic tracking error can be made dependent only on inherent network approximation errors and the frequency range of unmodelled dynamical modes. Two simulations are provided to demonstrate the features of the control method.