In this paper, we are dealing with the problem of directly regulating unknown multivariable
affine in the control nonlinear systems and its robustness analysis. The method
employs a new Neuro-Fuzzy Dynamical System definition, which uses the concept of
Fuzzy Systems (FS) operating in conjunction with High Order Neural Networks. In this
way the unknown plant is modeled by a fuzzy - recurrent high order neural network
structure (F-RHONN), which is of the known structure considering the neglected nonlinearities.
The development is combined with a sensitivity analysis of the closed loop
in the presence of modeling imperfections and provides a comprehensive and rigorous
analysis showing that our adaptive regulator can guarantee the convergence of states to
zero or at least uniform ultimate boundedness of all signals in the closed loop when a
not-necessarily-known modeling error is applied. The existence and boundedness of the
control signal is always assured by employing a method of parameter “Hopping” and
“Modified Hopping”, which appears in the weight updating laws. Simulations illustrate
the potency of the method showing that by following the proposed procedure one can obtain
asymptotic regulation despite the presence of modeling errors. Comparisons are also
made to simple recurrent high order neural network (RHONN) controllers, showing that
our approach is superior to the case of simple RHONN’s.
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