For a class of uncertain pure-feedback nonlinear dynamical systems

an adaptive neural control method using the extreme learning machine (ELM) is presented on the basis of mean value theorem and Backstepping control. As a kind of single-hidden layer feed forward networks (SLFNs)

ELM

which randomly chooses hidden node parameters and analytically determines the output weights

shows good generalized performance at extremely fast learning speed. In the process of each step for the Backstepping controller design

the ELM network is used to approximate unknown nonlinear part of the subsystem. Meanwhile

the adaptive adjustment law of weights parameter by Lyapunov stability analysis is derived so that the semiglobal uniform ultimate boundedness of all signals in the closed-loop nonlinear system can be guaranteed and the output of the system can also converge to a small neighborhood of the desired trajectory. The employed control method is then applied to the instance of continuous stirred tank reactor (CSTR) system in the chemical process and the simulation results are presented to verify the effectiveness of the method.