Nonlinear Identification of Triple Inverted Pendulum Based on GA-RBF-ARX

The triple inverted pendulum is a nonlinear, unsteady and dynamic system. The traditional model is built based on mathematical modeling method which has ignored many important factors in reality. In this paper, the GA-RBF-ARX is proposed to identify a nonlinear triple inverted pendulum model based on its input/ output data. RBF-ARX model is a combination of Gaussian radial basis function (RBF) neural network and Autoregressive model with exogenous input (ARX) model. It not only has the advantages of RBF neural network, such as the approximation ability, simple structure and quickly learning rate, but also has the ability of describing globally of ARX model. The structured nonlinear parameter optimization method (SNPOM) is generally used to optimize parameters of the RBF-ARX model. However, SNPOM needs to classify the parameters before optimization. It is too complex to popularize and apply in practical engineering. Due to this problem, genetic algorithm (GA) is proposed to replace SNPOM. The identification process based on GA is simpler than SNPOM. Besides, GA has good parallel design structure and characteristics of global optimization. Finally, the MATLAB simulation results show that GA-RBF-ARX identification is effective.