Approximate Output Regulation of Spherical Inverted Pendulum by Neural Network Control

Recently, the output regulation problem of the spherical inverted pendulum was studied in [8]. It is known that the solvability of the output regulation problem depends on the solvability of the regulator equations which are a set of nonlinear partial differential equations. Since the exact solution of the regulator equations associated with the spherical inverted pendulum is not available due to the complexity of the equations, the paper [8] tried a polynomial approximation of the regulator equations. In this paper, we first show that the regulator equations associated with the spherical inverted pendulum exist and then propose a neural network approach to obtain an approximate solution to the output regulation problem of the spherical inverted pendulum. We also make some comparison with the method in [8] and show that, the neural network controller leads to a much better tracking performance for larger exogenous signals.