Approximate discrete-time output regulation of spherical inverted pendulum by neural network control

The approximate continuous-time output regulation problem of the spherical inverted pendulum has been well addressed in recent years. Because most of the nonlinear control laws are implemented as digital controllers, this paper further studies the approximate discrete-time output regulation problem of the spherical inverted pendulum by neural network control. The solvability of the discrete-time output regulation problem relies on the solvability of the discrete regulator equations. However, the exact solution of the discrete regulator equations is not available due to the complexity of the equations. In this paper, we first show the solution of the discrete regulator equations associated with the spherical inverted pendulum exists and then use the neural network approximation method to solve the discrete-time output regulation problem. Finally, we compare our method with polynomial approximation method.