Position control of spherical inverted pendulum via improved discrete-time neural network approach

Much recently, a discrete-time neural network (NN) approach from the output regulation theory was adopted to solve the position tracking problem of the spherical inverted pendulum (SIP) system. The key of this approach is to find the approximate solution of the corresponding discrete regulator equations (DREs) of the SIP system, which are composed of 10 nonlinear algebraic functional equations. However, the procedure for calculating the approximate solution of the DREs is quite tedious and is dependent on the system parameters. In this paper, an improved discrete-time NN control algorithm is proposed, which relies on the NN approximation of the feedforward function. Since the feedforward function is two-dimensional, the improved NN approach is much simpler compared with the existing NN approach. Moreover, a distinct advantage of our approach is that it allows certain robustness to the system parameters when every state is available. Simulation results demonstrate that our approach leads to much smaller tracking errors than the existing NN approach