An improved discrete-time neural network controller design for spherical inverted pendulum position tracking system

Much recently, a tracking problem of spherical inverted pendulum system with multi-input, multi-output nature has been formulated as an approximate discrete-time nonlinear output regulation problem and well addressed by discrete-time neural network approach. The key of this approach is to find the approximate solution of the discrete regulator equations associated with the spherical inverted pendulum system, which are governed by ten nonlinear algebraic functional equations. However, it is quite tedious to obtain the approximate solution of the discrete regulator equations. In this paper, an improved discrete-time neural network controller is proposed, which is based on the neural network approximation of the feedforward function without solving the discrete regulator equations approximately. Since the dimension of the feedforward function is only equal to two, this new scheme is much simpler than the existing neural network approach. Simulation results are given to verify the effectiveness of our design.