Stability analysis using higher order derivatives of universal learning networks

Stability is one of the most important subjects in the control performance. As for the stability analysis of nonlinear systems in the past, Lyapunov method and linear stability methods based on linear approximation of nonlinear systems have been used. But, in many cases when Lyapunov method is applied, it is difficult to find suitable Lyapunov functions. And when using linear approximation, it can not be decided whether nonlinear systems are stable or not on the outside of the region where linear stability theory can be applied. Therefore, a new stability analysis method is required to develop, which can be easily applied to nonlinear systems. In this paper, stability analysis based on the higher order derivatives of Universal Learning Networks (ULNs) and its application to nonlinear systems are discussed. The stability analysis using ULNs is studied by the deviation of the system dynamics. The deviation of the system dynamics can be calculated by the higher order derivatives of ULNs. In this paper, simulations of an inverted pendulum balancing system are carried out. From the results of the simulations, it is shown that the inverted pendulum can be controlled effectively by ULNs. In addition, it is clarified that the stability of the nonlinear systems is easily analyzed by using the stability analysis of ULNs.