Construction of Neural Network Based Lyapunov Functions

A straightforward method for the construction of Lyapunov functions represented by neural networks is presented in this paper. The resulting neural networks are Lyapunov functions on the basis of which asymptotic stability or instability of a nonlinear system´s equilibrium point can be mathematically proven. One of the main advantages of this method is that it works for any nonlinear system even when the number of state variables is large. Several different Lyapunov functions can be constructed for each system, including Lyapunov functions of quadratic form. This enables us to select the most appropriate function for a given problem.