Lyapunov-based Intelligent Control
Neural networks; Intelligent control: Neuro-control; Control Lyapunov function.
Nonlinear dynamical systems play a crucial role in control systems because, in practice, all the plants are nonlinear. However, achieving control for nonlinear systems is not simple though many methods have been developed. There are still some problems to be improved, as robust control balance in humanoid robots and the modelling inaccuracies of the autonomous underwater vehicle, which has a small-pitch-angle. Usually, a Lyapunov function is used to perform a control and stability analysis of a nonlinear system. The procedure for obtaining a Lyapunov function is not a simple task. There have been many efforts and numerical methods in the literature on how to estimate Lyapunov functions for several kinds of systems. An artificial neural network is a useful tool for generating functions. Motivated by this, we explore the capability of a neural network to compute Lyapunov functions and provide a deep neural network to compute a control Lyapunov function without any linear approximation for nonlinear systems. Moreover, we are interested in checking the equilibrium point stability and obtaining an estimation of its region of attraction contained in the set.