Lyapunov-based intelligent control

Abstract

Nonlinear dynamical systems play a crucial role in control systems because, in practice, linear models could not be suitable for effective projects. However, achieving control for nonlinear systems is not simple though many methods have been developed. There are still some problems that need to be solved. Examples of some problems are robust control balance in humanoid robots and the modeling 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 investigated the capability of a neural network to compute Lyapunov functions and provide a deep neural network to compute a control Lyapunov function without linear approximation for nonlinear systems. Moreover, we examined the equilibrium point stability and obtained an estimation of its region of attraction contained in the Lyapunov invariant set. Numerical examples and experimental simulations using some nonlinear systems, such as the inverted pendulum and the rotary inverted pendulum, are performed and compared with some conventional control techniques.