An intelligent construction of control lyapunov function

Abstract

Lyapunov stability theorem has made an important contribution in the world of control engineering. The Lyapunov theory provides a connection between the presence of a control Lyapunov function and the stability of a control system. This research presents a novel approach to construct control Lyapunov function named Intelligent Control Lyapunov Function (ICLF) to test the stability of single input single output (SISO) nonlinear dynamic system using Artificial Neural Network (ANN). The proposed approach is considered the error signal in SISO nonlinear dynamic system as an input signal to Intelligent Control Lyapunov Function (ANN model) to determine the stability of the control system by training the ANN model using target signal. However, the proposed target function is satisfied the stability conditions of second method of the Lyapunov stability theory [Control Lyapunov Function V(x)]. The novel trained model (ICLF) shows the unique characteristics of Artificial Neural Networks in adapting itself to nonlinear dynamic system changes. The Intelligent Control Lyapunov Function has proven that the existence of smooth uniform control Lyapunov function is a condition for satisfying the robustness and stability of a nonlinear dynamic system.