Chaos Control of Lorenz Model via Direct Gradient Descent Control

Abstract

This paper is concerned with controlling chaos. Lorenz model, a well known chaotic system, is picked up as a controlled plant in which manipulated variables are additive control inputs. For a controlling technique, we apply a method called the direct gradient descent control(DGDC), which is a dynamic state feedback controller for general nonlinear systems. DGDC manipulates control inputs directly so as to decrease a performance function like the squared error, based on the gradients of the performance function and the steepest descent method. Several simulation results demonstrate the usefulness of the proposed method for the Lorenz chaotic system.