Tracking control of uncertain third order jerk equation Genesio-Tesi using adaptive backstepping

Abstract

This article presents the uncertain Genesio-Tesi, a third-order Jerk equation in the form of an ordinary differential equation, with the potential to exhibit chaos under certain conditions. The main focus of this article is to design a control function for the uncertain Genesio-Tesi, which has uncertain parameters with unknown values. The adaptive backstepping method designs the control function, demonstrating its ability to stabilize the system output towards a given trajectory using Lyapunov stability. To test the robustness of the proposed control method, simulations were conducted with various scenarios, including disturbances to the steady-state system. Simulation results show that the controller successfully drove the system output along a desired trajectory, whether constant or a function, and maintained system stability even with significant disturbances.