Control of Lorenz system with a novel fractional controller: A Caputo´s differintegration based approach

We address the problem of chaos suppression in Lorenz system with a novel fractional-order controller. Our approach relies on Caputo´s differintegration. Indeed, we introduce a new concept of sliding mode control based on Caputo´s definition of fractional derivative. Accordingly, a novel nonlinear fractional-order sliding surface is designed. Then an appropriate control law is established on the surface. Stability of the closed-loop system is presented via rigorous analyses by means of Lyapunov direct method. An adaptation law is derived for the switching gain which allows us to ensure the stability of control system without necessity of knowing the upper bounds of uncertainties and disturbances. The proposed method is also verified by numerical simulations and is compared with conventional sliding mode control. It is shown that the proposed control algorithm outperforms conventional sliding mode by providing higher performance and smaller control input. The controller provides fulfilling performance, high robustness and chattering free control effort.