A Fractional Atmospheric Circulation System under the Influence of a Sliding Mode Controller

Abstract

The earth’s surface is heated by the large-scale movement of air known as atmospheric circulation, which works in conjunction with ocean circulation. More than ${10}^5$ variables are involved in the complexity of the weather system. In this work, we analyze the dynamical behavior and chaos control of an atmospheric circulation model known as the Hadley circulation model, in the frame of Caputo and Caputo–Fabrizio fractional derivatives. The fundamental novelty of this paper is the application of the Caputo derivative with equal dimensionality to models that includes memory. A sliding mode controller (SMC) is developed to control chaos in this fractional-order atmospheric circulation system with uncertain dynamics. The proposed controller is applied to both commensurate and non-commensurate fractional-order systems. To demonstrate the intricacy of the models, we plot some graphs of various fractional orders with appropriate parameter values. We have observed the influence of thermal forcing on the dynamics of the system. The outcome of the analytical exercises is validated using numerical simulations.