Almost Finite-time Synchronization of Coronary Artery Systems via Adaptive Fractional-powered-integral-type Sliding Mode Control Method

Abstract

From the cardiac medical viewpoint, the treatment for a vasospasm caused by the diseased coronary artery system (CAS) is to synchronize the dynamic behavior of a diseased CAS with that of a healthy CAS such that the physiological change of the CAS is improved. In this study, for the bio-mathematical model of CAS, the novel fractional-powered-integral-type finite-timeconvergent sliding mode (FFSM), which is consisted of the fractional powered and the integral terms of the state variables, is introduced. The adaptive sliding mode control method based on the defined FFSM is proposed for achieving the almost finite-time synchronization between two CASs. Once the developed control is in action, the special type of stability is exhibited. That is, the two error states are stabilized in the sequel on the sliding surface, which induces the almost finite-time stability owing to the property of the model for CAS. The adaptive FFSM control scheme, which includes three online updated gains with the rules of adaption, can counter the nonlinear dynamical effects of the synchronized error system. Numerical experiments are executed to show the validation of the present scheme.