Prescribed-time synchronization of hyperchaotic fuzzy stochastic PMSM model with an application to secure communications

This study addresses the synchronization problem of grid-connected permanent magnet synchronous motors (PMSMs)-based wind energy conversion systems (WECSs). This study significantly enhances the existing WECSs into the four-dimensional hyperchaotic grid-connected WECSs by integrating the impact of a DC-link capacitor. Moreover, this study treats the aerodynamics of WECSs as stochastic differential equations (SDEs), taking into account the random nature of wind-speed characteristics. Further, the nonlinearities in WECSs are approximated to linear form through Takagi-Sugeno (T–S) fuzzy with the help of IF-THEN membership rules. Each IF-THEN membership rule represents a local linear model valid around specific operating bounds. Moreover, this study considers an adaptive continuous feedback controller scheme to ensure the fixed-time synchronization between WECSs with and without control input. This study utilizes mathematical techniques such as Lyapunov stability theory and Ito's calculus theory to derive the analytical settling-time (ST) expression. This expression aids in identifying the time frame that ensures the convergence of the error model. As an application, this study designs an encryption and decryption algorithm by utilizing the hyperchaotic WECSs as a cryptosystem that may outperform the existing algorithms proposed for secure communications.