Adaptive Synchronization of a Fractional-Order Complex T System With a Random Parameter

In this paper, the adaptive synchronization of a fractional-order complex T system with a random parameter is analyzed. Firstly, the Laguerre polynomial approximation method is applied to investigate the fractional-order system with a random parameter which obeys an exponential distribution. Based on this method, the stochastic system is reduced into the equivalent deterministic one. The improved Adams-Bashforth-Moulton algorithm with the predictor-correctors scheme is used to solve the approximately deterministic system numerically. Based on the stability theory of fractional-order systems, the synchronization for the deterministic system with unknown parameters is realized by designing appropriate synchronization controllers and estimation law for uncertain parameters. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.