Synchronization and energy consumption estimation for fractional-order chaotic systems by unified model within finite-time

Abstract

Due to the inherent sensitivity of the system output of fractional-order chaotic systems (FOCS) to initial state values, synchronization of FOCS has become a hot topic. The finite-time synchronization (FTS) for a unified model of FOCS is studied and the upper limit of its energy consumption is estimated in this paper. First, based on the integer-order unified model of chaotic systems, a unified model of FOCS is proposed. Second, the method of transforming the dynamic model of fractional Chen systems, Rosser systems, and Hopfield systems into the unified model of FOCS is given. In addition, to achieve FTS under unknown system parameters, a suitable adaptive feedback controller is designed by the properties of fractional calculus. This controller not only reduces the uncertainty of the system but also achieves synchronization within a limited time. Subsequently, based on energy theory, the upper limit of the energy consumed by the controller to achieve synchronization is obtained, which contributes to evaluating the working-time of the controller. Finally, the obtained results are validated through two practical examples.