Trade-off analysis between finite-time synchronization and energy consumption for fractional-order two-layer neural networks

This paper investigates the finite-time synchronization (FTS) of fractional-order two-layer neural networks with time delays and explores the energy consumption of their controllers, as well as the trade-off between the synchronization time cost and the controller energy consumption. The study makes the following key contributions: First, a sufficient criterion is derived to guarantee the FTS of fractional-order delayed complex networks by using a lemma based on fractional-order differential inequalities. This approach circumvents a potential methodological flaw present in some prior studies. Additionally, while existing research on FTS has primarily focused on fractional-order complex networks without time delays, this work extends the analysis to systems with time delays, thereby broadening the applicability of the results. Second, a switching controller is proposed to accelerate the synchronization of the error system. Third, a standardized evaluation function is introduced to analyze the trade-off between the FTS time cost and controller energy consumption in fractional-order systems, whereas previous research in this area has mostly focused on integer-order systems. Finally, the validity of the theoretical results is demonstrated through numerical simulations.