New results on finite-time synchronisation of fractional-order fuzzy reaction-diffusion gene regulatory networks with time-varying delays: an adaptive boundary control approach

Under the influence of reaction-diffusion, fuzzy logic (fuzzy MIN and MAX feedback templates), and time-varying delays, the synchronisation problem for fractional-order gene regulatory networks is addressed in this article. First, novel adaptive boundary controllers are developed under Neumann boundary conditions, which can effectively reduce control costs using dynamic control gains and actuators installed at the boundary of the spatial domain. Then, through the designed adaptive boundary controllers, new sufficient criteria based on linear matrix inequality (LMI) are obtained to guarantee both asymptotic and finite-time stability of the error dynamic system by using the direct Lyapunov approach and inequality techniques, which ensure that the drive system is synchronised with the response system. Lastly, a simulation example illustrates the effectiveness of designed adaptive boundary control protocols.