Projective Synchronization for Uncertain Fractional Reaction-Diffusion Systems via Adaptive Sliding Mode Control Based on Finite-Time Scheme

In this chapter, the projective synchronization of uncertain fractional-order reaction-diffusion systems is studied for the first time via the fractional adaptive sliding mode control method. The approach involves designing a fractional-order integral type switching function and deriving adaptive sliding mode control laws that facilitate the reachability of the fractional-order sliding mode surface within a finite-time interval. Additionally, an enhanced version of these control laws, characterized by reduced oscillations and improved control performance, is presented. A new lemma is developed to demonstrate the finite-time reachability of the fractional-order sliding mode surface, and numerical examples are included to validate the efficacy of these theoretical developments.