Intermittent boundary control for robust fixed‐time stabilization of uncertain reaction‐diffusion systems

Abstract

Achieving the robust fixed‐time stabilization (FxTS) of uncertain reaction‐diffusion systems (RDSs) utilizing intermittent boundary control is a valuable and unresolved problem. This paper simultaneously considers the influence of the uncertainty of non‐diffusion and diffusion coefficients on RDSs and provides an effective solution for the treatment of the uncertainty of diffusion coefficient in the investigation of FxTS. Then, a fixed‐time control scheme is presented to stabilize uncertain RDSs within a fixed time, which incorporates the merits of intermittent and boundary control and reduces control costs in both the spatial and temporal domains. Besides, some sufficient conditions in the form of linear matrix inequalities are deduced to guarantee the robust FxTS of uncertain RDSs with Neumann and mixed boundary conditions, respectively, which contain and generalize some existing results. Finally, the validity of the intermittent boundary control scheme and the FxTS criteria developed in this paper are verified by numerical simulations.