Fixed‐time event‐dependent intermittent control for reaction‐diffusion systems

Abstract

AbstractThis article discusses the fixed‐time stabilization (FxTS) problem for reaction‐diffusion systems (RDSs). First, this article designs a fixed‐time event‐dependent intermittent control strategy by introducing four nonlinear functions. The switching of the controller between the working and resting phases is no longer time‐dependent, avoiding the relatively stringent constraint on the control ratio in the existing studies of FxTS based on discontinuous‐time control. Under the presented event‐dependent intermittent control strategy, RDSs can be stabilized within a fixed time and the settling time can be estimated as the zero point of the pre‐defined nonlinear function. In contrast to the existing estimation methods, the estimation method of this article is more universal and less conservative. Moreover, this article derives several generalized stabilization criteria for RDSs under event‐dependent intermittent control employing the Lyapunov method and mathematical induction. Finally, an example is given to clarify the validity of the fixed‐time control strategy and the FxTS criteria.