Boundary Control Of Reaction-diffusion Equations On High Dimensional Regions

When the interval of the system is irregular,the method of simplifying the variable into one dimension is no longer applicable.Therefore,it is necessary to establish a new model to solve its boundary control problem.This paper is about boundary control of the reaction diffusion equation on the curved rectangle and curly top cylinder.Firstly,the boundary control of the reaction-diffusion equation on the two-dimensional curved rectangle is given,and then the conclusion is extended to three dimensions to achieve the purpose of this paper.By using the partial differential equation backstepping control method proposed by Krstic et al.,the given system is transformed into the target system which is stable exponential,so as to achieve the control target.Then,the stability of the closed-loop system is proved by using the stability of the target system and the boundedness of the Volterra integral transformation and its inverse transformation.The difficulty of this paper lies in the proof of the stability of the closed-loop system.By using the formulas mentioned in the preliminary knowledge,it is proved that the closed-loop system is exponentially stable.Finally,this paper uses MATLAB software to simulate the relevant results.The simulation results show that the theoretical derivation is consistent with the actual.