2021/08/24 by Hugo Lhachemi, Lhachemi, Hugo, Ammar Malik +3
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2108.10658
This paper is concerned with the regulation control of a one-dimensional\nreaction-diffusion equation in the presence of a state-delay in the reaction\nterm. The objective is to achieve the PI regulation of the right Dirichlet\ntrace with a command selected as the left Dirichlet trace. The control design\nstrategy consists of the design of a PI controller on a finite dimensional\ntruncated model obtained by spectral reduction. By an adequate selection of the\nnumber of modes of the original infinite-dimensional system, we show that the\nproposed control design procedure achieves both the exponential stabilization\nof the original infinite-dimensional system as well as the setpoint regulation\nof the right Dirichlet trace.\n