Boundary optimal control of coupled parabolic PDE-ODE systems

Abstract

This paper deals with boundary optimal control problem for coupled parabolic PDEODE systems. The problem is studied using infinite-dimensional state space representation of the coupled PDE-ODE system. Linearization of the non-linear system is established around a steady state profile. Using some state transformations, the linearized system is formulated as a well-posed infinite-dimensional system with bounded input and output operators. It has been shown that the resulting system is a Riesz Spectral system. The LQ-control problem is studied on the basis of the solution of the corresponding eigenvalues problem. The results have been applied to the case study of catalytic cracking reactor with catalyst deactivation. Numerical simulations are performed to illustrate the performances of the developed controller.