Boundary optimal control design for a system of parabolic–hyperbolic PDEs coupled with an ODE

Abstract

ABSTRACT This paper deals with the design of a boundary optimal controller for a general model of parabolic–hyperbolic PDEs coupled with an ODE. The augmented infinite-dimensional state-space representation has been used in order to solve the optimal state-feedback control problem. By using the perturbation theorem, it has been shown that the system generates a -semigroup on the augmented state space. Also, the dynamical properties of both the original and the augmented systems have been studied. Under some technical conditions, it has been shown that the augmented system generates an exponentially stabilisable and detectable -semigroups. The linear-quadratic control problem has been solved for the augmented system. A decoupling technique has been implemented to decouple and solve the corresponding Riccati equation. Monolithic catalyst reactor model has been used to test the performances of the developed controller through numerical simulations.