Boundary linear-quadratic control for a system of coupled parabolic-hyperbolic PDEs and ODE

The 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 control problem. It has been shown that the system generates a C 0 -semigroup by using the perturbation theorem and then the dynamical properties of the system have been studied. Lyapunov equation has been used to show the exponential stabilizability and detectability of the system. The linear-quadratic control problem has been solved and an algorithm has been developed to solve the corresponding operator Riccati equation. Monolithic catalyst reactor model has been used to test the performances of the developed controller through numerical simulations.