Optimal control of a time-varying system of coupled parabolic-hyperbolic PDEs

This paper is devoted to design an optimal linear quadratic controller for a time-varying system of coupled parabolic and hyperbolic partial differential equations (PDEs). Infinite-dimensional state space approach is adopted to solve the control problem via the well-known operator Riccati equation. The latter is converted into a scalar partial differential equation coupled with a set of ordinary differential equations. The main algorithm to solve the Riccati equation is presented. The designed controller is tested on a model of catalytic packed-bed chemical reactor to show the performances of the developed controller.