Linear quadratic regulator for time-varying hyperbolic distributed parameter systems

This paper addresses the linear quadratic (LQ) problem for a class of time-varying hyperbolic partial differential equation (PDEs) systems. The control method is based on two main ingredients: infinite-dimensional state space description and the well-known Riccati equation approach. First, the dynamical properties are studied, where the existence and uniqueness of the solution and exponential stability are proved. Next, an LQ-control feedback is computed by using the corresponding operator Riccati differential equation, whose solution can be obtained via a matrix Riccati PDE. The proposed method is applied to a catalytic fixed-bed reactor control problem. An optimal controller is designed for the linearized model and numerical simulations are performed to show the performance of the controller.