Riccati equations and LQ-optimal control for a class of hyperbolic PDEs

We derive an explicit solution to the operator Riccati equation solving the Linear–Quadratic (LQ) optimal control problem for a class of boundary controlled hyperbolic partial differential equations (PDEs) defined on a one-dimensional spatial domain. Different descriptions of the system are used to obtain different representations of the operator Riccati equation. By means of an example, we illustrate the importance of considering an extended operator Riccati equation to solve the LQ-optimal control problem for our class of systems.