Optimal boundary control of 2 × 2 linear hyperbolic PDEs

The present paper develops an optimal linear quadratic boundary controller for 2×2 linear hyperbolic partial differential equations (PDEs) with actuation on only one end of the domain. First-order necessary conditions for optimality is derived via weak variations and an optimal controller in state-feedback form is presented. The linear quadratic regulator (LQR) controller is calculated from differential algebraic Riccati equations. Numerical examples are performed to show the use of the proposed method.