Predictive feedback boundary control of semilinear and quasilinear 2 × 2 hyperbolic PDE–ODE systems

We present a control design for semilinear and quasilinear 2 × hyperbolic partial differential equations with the input at one boundary nonlinear ordinary equation coupled to other. The controller can be designed asymptotically stabilize system an equilibrium or relative reference signal. Two related but different controllers general systems are presented additional challenges in discussed. Moreover, we observer that estimates distributed PDE state unmeasured ODE from measurements actuated only, which used also solve output feedback problem.