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We present a control design for semilinear and quasilinear 2x2 hyperbolicpartial differential equations with the control input at one boundary and anonlinear ordinary differential equation coupled to the other. The controllercan be designed to asymptotically stabilize the system at an equilibrium orrelative to a reference signal. Two related but different controllers forsemilinear and general quasilinear systems are presented and the additionalchallenges in quasilinear systems are discussed. Moreover, we present anobserver that estimates the distributed PDE state and the unmeasured ODE statefrom measurements at the actuated boundary only, which can be used to alsosolve the output feedback control problem.

Predictive feedback boundary control of semilinear and quasilinear 2x2 hyperbolic PDE-ODE systems