Adaptive compensation of diffusion-advection actuator dynamics using boundary measurements

For (potentially unstable) Ordinary Differential Equation (ODE) systems with actuator delay, delay compensation can be obtained with a prediction-based control law. In this paper, we consider another class of PDE-ODE cascade, in which the Partial Differential Equation (PDE) accounts for diffusive effects. We investigate compensation of both convection and diffusion and extend a previously proposed control design to handle both uncertainty in the ODE parameters and boundary measurements. Robustness to small perturbations in the diffusion and convection coefficients is also proved.