Disturbance rejection in a class of adaptive control laws for distributed parameter systems

A recently introduced class of the well-posed error systems and the corresponding robust model reference adaptive control laws for the systems represented by the parabolic or the hyperbolic partial differential equations (PDEs) with the spatially varying parameters and a distributed sensing and actuation is extended to encompass the disturbance rejection capability. The disturbance is modeled as a space-time-varying signal generated by a parabolic PDE with the known parameters, a spatially varying time-invariant signal, and a space-time-varying signal with the known time variation. The case of the time-invariant disturbance model is shown to lead to a distributed adaptive PI control law, thereby making a well-posed connection to the classical finite-dimensional control structures. The numerical simulations indicate that the control laws proposed are robust with respect to the plant/reference model as well as the disturbance/disturbance observer mismatch in the boundary conditions.