Disturbance attenuation in nonlinear perturbed diffusion processes by sampled-in-space sensing and actuation

A diffusion equation perturbed by uncertain disturbances of both matching and unmatching nature is considered. The problem of disturbance attenuation is tackled by means of the sliding-mode control approach. It is assumed that only a finite number of pointwise sensing and actuation devices, suitably located in an equi-spaced manner along the spatial domain of interest, is available. We show that an arbitrary level of the unmatching disturbance attenuation can be achieved by employing a sufficiently high number of sensing and actuation devices. We also show that matching disturbances entering the control channels can be fully rejected by the proposed design.