ISS synthesis of parabolic systems with uncertain parameters using in-domain sensing and actuation

Linear proportional ISS synthesis of parabolic systems is developed within the practical framework of indomain embedded sensing and actuation. The underlying system is affected by external disturbances and it is governed by a non-homogeneous reaction-diffusion PDE with a priori unknown spatially varying parameters. The present investigation focuses on practically motivated sampled-in-space sensing and actuation. A finite number of available sensing and actuating devices are assumed to be located along the one-dimensional spatial domain of interest. Tuning of the controller gains is then constructively developed by means of the Lyapunov approach to achieve a desired attenuation level for external distributed disturbances, affecting the system in question. Dual observer design is additionally developed within the present framework. Theoretical results are finally supported by simulations.