Robust stabilization of an uncertain diffusion process with boundary control and sensing

The primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and Neumann-type actuation. It exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance, which is possibly unbounded in magnitude. The proposed robust synthesis is formed by a discontinuous version of a PI controller. It is applied here for the global asymptotic stabilization of an infinite dimensional system in a suitable Sobolev space. The Lyapunov based stability proof is accompanied by a set of simple tuning rules for the controller parameters. The effectiveness of the developed scheme is supported by simulation results.