Control of Normal Flow PDEs with ISS Properties

This paper establishes some input-to-state stability (ISS) properties w.r.t. in-domain process and measurement disturbances for systems described by a normal flow equation governed by an observer-based control scheme without knowledge of the spatial derivatives of the viscosity solution. The approach used to achieve the "a priori"ISS estimates of the solution is not based on Lyapunov arguments and assumes fixed boundary conditions. A one-dimensional case study is addressed by both analytical and numerical treatments, which show the effectiveness of the proposed approach.