Spreading Control for Distributed Parameter Systems

This note contains a description of the concepts of spreadability and feedback spreading control (FSC) for distributed parameter systems (DPS), the approaches used until now along with applications and a list of references to works including peer-reviewed papers, communications to international meetings and theses. Distributed biophysical processes usually involve spreads in space, e.g. biological control and invasion theory, pollution in air quality, desertification in vegetation dynamics, cancer cells in biomedicine, etc. In order to model and control such expansion phenomena, the concepts of spreadability and spreading control have been introduced by El Jai and Kassara [14] in 1994 for DPS and tested in [15] for transport systems. They consist of what follows : Let, Ω ⊂ R be an open and bounded domain with sufficiently smooth boundary ∂Ω. Let −A stand for an unbounded densely defined linear operator which generates a C0 analytic semigroup (S(t))t on Z = L(Ω) and consider the following semilinear control system,