Robust optimal control for a class of distributed parameter system

In this paper, we study some optimal control and stabilization problems for N dimensional linear heat-diffusion equations with state constraints. The originial motivation for considering such problems came from the development of automatic control systems in irrigation networks which ensure an optimal groundwater regime under uncertain external perturbations; see Skaggs [8] and Mordukhovich [4] for more details. A core problem arising in these considerations is robust stabilization of the system dynamics by state-feedback controls. We study a class of distributed parameter systems where control appear in boundary conditions and have a bounded amplitude. The later creates essential difficulties in employing Hx-optimal control theory based on Riccati equations; see, e.g., Khargonekar et al. [3], Curtain et al. [2] and references therein.