Feedback control of uncertain parabolic systems with hard constraints

This paper presents a method to design feedback control of constrained parabolic systems under uncertain perturbations with the aid of multi-step approximations. The design procedure essentially employs monotonicity properties of parabolic dynamics and its asymptotic on the infinite horizon. The results obtained show that there is a suboptimal three-positional structure of feedback controllers through the Neumann boundary conditions. We also provide calculations of their optimal parameters to ensure the required state performance and stability under any admissible perturbations.