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 multistep 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