ABSTRACT
This chapter concerns robust control design of constrained parabolic systems under uncertain disturbances (perturbations) and feedback controllers in the mixed boundary conditions. It develops an effective multi-step approximation procedure to design suboptimal feedback controllers for constrained parabolic systems. The chapter contains new results for the case of mixed boundary controllers. The results obtained include a justification of a suboptimal three-positional control structure with subsequent optimization of its parameters. The chapter formulates the robust feedback control problem of our study and present the main properties of the parabolic dynamics used in the sequel. It devotes to solving first-order ODE approximation problems under maximal perturbations that allow us to justify a suboptimal structure of boundary controls in the parabolic system. The chapter deals with computing a feedback boundary controller that ensures the best system behavior under maximal perturbations and keeps transients within the required state constraint region for any admissible disturbances on a sufficiently large control interval.
