Design of Abstract Controller for Symbolic Abstractions

This paper presents a method for designing an abstract controller for symbolic abstractions. The method is based on the synthesis of safety and reachability controllers using alternating simulation relations. The main result of the paper demonstrates the procedure for constructing an abstract controller that ensures non-blocking behavior, safety, and reachability for a given concrete system. The paper provides a detailed explanation of the method and illustrates its effectiveness through a numerical example. The results demonstrate the practical applicability of the proposed approach to various control problems. Overall, this paper contributes to the field of control theory by providing a systematic method for designing abstract controllers that guarantee desired properties in control systems.