Recent Results on Computable and Compositional Semantics for Hybrid Systems

Hybrid systems combine discrete and continuous behaviors and are prevalent in applications such as automotive, robotics, and avionics, where precise interaction between control logic and dynamic environments is critical. This paper summarizes the results of [1], where a computable and compositional semantics for hybrid systems was first proposed. The formalism supports the composition of smaller subsystems and enables algorithmic analysis using computable functions. The approach addresses the challenge of undecidability in hybrid system reachability by employing approximate decision procedures. A key feature is the use of multifunctions to handle nondeterministic systems and ensure computability is preserved during system composition and the introduction of atomic interfaces to avoid circular dependencies in the composition. Several classes of computable multifunctions are identified to guarantee computational feasibility. This framework provides a scalable, compositional approach to the modeling and verification of complex hybrid systems.