Switched Systems as Hybrid Programs

Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model analyze this combination dynamics, ranging from mathematical descriptions, e.g., using impulsive differential equations switching, automata-theoretic language-based approaches. This paper bridges two such by showing how various classes switched can be modeled the language programs dynamic logic (dL). The resulting models enable formal specification verification dL its existing deductive tools as KeYmaera X. Switched also provide a natural avenue for generalization dL's proof theory equations. completeness results invariants proved in effective safety those dL.