Considering Superposition in the Composable Hybrid Automata

In the existing abundance of different hybrid automata formalisms concurrent composition is seldom considered or requires additional semantics which is not always defined. This work considers three common reasons of problems with hybrid automata composition: contradicting resets in the discrete transitions, global time reference with contradicting initial conditions and redundant non-determinism for firing time. An overview is provided of the existing formalisms and the attempts to solve these particular problems. A reduced hybrid automata formalism, called linear time-invariant hybrid automata, is introduced. It avoids all those problems and yet provides a powerful modeling tool with practical applications. Also, a short discussion is provided for the problem of Zeno behavior and what conditions are demanded for a model to fulfill so that Zeno behavior would not arise during composition.