Superposition Principle in Composable Hybrid Automata

Hybrid automata are a well-established modelling approach. The formalism is used in many real-time and control systems engineering projects, which makes model composition an increasingly relevant topic. A well-defined composition support allows concurrent engineering activities and the validation of larger systems. However, many existing publications seldom consider it or make unrealistic assumptions on the model design. The article discusses the common problems with hybrid automata composition and presents a new formalism, called linear time-invariant hybrid automata (LTI-HA), which targets specifically these issues. Our approach considers the superposition principle for flow functions, which makes it specifically useful for practical modelling purposes in the spacecraft and control domain. We compare the approach to well-known related ideas, such as hybrid I/O automata. Several properties of composition, such as commutativity, are proven.