  Controlling hybrid systems is mostly very challenging due to the variety of
dynamics these systems can exhibit. Inspired by the concept of differential
flatness of nonlinear continuous systems and their inherent invertibility
property, the present contribution is focused on explicit input trajectory
calculation. To this end, a new class of hybrid systems called Flat Hybrid
Automata is introduced as a realisation of deterministic, reachable and
explicitly invertible hybrid automata. Relevant system properties are derived,
an approach for construction and for trajectory calculation is proposed and two
demonstrative examples are presented. The results constitute a generalisation
of control of invertible hybrid systems which is very useful if, e.g., fast
reaction for stabilisation or transitions is relevant.
