That's pretty complicated.
To validate the design you need to understand which sequence of states each machine is intended to go through, and what event triggers each state change. Doing that in words is going to get quite laborious with something this complex. Have you encountered state transition diagrams yet? This is one of the best ways to understand how a finite state machine is supposed to work. In your case you have three state machines that all interact. This would result in connections between the three diagrams, with actions by one machine causing events in another.