Modal Models

Modal models combine time-based signals with event sequences within the same state machine, as shown below:

A mode is represented by a state in a finite-state machine that has a refinement that is a time-based system.

The (complete) state of the hybrid system is a pair (i,s) where i is the mode and s is the state of the time-based refinement system associated with mode i.
State transitions in the FSM have an action. The action will typically set the initial refinement state of the time-based system in the destination mode.
The guards are sets of tuples containing event input symbols, time-based input values, and values of the refinement state.

Example: Overload of an electronic system might be modeled by a state transition that is triggered by the magnitude of the current refinement state exceeding some threshold.

When the system is in some mode, the refinement state is only affected by the time-based inputs. It is not affected by the event inputs. Hence, the time-based refinements don’t have to deal with stuttering inputs.
The FSM may react at any time in the time base. The mode in which it is before this reaction is called the current mode. It will take a discrete state transition and switch to the destination mode if the input values and the refinement state at that time match a guard. If it does not take a discrete state transition, then the FSM stutters. In either case, the refinement of the current mode also reacts to the time-based inputs, changes its state and produces outputs.

Hybrid Sys.

Modal Models