SEKE 2012 Proceedings - Knowledge Systems Institute

executing a continuous transition, it i s actually acting as a
whole, which means the continuous updates of variables in the
mode are described by the constraints contained in itself and
all its active sub-modes.
B. The Extension of HybridUML
1) The Stereotype for Classes::Kernel::Expression
In order to deal with varying number of CPS network
members and properly express the co-evolution of all members,
first-order function symbols are used to parameterize primitive
state variables, for example, x(i) denotes the location of car i,
and quantifiers and a type system are introduced to quantify
over all objects of a given type, for example, ∀i:C, which
represents all car members of type C. Correspondingly, an
extension of Expression named QuantifiedExpression is
introduced. Its Subclasses include QDifferentialExpression,
such as ∀i:C!x(i)″=a(i), QAlgebraicExpression, such as
∀i:C!x(i):=a, and QBooleanExpression, such as ∀i,j:C far(i,j),
in which far(i,j) expresses a constraint.
2) The Stereotype for Classes::Kernel::Constraint
Corresponding to the extension of Expression, a Stereotype
named QuantifiedConstraint for Constraint is given, endowing
Constraints with quantified features. QuantifiedConstraint
includes quantified differential constraints, which contain
QDifferentialExpression instances expressing flow constraints,
and quantified invariant constraints containing instances of
type QBooleanExpression describing invariant constraints.
3) The Stereotype for CommonBehaviors::Comunications::
Signal
To express the signal that new members emerge in CPS
network, NewObjectSignal is introduced as an extension for
Signal in UML. To express the type of the new member, a new
attribute named agentType is added in each NewObjectSignal.
4) The Stereotype for CommonBehaviors::Comunications::
SignalEvent and ChangeEvent
Corresponding to the extension of Signal, NewSignalEvent,
a stereotype for SignalEvent, is introduced. A NewSignalEvent
happens when a new member appears in the CPS network and
it contains a NewObjectSignal instance inside. Considering the
extension of Boolean expression, extending the ChangeEvent
of UML becomes essential. As the profile of ChangeEvent, a
QChangeEvent contains a QBooleanExpression representing
the condition triggering events when it becomes true.
5) The Stereotype for CommonBehaviors::Comunications::
Trigger
As only very limited event types are used in our paper, it
becomes essential to restrict the event types that a Trigger
contains. A profile of Trigger named ModeTrigger is proposed
and the event types a ModeTrigger contains are confined to
NewSignalEvent and QChangeEvent.
6) The Stereotype for ModeUpdateActivity
Due to the extension of algebraic expression,
QUpdateActivity, a stereotype for ModeUpdateActivity, is
given to d escribe discrete updates on variables of all CPS
network members, and it c ontains a QAlgebraicExpression
expressing discrete update behaviors.
III.
TOP-LEVEL MODE MODEL TO QHP CODE TRANSLATION
A. Metamodel of Hierarchical Hybrid StateMachine-Mode
Figure 1. Metamodel of Hierarchical Hybrid StateMachine-Mode
Definition 1. (Mode) A Mode is a tuple: < VS:{DataType},
SM:{Mode}, ES:{ModePseudostate}, XS:{ModePseudostate},
T:{ModeTransition}, Cons:{Mode!Constraint}> [14] , where VS
is the variable set, SM represents all sub-modes, ES represents
all entry pseudostates, XS denotes all exit pseudostates, T
represents all ModeTransition instances contained in the
Mode’s region and Cons denotes all constraints contained in
the Mode. A Mode without a parent Mode is called a top-level
Mode and the one without sub-modes is called a leaf
Mode.ModeTransition can be divided into t hree types:
EntryTransition (s∈ES), InternalTransition (s∈XS SM , t∈ES SM ),
ExitTransition (t∈XS). As for other element, see Figure 1.
Figure 2. The Hierarchical Hybrid StateMachine-Mode model for DATS
roundabout collision avoidance protocol
Being a Hierarchical Hybrid StateMachine, an active toplevel
Mode actually contains more than one active sub-modes
inside. All such active Mode instances actually form a path
starting from the top-level Mode down to the innermost active
leaf Mode. Such a path is called a StateConfiguration. As
shown in Figure 2, th e Mode path DATC:agree:entry:Circle
forms a StateConfiguration when Circle is active.
A Mode acquires control through an EntryStep seen as a
path that starts from an entry pseudostate of the Mode to the
entry pseudostate of the to-be-active innermost leaf Mode. As
shown in Figure 2, ( init, t 1 , free) is the EntryStep of Mode
DATC. A Mode relinquishes control via an ExitStep, which is
a path starting from the exit pseudostate of the innermost
active leaf Mode to an exit pseudostate of the Mode, for
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