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Dane Sabo 2025-09-14 22:44:54 -04:00
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@ -117,3 +117,49 @@ language called FRETish, and translate them automatically into linear temporal
logic specifications. From this point, it can be examined whether or not
the set of requirements define a realizable system, or if there exists conflicts
between different specifications.
We have previously discussed that a set of specifications can be checked as to
whether or not the constitute a realizable system. If a system is realizable,
there are a significant number of tools that can synthesize reactive control
systems from the set of logical specifications. Reactive systems are those that
take an input, and produce a reaction (an output). They depend on the current
system state and input to produce the next state. Competitions such as the
Reactive Synthesis Competition (SYNTCOMP) have existed for over a decade where
different groups try to produce the best reactive synthesis algorithm. These
systems are tested against a series of benchmarks to examine the number,
quality, and resources consumed to produce realizations of reactive systems from
logical specifications.
LIMITATION: while reactive synthesis exists, and we have an extensive amount of
documentation on nuclear power regulation and operating procedures exists, we
have not tried to combine the two together.
Finally, formal methods has contributed the hybrid automata and differential
dynamic logic to try and solve the hybrid system verification problem. Hybrid
automata are an expansion of finite automata. Hybrid automata define each node
as being a control mode, similar to how finite state automata define each node
as a single state. For hybrid automata, the node represents the \textit{discrete
state}. Meanwhile, the transitions between states indicate the transitions
between continuous modes. These transitions represent the executions of
\(\nu(\cdot)\) that change the discrete state \(q\). Hybrid automata introduce a
way to graphically represent the transitions between continuous dynamic modes.
Differential dynamic logic (dL), on the other hand, is an expansion of linear
temporal logic to include support for real numbers and differential equation
solving. dL introduces two new operators focused on including dynamic behaviors.
The first is the box modality \([\alpha]\phi\), which states that for all
possible executions of the hybrid system \(\alpha\), \(\phi\) holds. The second
is the diamond modality \(\langle \alpha \rangle \phi\), which states that for
the hybrid system \(\alpha\), there is a trajectory where \(\phi\) holds. With
these two additional modalities, hybrid systems can be reasoned about directly
while including the continuous dynamics. That does not mean that working with
dL is easy however, as the effort to perform verification is encumbered by the
knowledge requirement of differential equations, logical specifications, and
then finally, sequent calculus to actually try and prove things written in dL.
dL is expressive enough to capture any hybrid system behavior, but the effort to
actually prove requirement adherence is challenging, even with automated proof
assistant tools.
In the next section, we will discuss how this research will address these
limitations and provide a path forward for building high assurance hybrid
control systems.