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\section{Goals and Outcomes}
The goal of this research is to create a methodology for building high assurance
hybrid autonomous control systems.
%FIRST PARAGRAPH - INTRO HOOK
Commercial control systems for nuclear power have been stuck in the past, far
behind the state of the art of controls.
% 3-5 SENTENCES KNOWN INFO
Nuclear power control systems are extremely high assurance system, where
failures are intolerable. A control failure in nuclear power has a broader
impact than financial losses. Instead, a failure can create extensive economic
losses for the power utility, interruptions for local customers, or in the worst
case, radiological release in the local environment. Because of this, control of
nuclear power is performed by operators who are extensively trained, use
detailed operating procedures, and follow strict requirements.
% GAP
This method of control has been reliable, but is woefully behind the
capabilities of modern less critical control systems, and by relying on human
operators, prevents the introduction of autonomy.
% CRITICAL NEED
To bring nuclear power control into the 21st century, we need a way to develop
autonomous control systems that have strict guarantees and assurance of their
correct behavior across their operating range.
% SECOND PARAGRAPH - APPROACH SOLUTION
To do this, we will blend tools from computer science and formal methods with
those from engineering and control theory to build high assurance hybrid systems
to perform autonomous control.
% RATIONALE
Hybrids systems have switching behavior, where discrete transitions between
continuous dynamics occur. Verification of these systems is difficult because of
these transitions. We will address this difficulty by building autonomous hybrid
control systems that are correct by construction. We will synthesize the
discrete mode switching behavior from written operating procedures, while
utilizing reachability analysis and assume-guarantee contracts to prove that
continuous modes behave correctly.
% HYPOTHESIS PAY-OFF/IMPACT
If we are successful in creating a hybrid control system that is correct by
construction, we can implement autonomous control systems in nuclear power with
a great assurance of their safety and performance. Autonomous control is a
technology that is desperately needed for the future of nuclear power. Nuclear
plant designs such as small modular reactors or microcreactors have been
suggested as a way to reduce the enormous capital costs of nuclear power
construction, but are limited in their feasibility by the increased cost of
operator staffing per megawatt generated. If we can reduce the quantity of
operaters needed in these reactors, we can reduce the cost of generating clean
nuclear power and address increasing energy demands.
% QUALIFICATIONS
This work is also situated in the University of Pittsburgh Cyber Energy Center.
This research is colocated with collaboration across the energy industry and
benefits from having access to industry-ready control hardware from Emerson.
The accessibility to industry this research has will ensure that solutions and
capabilities generated are aligned with industry needs.
If this research is successful, we will be able to do the following:
\begin{enumerate}
% OUTCOME PARAGRAPH 1 TITLE
\item \textbf{ Synthesize written operating procedures into discrete automata.
}
% STRATEGY
Discrete automata are the backbone of a continuous hybrid system. These
automata control the swtiching behavior between continuous modes, and are
directly analogous to operators changing between control laws. The automated
creation of these automata is a mature field called reactive synthesis.
Reactive synthesis is enabled by specifying logical requriements of a
discrete system. These requirements will be created from current written
operating procedures directly, through an intermediate tool called FRET,
which uses a natural-language-like format called FRETish to embed
requirements.
% OUTCOME
By using written operating procedures to create the discrete automata, we
will provide a means for control systems engineers to create discrete
switching behavior without having to become logical experts. This reduces
the barrier to entry for using formal methods tools, making high assurance
switching mechanisms easier to attain.
% OUTCOME PARAGRAPH 2
% TITLE
\item \textbf{
Build hybrid systems using correct by construction principles.
}
% STRATEGY
In addition to the discrete system, hybrid systems use continuous modes
between discrete transitions. These continuous modes will be constructed
using standard control theory practices, but will use formal methods to
ensure their correctness. Because the discrete modes and their transitions
will already be specified from operating requirements, the continuous modes
will be examined to ensure that only allowable state transitions can be
reached.
% OUTCOME
This way, controls engineers can build continuous modes exactly as they
would before, but iterate on their designs to ensure broader system
correctness.
% OUTCOME PARAGRAPH 3 TITLE
\item \textbf{ Create autonomous control systems with strict safety
guarantees. }
% STRATEGY
By combining the discrete and continuous components while building proof of
their correctness along the way, we can translate these capabilities into
realizable autonomous systems for nuclear power. We will use the methodology
presented in this proposal to build a candidate control system using a
simulation of a small modular reactor in combination with an Emerson Ovation
control system.
% OUTCOME
By realizing an autonomous hybrid control system using this methodology, we
will generate evidence that autonomous hybrid control can be realized in the
nuclear industry with current controls equipment.
\end{enumerate}
% THIRD PARAGRAPH - IMPACT
% INNOVATION
The innovation in this work is the implementation of different formal methods
technologies for the purpose of building hybrid control systems. These
technologies will allow us to build hybrid systems with behavior we can ensure.
% OUTCOME IMPACT
The way that these technologies will be implemented is also designed to incur
the smallest amount of cost possible for possible recreation in industry.
Controls engineers should be able to find this work approachable, and
implementable in new nuclear technology control systems.
% GENERAL IMPACT
New control systems, especially autonomous control, are critical to advancing
the prevalence of nuclear power. Small modular reactors stand to answer the next
energy generation challenge in the United States, but must address the
significant operating cost required by current staffing limits. This work will
allow new reactors to reduce the amount of operators required and improve the
economic feasibility of new reactor designs.

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\section{Goals and Outcomes}
% GOAL PARAGRAPH
The goal of this research is to develop a methodology for creating autonomous
hybrid control systems with mathematical guarantees of safe and correct
behavior.
% INTRODUCTORY PARAGRAPH Hook
Nuclear power plants require the highest levels of control system reliability,
where failures can result in significant economic losses, service interruptions,
or radiological release.
% Known information
Currently, nuclear plant operations rely on extensively trained human operators
who follow detailed written procedures and strict regulatory requirements to
manage reactor control. These operators make critical decisions about when to
switch between different control modes— such as transitioning from startup
heating to power operation—based on their interpretation of plant conditions and
procedural guidance.
% Gap
However, this reliance on human operators prevents the introduction of
autonomous control capabilities and creates a fundamental economic challenge for
next-generation reactor designs. Emerging technologies like small modular
reactors face significantly higher per-megawatt staffing costs than conventional
plants, threatening their economic viability.
% Critical Need
What is needed is a way to create autonomous control systems that can safely
manage complex operational sequences with the same level of assurance as
human-operated systems, but without requiring constant human supervision.
% APPROACH PARAGRAPH Solution
To address this need, we will combine formal methods from computer science with
control theory to build hybrid control systems that are correct by construction.
% Rationale
Hybrid systems use discrete logic to switch between continuous control modes,
similar to how operators change control strategies. Existing formal methods can
generate provably correct switching logic from written requirements, but they
cannot handle the continuous dynamics that occur during transitions between
modes. Meanwhile, traditional control theory can verify continuous behavior but
lacks tools for proving correctness of discrete switching decisions.
% Hypothesis
By synthesizing discrete mode transitions directly from written operating
procedures and verifying continuous behavior between transitions, we can create
hybrid control systems with end-to-end correctness guarantees. If we can
formalize existing procedures into logical specifications and verify that
continuous dynamics satisfy transition requirements, then we can build
autonomous controllers that are provably free from design defects.
% Pay-off
This approach will enable autonomous control in nuclear power plants while
maintaining the high safety standards required by the industry.
% Qualifications
This work is conducted within the University of Pittsburgh Cyber Energy Center,
which provides access to industry collaboration and Emerson control hardware,
ensuring that solutions developed are aligned with practical implementation
requirements.
% OUTCOMES PARAGRAPHS
If this research is successful, we will be able to do the following:
\begin{enumerate}
% OUTCOME 1 Title
\item \textbf{Translate written procedures into verified control logic.}
% Strategy
We will develop a methodology for converting existing written operating
procedures into formal specifications that can be automatically synthesized
into discrete control logic. This process will use structured intermediate
representations to bridge natural language procedures and mathematical
logic.
% Outcome
Control system engineers will be able to generate verified mode-switching
controllers directly from regulatory procedures without requiring expertise
in formal methods, reducing the barrier to creating high-assurance control
systems.
% OUTCOME 2 Title
\item \textbf{Verify continuous control behavior across mode transitions.}
% Strategy
We will establish methods for analyzing continuous control modes to ensure
they satisfy the discrete transition requirements. Using a combination of
classical control theory for linear systems and reachability analysis for
nonlinear dynamics, we will verify that each continuous mode can safely
reach its intended transitions.
% Outcome
Engineers will be able to design continuous controllers using standard
practices while iterating to ensure broader system correctness, proving that
mode transitions occur safely and at the right times.
% OUTCOME 3 Title
\item \textbf{Demonstrate autonomous reactor startup control with safety
guarantees.}
% Strategy
We will apply this methodology to develop an autonomous controller for
nuclear reactor startup procedures, implementing it on a small modular
reactor simulation using industry-standard control hardware. This
demonstration will prove correctness across multiple coordinated control
modes from cold shutdown through criticality to power operation.
% Outcome
We will provide evidence that autonomous hybrid control can be realized in
the nuclear industry with current control equipment, establishing a path
toward reducing operator staffing requirements while maintaining safety.
\end{enumerate}
% IMPACT PARAGRAPH Innovation
The innovation in this work is the unification of discrete synthesis and
continuous verification to enable end-to-end correctness guarantees for hybrid
systems.
% Outcome Impact
If successful, control engineers will be able to create autonomous controllers
from existing procedures with mathematical proof of correct behavior, making
high-assurance autonomous control practical for safety-critical applications.
% Impact/Pay-off
This capability is essential for the economic viability of next-generation
nuclear power. Small modular reactors represent a promising solution to growing
energy demands, but their success depends on reducing per-megawatt operating
costs through increased autonomy. This research will provide the tools to
achieve that autonomy while maintaining the exceptional safety record required
by the nuclear industry.

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\begin{document}
\maketitle
\input{goals-and-outcomes/v4}
\input{goals-and-outcomes/v6}
\input{state-of-the-art/v2}
\input{research-approach/v2}
\input{broader-impacts/v1}