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\section{Budget and Budget Justification}

\subsection{Budget Summary}

The proposed research will be conducted over three (3) years, 
corresponding to the expected completion timeline for the PhD 
dissertation. Table~\ref{tab:budget} provides a detailed breakdown 
of costs by category and year.

\begin{table}[htbp]
\centering
\caption{Proposed Budget by Year and Category}
\label{tab:budget}
\small
\begin{tabular}{@{}lrrrr@{}}
\toprule
\textbf{Category} & \textbf{Year 1} & \textbf{Year 2} & 
  \textbf{Year 3} & \textbf{Total} \\
\midrule
\multicolumn{5}{l}{\textbf{Senior Personnel}} \\
\quad Faculty (PI Advisor, 1 mo.) & \$12,083 & \$12,566 & 
  \$13,069 & \$37,718 \\
\addlinespace
\multicolumn{5}{l}{\textbf{Other Personnel}} \\
\quad Graduate Research Assistant & \$38,000 & \$39,520 & 
  \$41,101 & \$118,621 \\
\addlinespace
\multicolumn{5}{l}{\textbf{Fringe Benefits}} \\
\quad Faculty Fringe Benefits (29.6\%) & \$3,577 & \$3,720 & 
  \$3,868 & \$11,165 \\
\quad GRA Fringe Benefits (50\%) & \$19,000 & \$19,760 & 
  \$20,551 & \$59,311 \\
\cmidrule{2-5}
\quad \textit{Fringe Benefits Subtotal} & \$22,577 & \$23,480 & 
  \$24,419 & \$70,476 \\
\addlinespace
\multicolumn{5}{l}{\textbf{Equipment}} \\
\quad (No equipment over \$5,000) & --- & --- & --- & --- \\
\addlinespace
\multicolumn{5}{l}{\textbf{Travel}} \\
\quad Conference Travel (Domestic) & \$4,000 & \$4,000 & 
  \$4,000 & \$12,000 \\
\quad Industry Collaboration Visits & \$1,500 & \$1,500 & 
  \$1,500 & \$4,500 \\
\cmidrule{2-5}
\quad \textit{Travel Subtotal} & \$5,500 & \$5,500 & 
  \$5,500 & \$16,500 \\
\addlinespace
\multicolumn{5}{l}{\textbf{Participant Support Costs}} \\
\quad (Not applicable) & --- & --- & --- & --- \\
\addlinespace
\multicolumn{5}{l}{\textbf{Other Direct Costs}} \\
\quad \textit{Materials and Supplies:} & & & & \\
\quad \quad High-Performance Workstation & \$3,500 & --- & 
  --- & \$3,500 \\
\quad \quad Laboratory Materials \& Supplies & \$1,500 & \$1,000 & 
  \$1,000 & \$3,500 \\
\quad \textit{Publication Costs} & \$1,000 & \$1,500 & 
  \$2,000 & \$4,500 \\
\quad \textit{Computing/Cloud Services} & \$1,500 & \$1,500 & 
  \$1,500 & \$4,500 \\
\cmidrule{2-5}
\quad \textit{Other Direct Costs Subtotal} & \$7,500 & \$4,000 & 
  \$4,500 & \$16,000 \\
\addlinespace
\midrule
\textbf{Total Direct Costs} & \$85,660 & \$85,066 & 
  \$88,589 & \$259,315 \\
\addlinespace
\multicolumn{5}{l}{\textbf{H. Indirect Costs (F\&A)}} \\
\quad On-Campus Research (56\% MTDC) & \$35,326 & \$34,488 & 
  \$35,935 & \$105,749 \\
\addlinespace
\midrule
\textbf{TOTAL PROJECT COST} & \$120,986 & \$119,554 & 
  \$124,524 & \$365,064 \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Budget Justification}

\subsubsection{Senior Personnel}

\paragraph{Faculty Advisor}
Funds are requested to support one month of summer salary per year 
for the faculty advisor (estimated at Associate Professor level, 
\$96,459/year base salary for 8 academic months = \$12,083/month). 
A 4\% annual salary increase is applied in subsequent years. The 
advisor will provide: (1) overall project direction and technical 
guidance; (2) expertise in control systems theory and formal methods; 
(3) coordination with industry partners at Emerson and through the 
Cyber Energy Center; (4) review of all technical deliverables; and 
(5) mentorship in proposal writing, publication preparation, and 
professional development.

\subsubsection{Other Personnel}

\paragraph{Graduate Research Assistant (Principal Investigator)}
Funds are requested to support one full-time graduate research 
assistant (the PI) for the entire duration of the project at 
\$38,000 per year in Year 1. This represents a standard graduate 
research assistantship stipend at the University of Pittsburgh for 
a PhD student in the Swanson School of Engineering. A 4\% annual 
salary increase is included in Years 2 and 3 to account for 
cost-of-living adjustments. The GRA will be responsible for all 
aspects of the research including: (1) formalizing nuclear reactor 
operating procedures into temporal logic specifications using FRET; 
(2) synthesizing discrete automata using reactive synthesis tools 
(Strix); (3) developing and verifying continuous control modes using 
reachability analysis and barrier certificates; (4) implementing the 
hybrid controller on industrial control hardware; and (5) conducting 
hardware-in-the-loop validation experiments.

\subsubsection{Fringe Benefits}

\paragraph{Faculty Fringe Benefits}
Faculty fringe benefits are calculated at 29.6\%, the University of 
Pittsburgh's approved rate for academic year faculty, covering 
retirement contributions, health insurance, and other benefits.

\paragraph{Graduate Research Assistant Fringe Benefits}
Fringe benefits for the GRA are calculated at 50\% of salary, 
consistent with University of Pittsburgh rates for graduate students 
on research assistantships. This covers health insurance and other 
mandatory benefits. Tuition remission is provided separately by the 
department and is not included in this budget.

\subsubsection{Equipment}

No equipment purchases over \$5,000 are requested. Computing 
equipment and software tools under this threshold are budgeted in 
Materials and Supplies (Section G).

\subsubsection{Travel}

\paragraph{Conference Travel (\$4,000 per year)} Funds are requested for the PI
and faculty advisor to attend one major control systems conference annually to
disseminate research results. The budget assumes domestic conference attendance
with costs including: airfare, hotel, meals and incidentals, ground
transportation, and registration for both attendees per conference.
\paragraph{Industry Collaboration Visits (\$1,500 per year)} Funds are requested
for travel to industry partner sites and potential nuclear facilities to: (1)
validate reactor operating procedures with domain experts; (2) present research
progress to industry stakeholders; (3) gather feedback on practical
implementation considerations; and (4) explore deployment pathways for the
developed technology. This includes travel to Emerson facilities or nuclear
industry conferences such as the American Nuclear Society Annual Meeting. Budget
covers mileage reimbursement at federal rates for regional travel plus hotel and
meals for 2-3 one-night trips.

No international travel is planned or budgeted.

\subsubsection{Participant Support Costs}

Not applicable to this project.

\subsubsection{Other Direct Costs}

\paragraph{Materials and Supplies}

\textit{High-Performance Workstation (\$3,500, Year 1):}
A dedicated high-performance workstation is required for 
computationally intensive tasks including: (1) reactive synthesis 
using Strix, which scales exponentially with specification 
complexity; (2) reachability analysis for continuous modes, requiring 
numerical integration of high-dimensional systems; (3) hardware-in-
the-loop simulation running at real-time rates with high-fidelity 
reactor models; and (4) barrier certificate computation using 
optimization solvers. The workstation specifications include: Intel 
Core i9 or AMD Ryzen 9 processor (minimum 16 cores), 64 GB RAM, 
2 TB NVMe SSD storage, and NVIDIA GPU for potential acceleration of 
numerical computations. This configuration enables timely completion 
of verification tasks that would be intractable on standard 
laboratory computers.

\textit{Laboratory Materials and Supplies (\$1,500 Year 1; \$1,000 Years 2--3):}
Funds are requested for laboratory supplies and materials including: electronic
components and sensors for hardware integration, cables and connectors for
hardware-in-the-loop setup, and miscellaneous computing accessories such as
external storage devices and backup media. Year 1 costs are higher to account for initial laboratory
setup; subsequent years reflect ongoing consumable costs.

\textit{Note on Software:} All required software tools are either 
open-source (FRET, Strix, various verification packages) or provided 
through University of Pittsburgh institutional licenses 
(MATLAB/Simulink). No software licensing costs are requested. The 
ARCADE interface software for hardware-in-the-loop testing is also 
provided through the Cyber Energy Center partnership at no cost to 
this project.

\textit{Note on Equipment:} The Emerson Ovation distributed control system
hardware required for hardware-in-the-loop validation will be provided through
an existing partnership between the University of Pittsburgh Cyber Energy Center
and Emerson Process Management. This represents significant in-kind cost sharing
and is detailed in Section~\ref{sec:cost-sharing}.

\paragraph{Publication Costs}
Funds are requested to cover publication fees for disseminating 
research results in high-quality peer-reviewed venues. Budget 
includes:
\begin{itemize}
\item Year 1 (\$1,000): Conference proceedings fees and one journal 
  submission
\item Year 2 (\$1,500): Open-access publication charges for first 
  major journal paper
\item Year 3 (\$2,000): Open-access publication charges for 
  dissertation-culminating journal papers
\end{itemize}

Open-access publication is prioritized to maximize research impact 
and accessibility, particularly important for work with potential 
nuclear safety applications. Many high-impact journals (IEEE 
Transactions on Automatic Control, Automatica) charge 
\$1,000--\$2,000 for open access.

\paragraph{Computing and Cloud Services} Funds are requested for cloud computing
resources and online services including: (1) high-performance computing credits
for large-scale verification tasks that exceed workstation capabilities; (2)
cloud storage and backup services for research data; (3) online collaboration
tools and project management platforms; (4) reference management and literature
access beyond institutional subscriptions. Cloud computing provides scalable
computational resources for particularly demanding verification problems without
requiring additional capital equipment purchases.

\subsubsection{H. Indirect Costs (Facilities \& Administrative)}

Indirect costs are calculated at 56\% of Modified Total Direct Costs 
(MTDC), which is the University of Pittsburgh's federally negotiated 
rate for on-campus research. MTDC includes all direct costs except 
equipment purchases over \$5,000, tuition remission, and certain 
other exclusions. The calculation base includes all personnel costs, 
travel, and other direct costs as shown in the budget table.

These indirect costs support essential research infrastructure 
including: laboratory space and utilities in Benedum Hall, 
administrative support from the Department of Mechanical Engineering 
and Materials Science, library and information technology services, 
research compliance and safety oversight, and institutional resources 
that enable the research enterprise.

\subsubsection{Cost Sharing}
\label{sec:cost-sharing}

While no direct cost sharing is proposed or required for this 
project, significant in-kind contributions will support the research:

\paragraph{Emerson Process Management Partnership} Through the University of
Pittsburgh Cyber Energy Center, Emerson Process Management will provide access
to Ovation distributed control system hardware and ARCADE hardware-in-the-loop
interface software. This equipment is essential for TRL 5 validation and
represents industry-standard control systems deployed in nuclear facilities.
Emerson will also provide technical consultation and domain expertise for
practical implementation considerations.

\paragraph{University Infrastructure}
The University of Pittsburgh provides comprehensive MATLAB/Simulink 
licenses with all necessary toolboxes through institutional 
agreements, representing approximately \$3,000--\$4,000 in annual 
value. Laboratory space in Benedum Hall, high-performance computing 
resources through the Center for Research Computing, and 
administrative support are covered through indirect cost recovery and 
are not included as explicit cost sharing.

\paragraph{Total In-Kind Contributions}
The estimated value of in-kind contributions over the three-year 
project duration exceeds \$20,000, primarily from the Emerson 
partnership. These contributions are essential to achieving project 
objectives and demonstrate strong industry support for the research.

\subsubsection{Budget Inflation and Escalation}

Personnel costs include a 4\% annual salary increase to account for 
cost-of-living adjustments, consistent with typical university 
practices. All other cost categories are held constant in nominal 
dollars across years, representing a conservative estimate that 
accommodates minor inflation through efficient resource management.
