% Required packages: % \usepackage{booktabs} % \usepackage{tabularx} % \usepackage{multirow} % \usepackage{array} % \usepackage[table]{xcolor} % optional, for alternating row colors \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.