\section{Schedule, Milestones, and Deliverables}

\textbf{Heilmeier Question: How long will it take?}

This research will be conducted over six trimesters (24 months) of full-time effort following the proposal defense in Spring 2026. The University of Pittsburgh Cyber Energy Center and NRC Fellowship provide all computational and experimental resources. The work progresses sequentially through three main research thrusts, culminating in integrated demonstration and validation.

The first semester (Spring 2026) focuses on Thrust 1, translating startup
procedures into formal temporal logic specifications using FRET. This
establishes the foundation for automated synthesis by converting natural
language procedures into machine-readable requirements. The second semester
(Summer 2026) addresses Thrust 2, using Strix to synthesize the discrete
automaton that defines mode-switching behavior. With the discrete structure
established, the third semester (Fall 2026) develops the continuous controllers
for each operational mode through Thrust 3, employing reachability analysis and
barrier certificates to verify that each mode satisfies its transition
requirements. Integration and validation occupy the remaining three semesters. 

Figure \ref{fig:gantt} shows the complete project schedule including research thrusts, major milestones, and planned publications.

\begin{figure}[htbp]
    \centering
    \begin{ganttchart}[
        hgrid,
        vgrid={*{4}{draw=none}, dotted},
        x unit=0.4cm,
        y unit title=0.6cm,
        y unit chart=0.4cm,
        title/.append style={fill=gray!30},
        title height=1,
        bar/.append style={fill=blue!50},
        bar height=0.5,
        bar label font=\small,
        milestone/.append style={fill=red, shape=diamond},
        milestone height=0.5
    ]{1}{24}
    
    % Timeline headers
    \gantttitle{2026}{12}
    \gantttitle{2027}{12} \\
    \gantttitle{Spring}{4}
    \gantttitle{Summer}{4}
    \gantttitle{Fall}{4}
    \gantttitle{Spring}{4}
    \gantttitle{Summer}{4}
    \gantttitle{Fall}{4} \\
    
    % Major thrusts
    \ganttbar{Thrust 1: Procedure Translation}{1}{5} \\
    \ganttbar{Thrust 2: Discrete Synthesis}{4}{10} \\
    \ganttbar{Thrust 3: Continuous Control}{9}{15} \\
    \ganttbar{Integration \& Simulation (TRL 4)}{13}{17} \\
    \ganttbar{Hardware-in-Loop Testing (TRL 5)}{16}{21} \\
    \ganttbar{Dissertation Writing}{18}{24} \\[grid]
    
    % Milestones row
    \ganttbar[bar/.append style={fill=orange!50}]{Milestones}{1}{24}
    \ganttmilestone{}{4}
    \ganttmilestone{}{8}
    \ganttmilestone{}{12}
    \ganttmilestone{}{16}
    \ganttmilestone{}{20}
    \ganttmilestone{}{24} \\
    
    % Publications row
    \ganttbar[bar/.append style={fill=green!50}]{Publications}{1}{24}
    \ganttmilestone{}{8}
    \ganttmilestone{}{16}
    \ganttmilestone{}{20}
    
    \end{ganttchart}
    \caption{Project schedule showing major research thrusts, milestones (orange row), and publications (green row). Red diamonds indicate completion points. Overlapping bars indicate parallel work where appropriate.}
    \label{fig:gantt}
\end{figure}

\subsection{Milestones and Deliverables}

Six major milestones mark critical validation points throughout the research. M1
(Month 4) confirms that startup procedures have been successfully translated to
temporal logic using FRET with realizability analysis demonstrating consistent
and complete specifications. M2 (Month 8) validates computational tractability
by demonstrating that Strix can synthesize a complete discrete automaton from
the formalized specifications. This milestone delivers a conference paper
submission to NPIC\&HMIT documenting the procedure-to-specification translation
methodology. M3 (Month 12) achieves TRL 3 by proving that continuous controllers
can be designed and verified to satisfy discrete transition requirements. This
milestone delivers an internal technical report demonstrating component-level
verification. M4 (Month 16) achieves TRL 4 through integrated simulation
demonstrating that component-level correctness composes to system-level
correctness. This milestone delivers a journal paper submission to IEEE
Transactions on Automatic Control presenting the complete hybrid synthesis
methodology. M5 (Month 20) achieves TRL 5 by demonstrating practical
implementability on industrial hardware. This milestone delivers a conference
paper submission to NPIC\&HMIT or CDC documenting hardware implementation and
experimental validation. M6 (Month 24) completes the dissertation documenting
the entire methodology, experimental results, and research contributions. 
