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%     {\Large \scshape Cover Letter} \\[2pt]
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%     {Amitabh Sharma}
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% \hspace*{-16pt}Dear Professor Deka,

% \vspace{10pt}

% I am writing to express my strong interest in the Doctoral Researcher position in the Nonlinear Systems and Control group at Aalto University. As a Graduate Research Associate at the Robotics Research Center, IIIT Hyderabad, I have spent the past two years designing and experimentally validating adaptive and impedance control strategies for robotic systems performing dynamic interaction tasks under uncertain system dynamics and environmental disturbances.

% \vspace{4pt}
% My research focuses on coupling rigorous Lyapunov-based stability analysis with full-stack experimental pipelines built around \textbf{ROS/ROS~2}, \textbf{PX4}, \textbf{Gazebo}, and \textbf{Isaac~Sim}. This ``simulation-to-hardware" workflow has enabled seamless deployment of controllers from GPU-accelerated simulations to hardware-in-the-loop experiments on aerial manipulators and multi-rotor platforms. My work emphasizes provable guarantees on performance and robustness, aligning closely with your group's mission to develop data-driven methodologies for learning control policies with formal guarantees.

% \section*{Selected Contributions}
% \begin{itemize}[leftmargin=0.2in,noitemsep,topsep=0pt]
%     \item \textbf{Adaptive Impedance Control for Aerial Manipulation}: Developed an Adaptive Impedance Control law ensuring uniformly ultimately bounded tracking and Impedance errors despite unknown vehicle–arm coupling dynamics~\cite{Impedance}.
%     \item \textbf{Integrated Grasp-and-Flight Architecture}: Designed an Adaptive Sliding Mode based control law for stable aerial grasping without prior bounds on model uncertainties~\cite{TMECH}.
%     \item \textbf{Fault-Tolerant Quadrotor Control}: Proposed a controller compensating for actuator loss-of-efficiency and state-dependent disturbances, validated in simulation~\cite{FTC}.
% \end{itemize}

% \section*{Fit with Nonlinear Systems and Control Group}
% Your group's work on nonlinear stability theory, system modeling, learning-based control, and control with formal guarantees resonates deeply with my research interests. In the course of my master's, I have realized that with the rapid progress in technology, there is a need for giving stronger guarantees on the behavior of systems, be it a robot or a neural network. Obtaining a guaranteed and reliable behavior from a system is possible with tools from systems and control theory. My experience with adaptive control for uncertain systems and hands-on expertise with robotic platforms have given me exposure to working with practical systems, along with a zeal to dive into the axiomatic thought process of a mathematician. 

% \vspace{4pt}
% I would love to work on problems involving computation of Lyapunov and barrier functions, along with slowly expanding my knowledge towards operator theoretic representations of dynamical systems, given my lack of exposure to any formal courses in the domain. My gaps in knowledge although may seem glaring at first, but being able to identify what I do not yet know, allows me to see what I should next learn. Which I believe makes me a strong Doctoral Research Candidate.

% \vspace{4pt}
% Thank you for considering my application. I would be honored to discuss how my skills and research interests align with your group's goals and to provide any additional information.

% \vspace{10pt}
% \begin{flushleft}
% Sincerely,\\[4pt]
% Amitabh Sharma\\
% Robotics Research Center, IIIT~Hyderabad\\
% \href{mailto:amitabh.sharma@research.iiit.ac.in}{amitabh.sharma@research.iiit.ac.in}
% \end{flushleft}

% \vspace{0.5cm}
% \begin{thebibliography}{99}
% \bibitem{TMECH}\href{https://arxiv.org/abs/2311.00769}{R.~D. Yadav \emph{et~al.}, \textit{An Integrated Approach to Aerial Grasping: Combining a Bistable Gripper with Adaptive Control}, arXiv:2311.00769, 2023.}
% \bibitem{Impedance}\href{https://arxiv.org/abs/2504.01983}{A.~Sharma \emph{et~al.}, \textit{Impedance and Stability Targeted Adaptation for Aerial Manipulator with Unknown Coupling Dynamics}, arXiv:2504.01983, 2025.}
% \bibitem{FTC}\href{https://ieeexplore.ieee.org/abstract/document/10711418}{S.~Gupta \emph{et~al.}, \textit{Adaptive Control of Quadrotor under Actuator Loss and Unknown State‑Dependent Dynamics}, Proc.\ IEEE CASE, 2024.}
% \end{thebibliography}

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\begin{document}

\begin{center}
    {\Large \scshape Motivation Letter} \\[2pt]
    \vspace{4pt}
    {Amitabh Sharma}
\end{center}

\hspace*{-16pt}Dear Professor Deka,

\vspace{10pt}

I am writing to express my strong interest in the Doctoral Researcher position in the Nonlinear Systems and Control group at Aalto University. As a Graduate Research Associate at the Robotics Research Center, IIIT Hyderabad, I have spent the past two years designing and experimentally validating adaptive and impedance control strategies for robotic systems performing dynamic interaction tasks under uncertain dynamics and environmental disturbances.

\vspace{4pt}
My research integrates rigorous Lyapunov-based stability analysis with full-stack experimental pipelines using \textbf{ROS/ROS~2}, \textbf{PX4}, \textbf{Gazebo}, and \textbf{Isaac~Sim}. This ``simulation-to-hardware" workflow enables seamless controller deployment from GPU-accelerated simulations to hardware-in-the-loop experiments on aerial manipulators and multi-rotor platforms. My work emphasizes provable guarantees on performance and robustness, aligning closely with your group's mission to develop data-driven methodologies for learning control policies with formal guarantees on safety and performance.

\section*{Selected Contributions}
\begin{itemize}[leftmargin=0.2in,noitemsep,topsep=0pt]
    \item \textbf{Adaptive Impedance Control for Aerial Manipulation}: Developed an adaptive impedance control law ensuring uniformly ultimately bounded tracking and impedance errors despite unknown vehicle–arm coupling dynamics~\cite{Impedance}.
    \item \textbf{Integrated Grasp-and-Flight Architecture}: Designed an adaptive sliding mode control law for stable aerial grasping without prior bounds on model uncertainties~\cite{TMECH}.
    \item \textbf{Fault-Tolerant Quadrotor Control}: Proposed a controller compensating for actuator loss-of-efficiency and state-dependent disturbances, validated in simulation~\cite{FTC}.
\end{itemize}

\section*{Fit with Nonlinear Systems and Control Group}
Your group's pioneering research in merging nonlinear stability theory with physics-informed machine learning, particularly in learning Lyapunov and barrier functions, deeply resonates with my research interests. I am motivated by the need to provide formal guarantees for complex systems, such as robots or neural networks, operating under uncertainty. My experience in adaptive control and hands-on expertise with robotic platforms has equipped me with a strong foundation in practical system design and theoretical analysis, which I aim to leverage in your group’s pursuit of certifiably safe and robust control.

\vspace{4pt}
While my current expertise centers on deterministic control, I am eager to expand my knowledge into data-driven methods for computing Lyapunov functions and operator-theoretic representations of dynamical systems. I view my limited formal exposure to these areas not as a gap, but as an opportunity to grow under your guidance and through Aalto’s vibrant research community. Hence, for all these reasons I believe I am a strong fit for this position.

\vspace{4pt}
Thank you for considering my application. I would be honored to discuss how my skills and research interests align with your group’s goals and to provide any additional information.

\vspace{4pt}
\begin{flushleft}
Sincerely,\\
Amitabh Sharma\\
Robotics Research Center, IIIT~Hyderabad\\
\href{mailto:amitabh.sharma@research.iiit.ac.in}{amitabh.sharma@research.iiit.ac.in}
\end{flushleft}

\vspace{0.5cm}
\begin{thebibliography}{99}
\bibitem{TMECH}\href{https://ieeexplore.ieee.org/abstract/document/11098573}{R.~D. Yadav \emph{et~al.}, \textit{An Integrated Approach to Aerial Grasping: Combining a Bistable Gripper with Adaptive Control}, IEEE/ASME Transactions on Mechatronics}
\bibitem{Impedance}\href{https://arxiv.org/abs/2504.01983}{A.~Sharma \emph{et~al.}, \textit{Impedance and Stability Targeted Adaptation for Aerial Manipulator with Unknown Coupling Dynamics}, accepted at 25th International Conference on Control, Automation, and Systems.}
\bibitem{FTC}\href{https://ieeexplore.ieee.org/abstract/document/10711418}{S.~Gupta \emph{et~al.}, \textit{Adaptive Control of Quadrotor under Actuator Loss and Unknown State‑Dependent Dynamics}, Proc.\ IEEE CASE, 2024.}
\end{thebibliography}

\end{document}