Senior Thesis (April 2026)

Nonlinear transmission lines (NLTLs) provide a practical platform for generating high-power, ultrashort electrical pulses, but their design remains largely heuristic and relies on continuum approximations for small-amplitude pulses. This work develops a computational framework for designing NLTLs that support localized, large-amplitude solitons directly at the level of the discrete lattice dynamics. Starting from an LC-ladder model, with voltage-dependent capacitors, we formulate the problem of selecting NLTL parameters as an optimization over traveling-wave solutions of the infinite lattice dynamics. Motivated by high-power ultrawideband applications, an objective, based on the spread of the pulse's energy, is introduced to quantify pulse localization. Feasible solutions are found numerically to lie on a one-dimensional curve in the parameter space, with larger solitons observed to be more localized. Time-domain simulations of the found solutions propagating through the lattice show that these appear dynamically stable. In addition, we show through numerical experiments that a trapezoidal pulse on the NLTL evolves into a train of localized pulses with amplitude-dependent speeds. These findings provide evidence that large-amplitude solitary waves exist in discrete NLTLs and are asymptotically stable.

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A System Level Approach to LQR Control of the Diffusion Equation

Accepted for publication and presentation at the 2026 American Control Conference.

Abstract - The continuous-time, infinite horizon LQR problem for the diffusion equation over the unit circle with fully distributed actuation is considered. It is well-known that the solution to this problem can be obtained from the solution to an operator-valued algebraic Riccati equation. Here, it is demonstrated that this solution can be equivalently obtained by solving an H₂ control problem through a closed-loop design procedure that is analogous to the "System Level Synthesis" methodology previously developed for systems over a discrete spatial domain and/or over a finite time horizon. The presented extension to the continuous spatial domain and continuous and infinite-horizon time setting admits analytical solutions that may complement computational approaches for discrete or finite-horizon settings. It is further illustrated that spatio-temporal constraints on the closed-loop responses can be incorporated into this new formulation in a convex manner.

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Optimal Control of Soft Robotic Crawlers Subject to Nonlinear Friction: A Perturbation Analysis Approach

Published in IEEE Control Systems Letters, DOI: 10.1109/LCSYS.2025.3581875.
Presented at the 64th IEEE International Conference on Decision and Control.

Abstract - This paper considers the dynamics of a limbless, soft-robotic crawler, modeled as a nonlinear wave equation, subject to a sliding friction force modeled as an asymmetric and nonlinear function that captures the effects of both wet and dry friction present in physical scenarios. A reduced-order model of the dynamics is formed utilizing perturbation method techniques. This reduced-order model is solved analytically and solutions are validated by comparison to numerical solutions for the full dynamics of a soft-robotic crawler in a sewer pipe. This analytic solution to the reduced-order approximation of the dynamics is utilized to derive expressions for the resulting velocity, energy, mileage (efficiency), and engineering stress of a crawler. Assuming actuation that takes the form of a periodic traveling wave, an open-loop control design problem to maximize velocity subject to mileage and stress constraints is formulated and solved numerically.

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Sectorial Operators and Stability of Parabolic Partial Differential Equations

This paper was written as a final project for a graduate course in Nonlinear Controls (ECEN 5738). The paper is a technical overview of a generalization of stability analysis for ordinary differential equations to systems modeled by partial differential equations, using semigroup theory, operator theory, and Complex Analysis. A 25-minute lecture was delivered in-class to accompany the project notes.

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