My research focuses on trajectory optimization and numerical methods, developing efficient algorithms to solve complex, constrained dynamic systems. Below is an overview of the computational tools, solvers, and publishing frameworks that power my computational pipeline.

Technical Stack

Domain Technologies & Libraries Application in Research
Optimization & Dynamics CasADi • IPOPT • JAX Non-linear programming (NLP) transcription, automatic differentiation, interior-point solving, and accelerated gradient computations.
Numerical Computing Python • NumPy • SciPy Numerical integration of dynamic systems, linear algebra operations, state estimation, and custom algorithm development.
Data Visualization Matplotlib • draw.io Publication-ready phase plots, state/control histories, convergence curves, and system schematics.
Publishing & Web LaTeX • Markdown • Jekyll Rigorous mathematical typesetting, reproducible project notes, and static site maintenance.

Methodology & Workflows

1. Trajectory Optimization & Optimal Control

  • Direct Methods: Transcribing continuous-time optimal control problems into discrete non-linear programs using CasADi via direct collocation and multiple shooting techniques.
  • Large-Scale Solvers: Interfacing transcriptions with IPOPT to solve high-dimensional trajectory optimization problems under state and control constraints.
  • Algorithmic Differentiation: Leveraging JAX for vectorized computations, fast gradient calculations, and parallelized trajectory rollouts.

2. Numerical Simulation & Analysis

  • Dynamic Simulation: Building dynamic forward-simulation pipelines using NumPy and SciPy differential equation solvers for trajectory validation.
  • Performance Benchmarking: Analyzing convergence rates, execution times, and solver robustness across initial state estimates.

3. Scientific Communication

  • Publication Graphics: Generating vector graphics and high-resolution plots via Matplotlib, paired with structural system diagrams created in draw.io.
  • Typesetting & Documentation: Deriving theoretical formulations in LaTeX and integrating documentation into Jekyll using Markdown.