A Page on Research Notes
Welcome! I’m launching this page to share some insights that come to mind while working on research. I usually explore and read about topics related to nonlinear systems, sensor placement, combinatorial optimization (submodular optimization) and control-theoretic applications in infrastructure networks.
If any idea sparks your interest, please let me know.
Robust Partitioning for Renewable-Heavy Power Networks
In this post, I’ll share insights from my current research on robust partitioning for renewable-heavy power networks using submodular optimization techniques—a paper I’m preparing for submission to PSCC 2026.
Renewables and Grid Complexity
Modern power grids are undergoing a fundamental transformation. With increasing integration of renewable energy resources (RERs) like solar and wind, we’re seeing:
- Intermittency and variability from renewable sources
- Decentralized generation replacing traditional centralized plants
- Complex interactions between conventional and inverter-based resources
- Higher vulnerability to cascading failures
Traditional grid partitioning approaches fall short because they rely on simplified linear models or static graph-theoretic methods that don’t capture the dynamic complexity of renewable-heavy systems.
Understanding Observability in Nonlinear Systems
In this post, I’ll explore the basics of observability in nonlinear systems—a topic central to my research.
What Is Observability?
Observability refers to whether a system’s internal state can be inferred from its outputs over time.
For a nonlinear system:
$$ \dot{x}(t) = f(x(t), u(t)),$$ $$ y(t) = h(x(t)), $$
where:
- $x(t) \in \mathbb{R}^n$ is the state,
- $u(t) \in \mathbb{R}^m$ is the input,
- $y(t) \in \mathbb{R}^p$ is the output.
We say the system is locally observable at $x_0$ if different initial states around $x_0$ produce different outputs.