As an Associate Research Scientist at the University of California, Irvine, I have been actively engaged in pioneering research spanning diverse domains, contributing to advancements in Discrete Curvature, Fractional Control Systems, Machine Learning, Neural Networks, and Graph and Network Science.
Model Predictive Control for Drones with Robotic Arms
A model predictive controller (MPC) has been developed for drones equipped with robotic arms to enhance the robustness and reliability of load transportation tasks. The design and simulation of the control system have been conducted using MATLAB Simscape.
Graph and Network Science
In the realm of Graph and Network Science, this research develops innovative concepts pertaining to torsion and circulation within graph structures. The primary objective is to quantitatively assess global features associated with functionality. This analytical approach holds significant importance in the identification of critical nodes and vulnerable links within networks, be they representative of traffic patterns, neuronal activity, or the propagation of excitation within the active tissue of the heart. The overarching aim is to contribute to a nuanced understanding of network dynamics, facilitating the enhancement of efficiency and resilience across diverse domains. The application of these insights has the potential to optimize complex systems by pinpointing key components and weak links, thereby informing strategies for improved performance and robustness.
Machine Learning and Neural Networks
The research centers on applying H∞ robust control techniques to neural networks and machine learning algorithms, with the goal of augmenting their ability to withstand adversarial attacks.
Discrete Curvature
Investigated the concept of “curvature” in discrete spaces, and explored applications in image processing, Graph theory, and Network analysis.
Fractional Control Systems
Investigated a specialized Bode integral limitation for irrational systems, integrating fractal PID controllers to enhance control capabilities.
Complex Dynamical Systems
Investigated a time domain approach to the dynamics of complex systems, utilizing nonlinear and statistical techniques. Developed a Kolmogorov-Sinai information theoretic technique to determine causality/feedback relations, with a focus on heart dynamics.
Cooperative Control/Game Theory
Developed a stable, real-time, curvature-driven control strategy for a network of mobile autonomous sensing agents. This strategy enables cooperative movement and reconfiguration in response to a sensed, distributed environment, providing a basis for effective self-organization.
Sensor Networks
Investigated the curvature of wireless sensor networks using clustering coefficient and Alexandrov angles. Utilized Gromov’s coarse geometry approach to the Riemannian model of graphs, balancing local details with a better understanding of global properties.
Hyperbolic Geometry
Explored the Gromov-hyperbolic δ or “fatness” of a hyperbolic geodesic triangle. Demonstrated, using Tarski-Seidenberg argument, that the δ scaled by the diameter of the triangle never exceeds 3/2 in a Riemannian manifold of constant nonpositive curvature.
Underactuated Mechanical Systems
Investigated a hovercraft model, analyzing system controllability, and designing controllers using both LDV and controlled Lagrangian methods.
Spatial 3-Body Problem
Investigated tracking periodic and quasi-periodic orbits around the L4 Lagrangian point of the spatial three-body problem (Sun-Jupiter-Asteroids) using the Linear Dynamically Varying (LDV) method.