DrThulasiMylvaganam

The focus of Thulasi's research is on nonlinear control theory. She has worked on several topics including mean-field games, coverage control and differential games. Her current research interests include differential games, control of multi-agent systems, distributed control, nonlinear output feedback design and control theoretic approaches to numerical methods. 

Some key contributions made by Thulasi are the following.

Constructive Approximate Solutions for Differential Games 
Game theory and differential games can model a large variety of phenomena. The differential game framework also provides a powerful tool in the design of systems from a control theoretic perspective. However, solving a differential game typically involves solving a system of partial differential equations. 

Systematic methods for constructing approximate solutions of (linear and nonlinear) differential games have been developed. These methods only require solving a system of algebraic equations (in place of partial differential equations) and the level of approximation is quantifiable through the new notion of ε_α-Nash equilibrium solutions. 

Multi-Agent Collision Avoidance  
A system of, possibly homogeneous, agents form a multi-agent system. The problem of designing control strategies for autonomously maneuvering such a system of agents while avoiding collisions (with other agents and with obstacles) can be formulated as a nonlinear differential game. Approximate solutions to the resulting differential game can be constructed in a systematic way and (local) stability results can be proved.  

Simulation videos of two scenarios can be viewed and/or downloaded here.

Numerical Analysis Using Control Theoretic Concepts and Tools
There are several parallels between numerical methods and certain problems studied in control theory. These parallels can be exploited to develop novel iterative algorithms for solving large-scale systems of equations.