Current Focus: Dynamics and optimal collective control of large scale interacting nonlinear systems
The overaching goal is to develop methods for design and control of macroscropic behavior of large population interacting nonlinear systems, where the agents are partially controllable, control authority is limited and interactions arise from structural, hydrodynamics, contact or social forces. We use the continuum approximation, and work with densities/ensembles of agents.
On theory side, our recent work has focussed on adapting optimal transport theory for optimal control of distributions, as well as on developing low-order models for mean-field games (MFG) systems, and the associated analysis of bifurcations/phase transitions. The aim is to devise computationally tractable methods for inverse design of collective behavior of large population of interacting dynamic (real or virtual) agents, and understand/implement emergent behavior.
The applications of interest include swarm robotics, mixed manual-autonomous traffic, active fluids/nematics, and functional active metamaterials.
Model reduction and Optimization of (thermo-)fluid systems: Work in this area has focussed on 1). applying optimal control and large scale optimization methods to problems of airflow design and control in indoor environment, 2). Use of Data-driven operator theoretic methods (such as Dynamic Mode Decompositions (DMD)) for sparse sensing of bifurcations in complex flows, and 3). DNS based assessment of 1D reduced order models for Rayleigh-Benard convection.
Mixing in laminar fluid flows: This work developed topological and operator-theoretic tools for quantifying mixing in laminar flows, including bifurcation/breakup of almost-invariant sets.
Nonlinear vibration mitigation, and nonlinear energy transfers : This work involves analytically and numerically characterizing energy transfers in nonlinear energy sinks (NES) in multi-degree-of-freedom systems, by studying the low-order Hamiltonian approximations of the lightly damped systems.
Low-energy mission design in the three-body system : Low-fuel trajectories for multi-moon orbiter in the Jupiter system, as well as a lunar mission, were designed to exploit the sensitive dynamics of the restricted three-body problem.