Dynamical Systems Lab Research


Research @DSL is carried out at the interface of dynamical systems theory, control and optimization. We focus on: 
  • Geometric and topological methods in dynamical systems

  • Data-driven operator theoretic methods (Perron-Frobenius/Koopman) for analysis and control

  • Continuum approach to multi-agent system control and decision making (Mean-field control and mean-field games, Optimal Transport)

The current application areas of interest include:
  • Swarm robotics and large-population multi-agent control systems (paper1, paper2, paper3video)

  • Active fluids/nematics ( paper1)

  • Nonlinear dynamics and design of functional passive/active metamaterials.

  • Mixed manual-autonomous traffic control (paper1)

Past research projects:

Mixing and topology of chaos 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. (paper1,paper2,Video1Video2)

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 (paper1)

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. (paper1,Video1Video2)

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. (paper1,paper2,paper3)