Research @DSL is carried out at the interface of dynamical systems theory, control and optimization. We focus on:
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Geometric and topological methods in dynamical systems
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Data-driven operator theoretic methods (Perron-Frobenius/Koopman) for analysis and control
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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:
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Swarm robotics and large-population multi-agent control systems (paper1, paper2, paper3, video)
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Active fluids/nematics ( paper1)
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Nonlinear dynamics and design of functional passive/active metamaterials.
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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,Video1, Video2)
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,Video1, Video2)
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)
Funding
