Dynamical Systems Lab


Areas of Research

Dynamical Systems theory, control and optimization:

  • Geometric and topological methods in dynamical systems
  • 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)

Applications to:

  • Large-scale multi-agent systems (swarm robotics, traffic)
  • Microfluidics and active fluids (chaotic mixing, topological chaos, flow control)
  • Metamaterial design (Energy transfers in nonlinear media)
  • Atmospheric Flows (Reduced-order modeling , LiDAR data-assimilation)
  • Astrodynamics (Low-energy space mission design)
  • Buoyancy driven flow in built environment (control of HVAC)

Dynamical Systems Lab (DSL), led by Prof. Piyush Grover in Mechanical and Materials Engineering (MME) at University of Nebraska-Lincoln, focusses on developing analysis, control and optimization methods for nonlinear dynamical systems, and their application to several areas including large-scale multi-agent robotics, fluid mechanics, structural mechanics/nonlinear vibration and astrodynamics. Dynamical systems and control theory provides a strong foundation for tackling problems in (solid/fluid/bio) mechanics, and robotics, among other areas.

Updates:

      • Sept 2020: Paper with colleagues from Georgia Tech, accepted at Conference on Decision and Control (CDC 2020) 'Stabilizing Optimal Density Control of Nonlinear Agents with Multiplicative Noise'. Preprint coming soon.

      • August 2020:  Caleb Wagner will join the group as a postdoctoral researcher, after finishing his Ph.D. in non-equilibrium statistical mechanics at Brandeis University.

      • July 2020: Check out our new preprint "Optimal Control of Active Nematics" with Mike Norton and collaborators.  Accepted at Physical Review Letters (9/18)
      • May 2020:  New undergraduate online course "Nonlinear Dynamics and Chaos' will be offered during 8 week summer session (MECH 98-401, May 18-July 10). Sign up now to learn about this exciting topic. 
        • April 2020:  Our paper 'Optimization-based incentivization and control scheme for autonomous traffic' with Uros Kalabic (MERL) and Shuchin Aeron (Tufts) on PDE based optimal control of mixed manual-autonomous traffic accepted to IEEE Intelligent Vehicles 2020. Preprint here
        • Feb 2020:  Joint work with Mike Norton on optimal control of active nematics  will be presented by Mike at the APS March Meeting.
          • Jan 2020: Paper accepted at American Control Conference (ACC 2020) with colleagues from MERL and Univ. Minnesota on robust estimation of airflow in buildings. Preprint forthcoming.
          • Nov 2019: Conference APS Division of Fluid Dynamics Meeting Nov 2019: 2 Talks with collaborators from MERL and Univ. Cambridge.
          • Oct 2019: New poster on LiDAR based data assimilimation.
          • Oct 2019: A new postdoctoral position is available. See ad here.
          • Sept 2019: New paper with colleagues from MERL and Univ. Cambridge on optimal control of airflow in buildings.