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:

July 2021 : New NSF CMMI DCSD award will support our research on bifurcations and phase space analysis of Mean field games and mean field control problems.
July 2021: Invited talk at Active matter workshop @ Telluride Science Research Center, Colorado.
July 2021: Ph.D. Position: We are looking for a Ph.D. student in the area of active fluids. Please email me with any inquiries.
June 2021: Upcoming talks at: Midwest Thermodynamics and Statistical Mechanics Workshop, and ICRA workshop on nano and micro-robots.
May 2021: 3 Talks at SIAM Dynamical Systems Conference: On Mean field games, Exact coherent structures in active nematics, and control of active nematics
March 2021: Caleb presented work on Exact Coherent Structures in active nematics at APS

Oct 2020: Our paper Optimal Control of Active Nematics is highlighted in Physical Review Letters as Editor's Suggestion.

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.

Nov 2019: Presented work on mean-field games at UNL Math Department's Continuum Mechanics Seminar

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.

August 2019: DSL is established. We are looking for undergraduate and graduate students to join the lab.

July 2019: Workshop Particulate and Granular Networks, Max Planck Institute for Physics of Complex Systems, Dresden, Germany
June 2019:Workshop Crowds: Models and Control workshop, CIRM, Marseille, France
May 2019: Conference SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah. Presented a talk on MFG based flocking models and their stability analysis.