A5075822666- Micro and Nano Robotics
- Fluid Dynamics and Turbulent Flows
- Model Reduction and Neural Networks
- Transportation Planning and Optimization
- Nonlinear Dynamics and Pattern Formation
- Traffic control and management
- Advanced Thermodynamics and Statistical Mechanics
- Wind and Air Flow Studies
- Mathematical Biology Tumor Growth
- Astro and Planetary Science
- Stochastic processes and financial applications
- Spacecraft Dynamics and Control
- Mathematical Dynamics and Fractals
- Computational Fluid Dynamics and Aerodynamics
- Aerospace Engineering and Control Systems
- Lattice Boltzmann Simulation Studies
- Meteorological Phenomena and Simulations
- Mathematical and Theoretical Epidemiology and Ecology Models
- Pickering emulsions and particle stabilization
- Target Tracking and Data Fusion in Sensor Networks
- Quantum chaos and dynamical systems
- Complex Systems and Time Series Analysis
- Advanced Materials and Mechanics
- Reinforcement Learning in Robotics
- Adaptive Dynamic Programming Control
University of Nebraska–Lincoln
2019-2025
Mitsubishi Electric (United States)
2012-2020
Brandeis University
2020
Pennsylvania State University
2020
Georgia Institute of Technology
2018
American Institute of Aeronautics and Astronautics
2016
Massachusetts Institute of Technology
2016
Mitsubishi Electric (Japan)
2013-2014
Virginia Tech
2009-2011
We present a sparse sensing framework based on Dynamic Mode Decomposition (DMD) to identify flow regimes and bifurcations in large-scale thermo-fluid systems. Motivated by real-time control of thermal-fluid flows buildings equipment, we apply this method Direct Numerical Simulation (DNS) data set 2D laterally heated cavity. The resulting solutions can be divided into several regimes, ranging from steady chaotic flow. DMD modes eigenvalues capture the main temporal spatial scales dynamics...
In this work we present the first systematic framework to sculpt active nematic systems, using optimal control theory and a hydrodynamic model of nematics. We demonstrate use two different fields, (i) applied vorticity (ii) activity strength, shape dynamics an extensile that is confined disk. absence inputs, system exhibits attractors, clockwise counterclockwise circulating states characterized by co-rotating topological +1/2 defects. specifically seek spatiotemporal inputs switch from one...
Mean-field games (MFGs) provide a statistical physics-inspired modelling framework for decision-making in large populations of strategic, non-cooperative agents. Mathematically, these systems consist forwards–backwards time-system two coupled nonlinear partial differential equations (PDEs), namely, the Fokker–Plank (FP) and Hamilton–Jacobi–Bellman (HJB) equations, governing agent state control distribution, respectively. In this work, we study finite-time MFG with rich global bifurcation...
The deformable and continuum nature of soft robots promises versatility adaptability. However, control modular, multi-limbed for terrestrial locomotion is challenging due to the complex robot structure, actuator mechanics robot-environment interaction. Traditionally, performed by modeling kinematics using exact geometric equations finite element analysis.
Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic "active turbulence." Here, we study these phenomena using the framework of exact coherent structures, which has been successful in characterizing routes to high Reynolds number turbulence passive fluids. Exact structures are stationary, periodic, quasiperiodic, or traveling wave solutions hydrodynamic equations that, together with their invariant manifolds, serve as an...
The design of fuel-efficient trajectories that visit different moons a planetary system is best handled by breaking the problem up into multiple three-body problems. This approach, called patched has received considerable attention in recent years and proved to lead substantial fuel savings compared with traditional patched-conic approach. We consider designing multimoon orbiter spacecraft Jupiter―Europa―Ganymede realistic transfer times. First, fuel- optimal (i.e., near-zero-fuel) without...
In certain (2+1)-dimensional dynamical systems, the braiding of periodic orbits provides a framework for analyzing chaos in system through application Thurston-Nielsen classification theorem. Periodic generated by dynamics can behave as physical obstructions that "stir" surrounding domain and serve basis this topological analysis. We provide evidence that, even absence orbits, almost-cyclic regions identified using transfer operator approach reveal an underlying structure enables analysis domain.
Empirically derived continuum models of collective behavior among large populations dynamic agents are a subject intense study in several fields, including biology, engineering, and finance. We formulate mean-field game model whose mimics an empirically nonlocal homogeneous flocking for with gradient self-propulsion dynamics. The framework provides non-cooperative optimal control description the population distributed setting. In this description, each agent's state is driven by optimally...
This letter considers the relaxed version of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">transport problem</i> for general nonlinear control systems, where objective is to design time-varying feedback laws that transport a given initial probability measure target under action closed-loop system. To make problem analytically tractable, we consider are xmlns:xlink="http://www.w3.org/1999/xlink">stochastic</i> , i.e., maps from state space...
In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in system through application Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced TNCT almost-cyclic sets, which are individual components almost-invariant sets [Stremler et al., “Topological and sets,” Phys. Rev. Lett. 106, 114101 (2011)]. this context, regions flow with high local residence time act as stirrers or “ghost rods” around...
We study the dynamics of solitary waves traveling in a one-dimensional chain bistable elements presence local inhomogeneity (``defect''). Numerical simulations reveal that depending upon its initial speed, an incoming wave can get transmitted, captured, or reflected interaction with defect. The are dominated by energy exchange between and breather mode localized at derive reduced-order two degree freedom Hamiltonian model for wave-breather analyze it using dynamical systems techniques. Lobe...
A novel method for reduced-order modeling of turbulent flows is discussed in the context fully Rayleigh-B\'enard convection. The can be used to control mean profiles, discern spectral properties flows, and improve data-driven techniques.
The recently introduced feedback particle filter (FPF) is a control-oriented (PF), aimed at estimation of nonlinear/non-Gaussian systems. FPF controls each using from the measurements and resampling free, which in contrast to conventional PFs based on importance sampling. control gains are computed by solving boundary value problems. In general, numerical approximations required it an open question how properly compute approximate solution. This paper outlines novel method inspired...
We present results on stabilization for reduced order models (ROM) of partial differential equations using learning. Stabilization is achieved via closure ROMs, where we use a model-free extremum seeking (ES) dither-based algorithm to optimally learn the models' parameters. first propose auto-tune linear ES, and then extend model combining nonlinear terms, better performance. The coupled Burgers' equation employed as test-bed proposed tuning method.
Mean field games (MFG) have emerged as a viable tool in the analysis of large-scale self-organizing networked systems. In particular, MFGs provide game-theoretic optimal control interpretation emergent behavior noncooperative agents. The purpose this paper is to study MFG models which individual agents obey multidimensional nonlinear Langevin dynamics, and analyze closed-loop stability fixed points corresponding coupled forward-backward partial differential equation (PDE) such models,...
Active fluids operating at negligible Reynolds numbers can exhibit spontaneous coherent motion, dynamical vortex patterns, and mesoscale turbulence. We employ tools from nonlinear systems theory to uncover the global phase space of two-dimensional active nematic channel flow. compute several Exact Coherent Structures (ECSs), which are exact solutions physical dynamics with distinct regular spatiotemporal structure; examples include unstable equilibria, periodic orbits, traveling waves....
We present a set-oriented graph-based computational framework for continuous-time optimal transport over nonlinear dynamical systems. recover provably control laws steering given initial distribution in phase space to final prescribed finite time the case of non-autonomous control-affine systems, while minimizing quadratic cost. The resulting law can be used obtain approximate feedback individual agents swarm application. Using infinitesimal generators, problem is reduced modified...
This paper focuses on an application of dynamic mode decomposition (DMD) identification methods and robust estimation theory to thermo-fluid systems modelled by the Boussinesq equations. First, we use Dynamic Mode Decomposition with control (DMDc) construct a reduced order linear model for Due inherent uncertainties in real applications, propose estimators that minimize H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm from...
This paper formulates a class of partial differential equation (PDE) control problems as reinforcement learning (RL) problem. We design an RL-based algorithm that directly works with the state PDE, infinite dimensional vector, thus allowing us to avoid model order reduction, commonly used in conventional PDE controller approaches. apply method problem flow for time-varying 2D convection-diffusion simplified heating, ventilating, air conditioning (HVAC) room.
This paper addresses the continuous discrete-time nonlinear filtering problem for stochastic dynamical systems using feedback particle filter (FPF). The FPF updates each from measurements, where gain function that controls particles is solution of a Poisson equation. main difficulty in to approximate this probability distribution. We develop novel Galerkin-based method inspired by high-dimensional data-analysis techniques. Based on time evolution cloud, we determine basis functions and...
Recent work has shown that reinforcement learning (RL) is a promising approach to control dynamical systems described by partial differential equations (PDE). This paper shows how use RL tackle more general PDE problems have continuous high-dimensional action spaces with spatial relationship among dimensions. In particular, we propose the concept of descriptors, which encode regularities spatially-extended dimensions and enable agent PDEs. We provide theoretical evidence suggesting this can...