## About

60

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Introduction

My research involves developing new analysis, control and optimization methods for nonlinear dynamical systems, and their applications.
Current areas of focus are: active matter, mean-field control theory, mean-field game theory and nonlinear waves in mechanical metamaterials.

## Publications

Publications (60)

We present a sparse sensing and Dynamic Mode Decomposition (DMD) based
framework to identify flow regimes and bifurcations in complex thermo-fluid
systems. Motivated by real time sensing and control of thermal fluid flows in
buildings and equipment, we apply this method to a Direct Numerical Simulation
(DNS) data set of a 2D laterally heated cavity...

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game model whose behavior mimics an empirically derived non-local homogeneous flocking model for agents with gradient...

In this work we present the first systematic framework to sculpt active nematics systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (1) applied vorticity and (2) activity strength, to shape the dynamics of an extensile active nematic that is confined to a disk....

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 the routes to high Reynolds number turbulence of passive fluids. Exact coherent...

We study the dynamics of solitary waves traveling in a one-dimensional chain of bistable elements in the presence of a local inhomogeneity (‘defect’). Numerical simulations reveal that depending upon its initial speed, an incoming solitary wave can get transmitted, captured or reflected upon interaction with the defect. The dynamics are dominated b...

We compare the performance of direct-adjoint-looping (DAL) and one-shot methods in a design optimization task involving turbulent flow modeled using Reynolds-Averaged-Navier–Stokes equations. Two preconditioned variants of the one-shot algorithm are proposed and tested. The role of an approximate Hessian as a preconditioner for the one-shot method...

This paper presents a method of co-design of models and observers for buoyancy-driven turbulent flows. Recent work on data-driven techniques for estimating turbulent flows typically involve obtaining a dynamical model using Dynamical Mode Decomposition (DMD) and using the model to design estimators. Unfortunately, such a sequential design could res...

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 the routes to high Reynolds number turbulence of passive fluids. Exact Coherent...

Mean Field Games (MFGs) model a continuum of interacting agents, each of whom aims to minimize a cost that depends upon its own state and control effort, as well as the collective state of the population. Mathematically, MFGs are described by a coupled set of forward and backward in-time partial differential equations for state and control distribu...

Mean Field Game (MFG) systems model a continuum of agents, each of whom aims to minimize a cost that depends upon its own state and control effort, as well as the state of the population. Mathematically, MFGs are described by a coupled set of forward and backward in-time partial differential equations for state and control distributions, respective...

In this work we present the first systematic framework to sculpt active nematic systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (i) applied vorticity and (ii) activity strength, to shape the dynamics of an extensile active nematic that is confined to a disk....

We consider the problem of incentivization and optimal control of autonomous vehicles for improving traffic congestion. In our scenario, autonomous vehicles must be incentivized in order to participate in traffic improvement. Using the theory and methods of optimal transport, we propose a constrained optimization framework over dynamics governed by...

Control of continuous time dynamics with multi-plicative noise is a classic topic in stochastic optimal control. This work addresses the problem of designing infinite horizon optimal controls with stability guarantees for large populations of identical, non-cooperative and non-networked agents with multi-dimensional and nonlinear stochastic dynamic...

Naïve estimation of horizontal wind velocity over complex terrain using measurements from a single wind-LiDAR introduces a bias due to the assumption of uniform velocity in any horizontal plane. While Computational Fluid Dynamics (CFD)-based methods have been proposed for bias removal, there are several issues exist in the implantation. For instanc...

A wind flow sensing system determines a first approximation of the velocity field at each of the altitudes by simulating computational fluid dynamics ( CFD ) of the wind flow with operating parameters reducing a cost function of a weighted combination of errors , determines a horizontal derivative of vertical velocity at each of the altitudes from...

Motion of multiple agents with identical non - linear dynamics is controlled to change density of the agents from the initial to the final density . A first control problem is formulated for optimizing a control cost of changing density of the agents from the initial density to the final density subject to dynamics of the agents in a density space...

We consider the problem of optimally controlling turbulent buoyancy-driven flows in the built environment, focusing on a model test case of displacement ventilation with a time-varying heat source. The flow is modeled using the unsteady Reynolds-averaged equations (URANS). A direct-adjoint-looping implementation of the nonlinear optimal control pro...

Mean Field Games (MFG) have emerged as a promising tool in the analysis of large-scale self-organizing networked systems. The MFG framework provides a non-cooperative
game theoretic optimal control description of emergent behavior of large population of rational dynamic agents. Each agents state is driven by optimally controlled dynamics that resul...

Mean Field Games (MFG) have emerged as a viable tool in the analysis of large-scale self-organizing networked systems. In particular, MFGs provide a game-theoretic optimal control interpretation of emergent behavior of non-cooperative agents. The purpose of this paper is to study MFG models in which individual agents obey multidimensional nonlinear...

The ARC pilot plant conceptual design study has been extended beyond its initial scope [B. N. Sorbom et al., FED 100 (2015) 378] to explore options for managing ∼525 MW of fusion power generated in a compact, high field (B0 = 9.2 T) tokamak that is approximately the size of JET (R0 = 3.3 m). Taking advantage of ARC's novel design – demountable high...

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 to use RL to tackle more general PDE control problems that have continuous high-dimensional action spaces with spatial relationship among action dimensions. In particular...

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 to use RL to tackle more general PDE control problems that have continuous high-dimensional action spaces with spatial relationship among action dimensions. In particular...

A method controls an operation of an air - conditioning system generating airflow in a conditioned environment . The method updates a model of airflow dynamics connecting values of flow and temperature of air conditioned during the operation of the air - conditioning system . The model is updated interactively iteratively to reduce an error between...

A One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D Rayleigh-Bénard convection system in the turbulent regime with Rayleigh number Ra = 10 6. The state vector of the 1D ROM is horizontally averaged temperature. Using the Green's Function (GRF) method, which involves applying many localized, weak forcings to the system and c...

A One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D Rayleigh-Benard convection system in the turbulent regime with Rayleigh number $Ra=10^6$. The state vector of the 1D ROM is horizontally averaged temperature. Using the Green's Function (GRF) method, which involves applying many localized, weak forcings to the system and c...

A controller for controlling an operation of an air - conditioning system conditioning an indoor space includes a data input to receive state data of the space at multiple points in the space , a memory to store a code of a reinforcement learning algorithm and a history of the state data and a history of control commands having been applied to the...

This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability measure under the action of the closed-loop system. To make the problem analytically tractable, we consider co...

This paper addresses the continuous-discrete time nonlinear filtering problem for stochastic dynamical systems using the feedback particle filter (FPF). The FPF updates each particle using feedback from the measurements, where the gain function that controls the particles is the solution of a Poisson equation. The main difficulty in the FPF is to a...

We demonstrate the use of the ‘Direct-Adjoint-Looping method’ for the identification of optimal buoyancy-driven ventilation flows governed by Boussinesq equations. We use the incompressible Reynolds-averaged Navier-Stokes (RANS) equations, derive the corresponding adjoint equations and solve the resulting sensitivity equations with respect to inlet...

We demonstrate the use of the ‘Direct-Adjoint-Looping method’ for the identification of optimal buoyancy-driven ventilation flows governed by Boussinesq equations. We use the incompressible Reynolds-averaged Navier-Stokes (RANS) equations, derive the corresponding adjoint equations and solve the resulting sensitivity equations with respect to inlet...

Perron-Frobenius Meet Monge-Kantorovich: A Set-Oriented Graph-Based Approach to Optimal Transport

This paper formulates a class of partial differential equation (PDE) control problems as a reinforcement learning (RL) problem. We design an RL-based algorithm that directly works with the state of PDE, an infinite dimensional vector, thus allowing us to avoid the model order reduction, commonly used in the conventional PDE controller design approa...

Video of optimal transport in Double-gyre system

We present a set-oriented graph-based computational framework for continuoustime
optimal transport over nonlinear dynamical systems. We recover provably optimal
control laws for steering a given initial distribution in phase space to a final distribution
in prescribed finite time for the case of non-autonomous nonlinear control-affine
systems, whil...

We present a set-oriented framework for obtaining optimal discrete-time perturbations in nonlinear dynamical systems that transport a given phase space measure to a final prescribed measure in given finite time. The measure is propagated under system dynamics between the perturbations via the associated transfer operator. Each perturbation is descr...

We study the problem of optimizing the performance of a nonlinear spring–mass–damper attached to a class of multiple-degree-of-freedom systems. We aim to maximize the rate of one-way energy transfer from primary system to the attachment, and focus on impulsive excitation of a two-degree-of-freedom primary system with an essentially nonlinear attach...

We present results on stabilization for reduced order models (ROM) of partial
differential equations using learning. Stabilization is achieved via closure
models for ROMs, where we use a model-free extremum seeking (ES) dither-based
algorithm to learn the best closure models' parameters, for optimal ROM
stabilization. We first propose to auto-tune...

The deformable and continuum nature of soft robots promises versatility and adaptability. However, control of modular, multi-limbed soft robots for terrestrial locomotion is challenging due to the complex robot structure, actuator mechanics and robot-environment interaction. Traditionally, soft robot control is performed by modeling kinematics usin...

A method estimates a state of a spacecraft in a planet-moon environment by executing iteratively a particle filter. The particle filter comprising integrates individually states of each particle of the particle filter according to a probability-evolution equation using a model of the state of the spacecraft represented as a planar circular restrict...

In case of a failure on a Hohmann-type translunar trajectory, a reconfiguration of the trajectory that utilizes the three body dynamics of the interior realm of Earth-moon system is proposed. The stable manifold and unstable manifold of a periodic orbit around L1 point extended toward the Earth side have homoclinic intersections. In the proposed me...

A motion of an object is controlled from a geostationary transit orbit (GTO) of an earth to an orbit of a moon. A first trajectory of the motion of the object is determined from an intermediate orbit of an earth to a neighborhood of a stable manifold of a first Lagrange point (L1). A second trajectory of the motion of the object is determined from...

A motion of an object is controlled from a geostationary transit orbit (GTO) of an earth to an orbit of a moon. A first trajectory of the motion of the object is determined from an intermediate orbit of an earth to a neighborhood of a stable manifold of a first Lagrange point (L1). A second trajectory of the motion of the object is determined from...

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost...

The problem of efficient and accurate orbit estimation of space trajectories is discussed. For highly sensitive low-fuel trajectories designed to exploit the complex nonlinear dynamics of the three-body problem , it is vital to have accurate state estimation during maneuvers and ability to deal with irregular observation update times. For instance,...

We describe a modular optimization framework for GTO-to-moon mission design using the planar circular restricted three-body problem (PCR3BP) model. The three-body resonant gravity assists and invariant manifolds in the planar restricted three-body problem are used as basic building blocks of this mission design. The mission is optimized by appropri...

In certain (2+1)-dimensional dynamical systems, the braiding of periodic orbits provides a framework for analyzing chaos in the system through application of the Thurston-Nielsen classification theorem. Periodic orbits generated by the dynamics can behave as physical obstructions that "stir" the surrounding domain and serve as the basis for this to...

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We build upon our earlier work that showed the first application of the TNCT to braiding of almost-invariant sets (AIS). AIS in a fluid flow are reg...

In two-dimensional time-dependent flows or three-dimensional flows with a certain symmetry, the braiding of periodic orbits provides a framework for analyzing chaos in the system through application of the Thurston-Nielsen (TN) classification theorem. ``Ghost rods,'' or periodic orbits generated by the dynamics, behave as physical obstructions that...

The design of fuel-efficient trajectories that visit different moons of a planetary system is best handled by breaking the problem up into multiple three-body problems. This approach, called the patched three-body approach, has received considerable attention in recent years and has proved to lead to substantial fuel savings compared with the tradi...

For low energy spacecraft trajectories such as multi-moon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we outline a procedure to obtain a family of zero-fuel multi-moon orbiter trajectories, using a family of Keplerian maps d...

## Projects

Projects (5)

Use of Hamiltonian formalism and phase space techniques to study and control nonlinear waves in mechanical metamaterials

Bifurcations, transition to turbulence and control of active nematics via analysis of exact coherent structures and their invariant manifolds. Supported by DOE BES grant DE-SC0022280

Bifurcation and phase space analysis of closed loop MFG systems
Funded by NSF CMMI 2102112