arXiv subjects

Dohyun Kwon

Publications and source records attributed to Dohyun Kwon.

28 records · Page 2Linked to original sources

arXiv2021

Quality-Aware Deep Reinforcement Learning for Streaming in Infrastructure-Assisted Connected Vehicles

This paper proposes a deep reinforcement learning-based video streaming scheme for mobility-aware vehicular networks, e.g., vehicles on the highway. We consider infrastructure-assisted and mmWave-based scenarios in which the macro base station (MBS) cannot directly provide the streaming service to vehicles due to the short range of mmWave beams so that small mmWave base stations (mBSs) along the road deliver the desired videos to users. For a smoother streaming service, the MBS proactively pushes video chunks to mBSs. This is done to support vehicles that are currently covered and/or will be by each mBS. We formulate the dynamic video delivery scheme that adaptively determines 1) which content, 2) what quality and 3) how many chunks to be proactively delivered from the MBS to mBSs using Markov decision process (MDP). Since it is difficult for the MBS to track all the channel conditions and the network states have extensive dimensions, we adopt the deep deterministic policy gradient (DDPG) algorithm for the DRL-based video delivery scheme. This paper finally shows that the DRL agent learns a streaming policy that pursues high average quality while limiting packet drops, avoiding playback stalls, reducing quality fluctuations and saving backhaul usage.

cs.NI↗

arXiv2021

Flocking formation and stabilizer of boosted cooperative control on a sphere

The purpose of this paper is to consider flocking formations of a second order dynamic system on a sphere with a Cucker-Smale type flocking operator and cooperative control. The flocking operator consists of a weighted control parameter and a natural relative velocity. The cooperative control law is given by a combination of attractive and repulsive forces. We prove that the solution to this system converges to an asymptotic spherical configuration depending on the control parameters of the cooperative control law. All possible asymptotic configurations for this system are classified and sufficient conditions for rendezvous, deployment, and local deployment, respectively, are presented. In addition, we provide several numerical simulations to confirm our analytic results. We numerically verify that the solution to this system converges to a formation flight with a nonzero constant speed if we add a boost term. The flocking operator acts as a stabilizer on the spherical cooperative control laws.

math.DS↗

arXiv2021

Multi-agent system for target tracking on a sphere and its asymptotic behavior

We propose a second-order multi-agent system for target tracking on a sphere. The model contains a centripetal force, a bonding force, a velocity alignment operator to the target, and cooperative control between flocking agents. We propose an appropriate regularized rotation operator instead of Rodrigues' rotation operator to derive the velocity alignment operator for target tracking. By the regularized rotation operator, we can decompose the phase of agents into translational and structural parts. By analyzing the translational part of this reference frame decomposition, we can obtain rendezvous results to the given target. If the multi-agent system can obtain the target's position, velocity, and acceleration vectors, then the complete rendezvous occurs. Even in the absence of the target's acceleration information, if the coefficients are sufficiently large enough, then the practical rendezvous occurs.

math.DS↗

arXiv2021

Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients

This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in particular on gradient flows in the space of probability measures equipped with the distance arising in the Monge-Kantorovich optimal transport problem. The associated internal energy functionals in general fail to be differentiable, therefore classical results do not apply directly in our setting. We study the combination of both linear and porous medium type diffusions and we show the existence and uniqueness of the solutions in the sense of distributions in suitable Sobolev spaces. Our notion of solution allows us to give a fine characterization of the emerging critical regions, observed previously in numerical experiments. A link to a three phase free boundary problem is also pointed out.

math.AP↗

arXiv2021

Uniform position alignment estimate of spherical flocking model with inter-particle bonding forces

We present a sufficient condition of the complete position flocking theorem for the Cucker-Smale type model on the unit sphere with an inter-particle bonding force. For this second order dynamical system derived in [Choi, S.-H., Kwon, D. and Seo, H.: Cucker-Smale type flocking models on a sphere. arXiv preprint arXiv:2010.10693, 2020] by using the rotation operator in three dimensional sphere, we obtain an exponential decay estimate for the diameter of agents' positions as well as time-asymptotic flocking for a class of initial data. The sufficient condition for the initial data depends only on the communication rate and inter-particle bonding parameter but not the number of agents. The lack of momentum conservation and the curved space domain make it difficult to apply the standard methodology used in the original Cucker-Smale model. To overcome this and obtain a uniform position alignment estimate, we use an energy dissipation property of this system and transform the Cucker-Smale type flocking model into an inhomogeneous system of differential equations of which solution contains the position and velocity diameters. The coefficients of the transformed system are controlled by the communication rate and a uniform upper bound of velocities obtained by the energy dissipation.

math.DS↗

arXiv2020

On volume-preserving crystalline mean curvature flow

In this work we consider the global existence of volume-preserving crystalline curvature flow in a non-convex setting. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using this geometric property, we address global existence and regularity of the flow for smooth anisotropies. For the non-smooth case we establish global existence results for the types of anisotropies known to be globally well-posed.

math.AP↗

arXiv2020

Cucker-Smale type flocking models on a sphere

We present a Cucker-Smale (C-S) type flocking model on a sphere. We study velocity alignment on a sphere and prove the emergence of flocking for the proposed model. Our model includes three new terms: a centripetal force, multi-agent interactions on a sphere and inter-particle bonding forces. To compare velocity vectors on different tangent spaces, we introduce a rotation operator in our new interaction term. Due to the geometric restriction, the rotation operator is singular at antipodal points and the relative velocity between two agents located at these points is not well-defined. Based on an energy dissipation property of our model and a variation of Barbalat's lemma, we show the alignment of velocities for an admissible class of communication weight functions. In addition, for sufficiently large bonding forces we prove time-asymptotic flocking which includes the avoidance of antipodal points.

math.DS↗

arXiv2020

Multi-Agent Deep Reinforcement Learning for Cooperative Connected Vehicles

Millimeter-wave (mmWave) base station can offer abundant high capacity channel resources toward connected vehicles so that quality-of-service (QoS) of them in terms of downlink throughput can be highly improved. The mmWave base station can operate among existing base stations (e.g., macro-cell base station) on non-overlapped channels among them and the vehicles can make decision what base station to associate, and what channel to utilize on heterogeneous networks. Furthermore, because of the non-omni property of mmWave communication, the vehicles decide how to align the beam direction toward mmWave base station to associate with it. However, such joint problem requires high computational cost, which is NP-hard and has combinatorial features. In this paper, we solve the problem in 3-tier heterogeneous vehicular network (HetVNet) with multi-agent deep reinforcement learning (DRL) in a way that maximizes expected total reward (i.e., downlink throughput) of vehicles. The multi-agent deep deterministic policy gradient (MADDPG) approach is introduced to achieve optimal policy in continuous action domain.

eess.SP↗

arXiv2019

On mean curvature flow with forcing

This paper investigates geometric properties and well-posedness of a mean curvature flow with volume-dependent forcing. With the class of forcing which bounds the volume of the evolving set away from zero and infinity, we show that a strong version of star-shapedness is preserved over time. More precisely, it is shown that the flow preserves the $ρ$-reflection property, which corresponds to a quantitative Lipschitz property of the set with respect to the nearest ball. Based on this property we show that the problem is well-posed and its solutions starting with $ρ$-reflection property become instantly smooth. Lastly, for a model problem, we will discuss the flow's exponential convergence to the unique equilibrium in Hausdorff topology. For the analysis, we adopt the approach developed in [Kim-Feldman, 2014] to combine viscosity solutions approach and variational method. The main challenge lies in the lack of comparison principle, which accompanies forcing terms that penalize small volume.

math.AP↗

arXiv2018

Volume preserving mean curvature flow for star-shaped sets

We study the evolution of star-shaped sets in volume preserving mean curvature flow. Constructed by approximate minimizing movements, our solutions preserve a strong version of star-shapedness. We also show that the solutions converges to a ball as time goes to infinity. For asymptotic behavior of the solutions we use the gradient flow structure of the problem, whereas a modified notion of viscosity solutions is introduced to study the geometric properties of the flow by moving planes method.

math.AP↗