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Papers - PENG Linyu

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Towards Efficient Battery Swapping Service Operation under Battery Heterogeneity

X Zhang, Y Cao, L Peng, N Ahmad, L Xu

IEEE Transactions on Vehicular Technology 69 ( 6 ) 6107 - 6118 2020.06

Research paper (scientific journal), Joint Work, Accepted, ISSN 1939-9359

© 1967-2012 IEEE. The proliferation of electric vehicles (EVs) has posed significant challenges to the existing power grid infrastructure. It thus becomes of vital importance to efficiently manage the Electro-Mobility for large demand from EVs. Due to limited cruising range of EVs, vehicles have to make frequent stops for recharging, while long charging period is one major concern under plug-in charging. We herein leverage battery swapping (BS) technology to provide an alternative charging service, which substantially reduces the charging duration (from hours down to minutes). Concerning in practice that various battery is generally not compatible with each other, we thus introduce battery heterogeneity into the swapping service, concerning the case that different types of EVs co-exist. A battery heterogeneity-based swapping service framework is then proposed. Further with reservations for swapping service enabled, the demand load can be anticipated at BS stations as a guidance to alleviate service congestion. Therefore, potential hotspots can be avoided. Results show the performance gains under the proposed scheme by comparing to other benchmarks, in terms of service waiting time, etc. In particular, the diversity of battery stock across the network can be effectively managed.

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Application of gradient descent algorithms based on geodesic distances

X Duan, H Sun, L Peng

Science China Information Sciences 63 ( 5 ) 152201 2020.05

Research paper (scientific journal), Joint Work, Accepted, ISSN 1674733X

© 2020, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature. In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the objective function. The first proposed problem is the control for positive definite Hermitian matrix systems whose outputs only depend on their inputs. The geodesic distance is adopted as the difference of the output matrix and the target matrix. The controller to adjust the input is obtained such that the output matrix is as close as possible to the target matrix. We show the trajectory of the control input on the manifold using the Riemannian gradient algorithm. The second application is to compute the Karcher mean of a finite set of given Toeplitz positive definite Hermitian matrices, which is defined as the minimizer of the sum of geodesic distances. To obtain more efficient iterative algorithm than traditional ones, a natural gradient algorithm is proposed to compute the Karcher mean. Illustrative simulations are provided to show the computational behavior of the proposed algorithms.

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Discrete Crum’s theorems and lattice KdV-type equations

C Zhang, L Peng, D Zhang

Theoretical and Mathematical Physics 202 ( 2 ) 165 - 182 2020.03

Research paper (scientific journal), Joint Work, Accepted, ISSN 00405779

© 2020, Pleiades Publishing, Ltd. We develop Darboux transformations (DTs) and their associated Crum’s formulas for two Schrödinger-type difference equations that are themselves discretized versions of the spectral problems of the KdV and modified KdV equations. With DTs viewed as a discretization process, classes of semidiscrete and fully discrete KdV-type systems, including the lattice versions of the potential KdV, potential modified KdV, and Schwarzian KdV equations, arise as the consistency condition for the differential/difference spectral problems and their DTs. The integrability of the underlying lattice models, such as Lax pairs, multidimensional consistency, τ-functions, and soliton solutions, can be easily obtained by directly applying the discrete Crum’s formulas.

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An assignment model with local constraints: Competitive equilibrium and ascending auction

L Pan, L Peng, Y Zhou

Economics Letters 188 108905 2020.03

Research paper (scientific journal), Joint Work, Accepted, ISSN 01651765

© 2019 Elsevier B.V. We consider an assignment model where each agent has unit-demand quasi-linear preferences and may face some local constraint, i.e., her possible assignment is restricted to a subset of items. Our model takes the assignment models without and with outside options, e.g., Andersson (2007) and Andersson et al. (2013), as special cases. We show that local constraints may lead to the non-existence of competitive equilibrium (CE), and provide a sufficient and necessary condition that ensures its existence. We establish the lattice of CE prices. Besides, an ascending auction is proposed, either finding a CE or validating its non-existence in finitely many steps. It generalizes Andersson et al. (2013)’s auction by adjusting increments stepwise.

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Modified Formal Variational Structures for General Differential Equations

PENG Linyu, OBATA Kenji

日本応用数理学会年会講演予稿集(CD-ROM) 2020 2020

Research paper (other academic), Joint Work, Accepted, ISSN 1345-3378

Regular symmetries of differential-difference equations and Noether's conservation laws

L Peng

数理解析研究所講究録 (RIMS) 2137 130 - 139 2019.12

Research paper (bulletin of university, research institution), Single Work, ISSN 1880-2818

CiNii Research

An automatic dynamic balancer in a rotating mechanism with time-varying angular velocity

JA Wright, L Peng

Results in Applied Mathematics 2 100015 2019.12

Research paper (scientific journal), Joint Work, Accepted, ISSN 2590-0374

© 2019 The Author(s) We consider the system of a two ball automatic dynamic balancer attached to a rotating disc with nonconstant angular velocity. We directly compare the scenario of constant angular velocity with that when the acceleration of the rotor is taken into consideration. In doing so we show that there are cases where one must take the acceleration phase into consideration to obtain an accurate picture of the dynamics. Similarly we identify cases where the acceleration phase of the disc may be ignored. Finally, we briefly consider nonmonotonic variations of the angular velocity, with a view of maximising the basin of attraction of the desired solution, corresponding to damped vibrations.

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Statistical Einstein manifolds of exponential families with group-invariant potential functions

L Peng, Z Zhang

Journal of Mathematical Analysis and Applications 479 ( 2 ) 2104 - 2118 2019.11

Research paper (scientific journal), Joint Work, Accepted, ISSN 0022247X

© 2019 Elsevier Inc. This paper mainly contributes to a classification of statistical Einstein manifolds, namely statistical manifolds at the same time are Einstein manifolds. A statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. With the Fisher information metric as a Riemannian metric, information geometry was developed to understand the intrinsic properties of statistical models, which play important roles in statistical inference, etc. Among all these models, exponential families is one of the most important kinds, whose geometric structures are fully determined by their potential functions. To classify statistical Einstein manifolds, we derive partial differential equations for potential functions of exponential families; special solutions of these equations are obtained through the ansatz method as well as group-invariant solutions via reductions using Lie point symmetries.

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Symmetries and reductions of integrable nonlocal partial differential equations

L Peng

Symmetry 11 ( 7 ) 884 2019.07

Research paper (scientific journal), Single Work, Accepted

© 2019 by the authors. In this paper, symmetry analysis is extended to study nonlocal differential equations. In particular, two integrable nonlocal equations are investigated, the nonlocal nonlinear Schrödinger equation and the nonlocal modified Korteweg-de Vries equation. Based on general theory, Lie point symmetries are obtained and used to reduce these equations to nonlocal and local ordinary differential equations, separately; namely, one symmetry may allow reductions to both nonlocal and local equations, depending on how the invariant variables are chosen. For the nonlocal modified Korteweg-de Vries equation, analogously to the local situation, all reduced local equations are integrable. We also define complex transformations to connect nonlocal differential equations and differential-difference equations.

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MEGEE: Mobile Edge computer Geared v2x for E-mobility Ecosystem

Y Cao, C Wu, X Zhang, W Liu, L Peng, M Khalid

2019 IEEE Wireless Communications and Networking Conference (WCNC) (IEEE) 2019-April 1 - 6 2019.04

Research paper (international conference proceedings), Joint Work, Accepted

© 2019 IEEE. The introduction of Electric Vehicles (EVs) leads to new concern on the E-Mobility. Making charging reservation, by considering the EV's arrival time and its expected charging time at Charging Stations (CSs) has been studied to predict the dynamic status of CSs. In this paper, we propose a Mobile Edge computer Geared v2x for E-mobility Ecosystem (MEGEE), as a decentralized alternative to the conventional centralized cloud based architecture. MEGEE enables the Vehicular Delay/Disruption Tolerant Networking (VDTN)-driven anycasting for information delivery, and Mobile Edge Computing (MEC) functioned CSs for information mining and aggregation. MEGEE efficiently and timely processes essential charging reservations and charging control information, through the Internet of EVs and MEC servers. Our studies show that MEGEE can achieve the close charging performance as performed by the centralized system, while offers a significant saving in communications cost.

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Moving frames and Noether’s finite difference conservation laws I

EL Mansfield, A Rojo-Echeburua, PE Hydon, L Peng

Transactions of Mathematics and its Applications 3 ( 1 ) tnz004 2019

Research paper (scientific journal), Joint Work, Accepted, ISSN 2398-4945

We consider the calculation of Euler–Lagrange systems of ordinary difference equations, including the difference Noether’s theorem, in the light of the recently-developed calculus of difference invariants and discrete moving frames. We introduce the difference moving frame, a natural discrete moving frame that is adapted to difference equations by prolongation conditions. For any Lagrangian that is invariant under a Lie group action on the space of dependent variables, we show that the Euler–Lagrange equations can be calculated directly in terms of the invariants of the group action. Furthermore, Noether’s conservation laws can be written in terms of a difference moving frame and the invariants. We show that this form of the laws can significantly ease the problem of solving the Euler–Lagrange equations, and we also show how to use a difference frame to integrate Lie group invariant difference equations. In this Part I, we illustrate the theory by applications to Lagrangians invariant under various solvable Lie groups. The theory is also generalized to deal with variational symmetries that do not leave the Lagrangian invariant. Apart from the study of systems that are inherently discrete, one significant application is to obtain geometric (variational) integrators that have finite difference approximations of the continuous conservation laws embedded a priori. This is achieved by taking an invariant finite difference Lagrangian in which the discrete invariants have the correct continuum limit to their smooth counterparts. We show the calculations for a discretization of the Lagrangian for Euler’s elastica, and compare our discrete solution to that of its smooth continuum limit.

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A Stochastic Analytical Modeling Framework on ISP-P2P Collaborations in Multi domain Environments

Zhang Xu, Wang Ning, Cao Yue, Peng Linyu, Meng Haining

IEEE Systems Journal 12 ( 3 ) 2320 - 2331 2018.09

Research paper (scientific journal), Joint Work, Accepted, ISSN 19328184

Cooperation between peer-to-peer (P2P) overlays and underlying networks has been proposed as an effective approach to improve the efficiency of both the applications and the underlying networks. However, fundamental characteristics with respect to Internet service providers (ISP) business relationships and inter-ISP routing information are not sufficiently investigated in the context of collaborative ISP-P2P paradigms in multidomain environments. In this paper, we focus on such issues and develop an analytical modeling framework for analyzing optimized interdomain peer selection schemes concerning ISP policies, with the main purpose of mitigating cross-ISP traffic and enhancing service quality of end users. In addition, we introduce an advanced hybrid scheme for peer selections based on the proposed analytical theory framework, in accordance with practical network scenarios, wherein cooperative and noncooperative behaviors coexisting. Numerical results show that the proposed scheme incorporating ISP policies is able to achieve desirable network efficiency as well as great service quality for P2P users. Our analytical modeling framework can be used as a guide for analyzing and evaluating future network-aware P2P peer selection paradigms in general multidomain scenarios.

Towards autonomy: Cost-effective scheduling for long-range autonomous valet parking (lavp)

M Khalid, Y Cao, X Zhang, C Han, L Peng, N Aslam, N Ahmad

2018 IEEE Wireless Communications and Networking Conference (WCNC) (IEEE) 1 - 6 2018.06

Research paper (international conference proceedings), Joint Work, Accepted

© 2018 IEEE. Continuous and effective developments in Autonomous Vehicles (AVs) are happening on daily basis. Industries nowadays, are interested in introducing less costly and highly controllable AVs to public. Current so-called AVP solutions are still limited to a very short range (e.g., even only work at the entrance of car parks). This paper proposes a parking scheduling scheme for long-range AVP (LAVP) case, by considering mobility of Autonomous Vehicles (AVs), fuel consumption and journey time. In LAVP, Car Parks (CPs) are used to accommodate increasing numbers of AVs, and placed outside city center, in order to avoid traffic congestions and ensure road safety in public places. Furthermore, with positioning of reference points to guide user-centric long-term driving and drop-off/pick-up passengers, simulation results under the Helsinki city scenario shows the benefits of LAVP. The advantage of LAVP system is also reflected through both analysis and simulation.

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Discrete Crum's theorems and integrable lattice equations

C Zhang, L Peng, D Zhang

arXiv preprint arXiv:1802.10044 2018

Research paper (other academic)

In this paper, we develop discrete versions of Darboux transformations and
Crum's theorems for two second order difference equations. The difference
equations are discretised versions (using Darboux transformations) of the
spectral problems of the KdV quation, and of the modified KdV equation or
sine-Gordon equation. Considering the discrete dynamics created by Darboux
transformations for the difference equations, one obtains the lattice potential
KdV equation, the lattice potential modified KdV equation and the lattice
Schwarzian KdV equation, that are prototypes of integrable lattice equations.
It turns out that, along the discretisation processes using Darboux
transformations, two families of integrable systems (the KdV family, and the
modified KdV or sine-Gordon family), including their continuous, semi-discrete
and lattice versions, are explicitly constructed. As direct applications of the
discrete Crum's theorems, multi-soliton solutions of the lattice equations are
obtained.

Variational Integrators for Interconnected Systems with Holonomic Constraints

PENG Linyu, MOMOSE Hiroki, YOSHIMURA Hiroaki

日本応用数理学会年会講演予稿集(CD-ROM) 2017 273‐274 2017.09

Research paper (other academic), Joint Work, Accepted, ISSN 1345-3378

Applying DTN routing for reservation-driven EV Charging management in smart cities

Y Cao, X Zhang, R Wang, L Peng, N Aslam, X Chen

13th International Wireless Communications and Mobile Computing Conference, IWCMC 2017 1471 - 1476 2017.07

Research paper (international conference proceedings), Accepted

© 2017 IEEE. Charging management for Electric Vehicles (EVs) on-the-move (moving on the road with certain trip destinations) is becoming important, concerning the increasing popularity of EVs in urban city. However, the limited battery volume of EV certainly influences its driver's experience. This is mainly because the EV needed for intermediate charging during trip, may experience a long service waiting time at Charging Station (CS). In this paper, we focus on CS-selection decision making to manage EVs' charging plans, aiming to minimize drivers' trip duration through intermediate charging at CSs. The anticipated EVs' charging reservations including their arrival time and expected charging time at CSs, are brought for charging management, in addition to taking the local status of CSs into account. Compared to applying traditionally applying cellular network communication to report EVs' charging reservations, we alternatively study the feasibility of applying Vehicle-to-Vehicle (V2V) communication with Delay/Disruption Tolerant Networking (DTN) nature, due primarily to its flexibility and cost-efficiency in Vehicular Ad hoc NETworks (VANETs). Evaluation results under the realistic Helsinki city scenario show that applying the V2V for reservation reporting is promisingly cost-efficient in terms of communication overhead for reservation making, while achieving a comparable performance in terms of charging waiting time and total trip duration.

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Symmetries, Conservation Laws, and Noether's Theorem for Differential‐Difference Equations

L Peng

Studies in Applied Mathematics 139 ( 3 ) 457 - 502 2017

非ホロノミック拘束を受ける力学系と離散ラグランジュ・ディラック構造

百瀬宏樹, 彭林玉, 吉村浩明

日本応用数理学会年会講演予稿集(CD-ROM) 2016 2016

Research paper (other academic), Joint Work, Accepted, ISSN 1345-3378

Self-adjointness and conservation laws of difference equations

L Peng

Communications in Nonlinear Science and Numerical Simulation 23 ( 1-3 ) 209 - 219 2015.06

Research paper (scientific journal), Accepted, ISSN 10075704

© 2014 Elsevier B.V. A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.

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Entropic dynamical models with unstable Jacobi fields

C Li, L Peng, H Sun

Romanian Journal of Physics 60 ( 9-10 ) 1249 - 1262 2015

Research paper (scientific journal), Accepted, ISSN 1221146X

© 2015, Editura Academiei Romane. All rights reserved. The instability of an entropic dynamical model is considered via Jacobi vector field and the Lyapunov exponent. From the viewpoint of information geometry, geometric structure of the statistical manifold underlying this model is investigated, and we conclude that it is a manifold with constant negative scalar curvature. By use of the Jacobi vector field associated with the geodesics, we study the asymptotic behavior of the geodesic spread on the statistical manifold and reach that it is described by an exponentially divergent Jacobi vector field with respect to time. A positive Lyapunov exponent is also obtained, that explains the local instability of the system as well. Furthermore, submanifolds are studied similarly.

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