This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information avail...This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.展开更多
Unmanned Aerial Vehicles(UAVs)enabled Aerial Base Stations(UABSs)have been studied widely in future communications.However,there are a series of challenges such as interference management,trajectory design and resourc...Unmanned Aerial Vehicles(UAVs)enabled Aerial Base Stations(UABSs)have been studied widely in future communications.However,there are a series of challenges such as interference management,trajectory design and resource allocation in the scenarios of multi-UAV networks.Besides,different performances among UABSs increase complexity and bring many challenges.In this paper,the joint downlink transmission power control and trajectory design problem in multi-type UABSs communication network is investigated.In order to satisfy the signal to interference plus noise power ratio of users,each UABS needs to adjust its position and transmission power.Based on the interactions among multiple communication links,a non-cooperative Mean-Field-Type Game(MFTG)is proposed to model the joint optimization problem.Then,a Nash equilibrium solution is solved by two steps:first,the users in the given area are clustered to get the initial deployment of the UABSs;second,the Mean-Field Q(MFQ)-learning algorithm is proposed to solve the discrete MFTG problem.Finally,the effectiveness of the approach is verified through the simulations,which simplifies the solution process and effectively reduces the energy consumption of each UABS.展开更多
This paper solves a mean-field type hierarchical optimal control problem in electricity market.The authors consider n-1 prosumers and one producer.The ith prosumer,for 1<i<n,is a leader of the(i-1)th prosumer an...This paper solves a mean-field type hierarchical optimal control problem in electricity market.The authors consider n-1 prosumers and one producer.The ith prosumer,for 1<i<n,is a leader of the(i-1)th prosumer and is a follower of the(i+1)th prosumer.The first player(agent)is the follower at the bottom whereas the nth is the leader at the top.The problem is described by a linear jump-diffusion system of conditional mean-field type,where the conditioning is with respect to common noise,and a quadratic cost functional involving,the square of the conditional expectation of the controls of the agents.The authors provide a semi-explicit solution of the corresponding meanfield-type hierarchical control problem with common noise.Finally,the authors illustrate the obtained result via a numerical example with two different scenarios.展开更多
文摘This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.
基金co-supported by the National Natural Science Foundation of China(Nos.62001387,61901379)the Natural Science Basic Research Plan in Shaanxi Province(No.2019JQ253)+4 种基金the Key R&D Plan of Shaanxi Province(No.2020GY034)the Aerospace Science and Technology Innovation Fund of China Aerospace Science and Technology Corporationthe Shanghai Aerospace Science and Technology Innovation Fund(No.SAST2018045)the China Fundamental Research Fund for the Central Universities(No.3102018QD096)the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(No.CX2020152)。
文摘Unmanned Aerial Vehicles(UAVs)enabled Aerial Base Stations(UABSs)have been studied widely in future communications.However,there are a series of challenges such as interference management,trajectory design and resource allocation in the scenarios of multi-UAV networks.Besides,different performances among UABSs increase complexity and bring many challenges.In this paper,the joint downlink transmission power control and trajectory design problem in multi-type UABSs communication network is investigated.In order to satisfy the signal to interference plus noise power ratio of users,each UABS needs to adjust its position and transmission power.Based on the interactions among multiple communication links,a non-cooperative Mean-Field-Type Game(MFTG)is proposed to model the joint optimization problem.Then,a Nash equilibrium solution is solved by two steps:first,the users in the given area are clustered to get the initial deployment of the UABSs;second,the Mean-Field Q(MFQ)-learning algorithm is proposed to solve the discrete MFTG problem.Finally,the effectiveness of the approach is verified through the simulations,which simplifies the solution process and effectively reduces the energy consumption of each UABS.
基金support from Tamkeen under the NYU Abu Dhabi Research Institute grant CG002U.S.Air Force Office of Scientific Research under Grant No.FA955017-1-0259。
文摘This paper solves a mean-field type hierarchical optimal control problem in electricity market.The authors consider n-1 prosumers and one producer.The ith prosumer,for 1<i<n,is a leader of the(i-1)th prosumer and is a follower of the(i+1)th prosumer.The first player(agent)is the follower at the bottom whereas the nth is the leader at the top.The problem is described by a linear jump-diffusion system of conditional mean-field type,where the conditioning is with respect to common noise,and a quadratic cost functional involving,the square of the conditional expectation of the controls of the agents.The authors provide a semi-explicit solution of the corresponding meanfield-type hierarchical control problem with common noise.Finally,the authors illustrate the obtained result via a numerical example with two different scenarios.
