In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery p...In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.展开更多
This paper studies linear quadratic games problem for stochastic Volterra integral equations(SVIEs in short) where necessary and sufficient conditions for the existence of saddle points are derived in two different wa...This paper studies linear quadratic games problem for stochastic Volterra integral equations(SVIEs in short) where necessary and sufficient conditions for the existence of saddle points are derived in two different ways.As a consequence,the open problems raised by Chen and Yong(2007) are solved.To characterize the saddle points more clearly,coupled forward-backward stochastic Volterra integral equations and stochastic Fredholm-Volterra integral equations are introduced.Compared with deterministic game problems,some new terms arising from the procedure of deriving the later equations reflect well the essential nature of stochastic systems.Moreover,our representations and arguments are even new in the classical SDEs case.展开更多
A switched linear quadratic（LQ） differential game over finite-horizon is investigated in this paper. The switching signal is regarded as a non-conventional player, afterwards the definition of Pareto efficiency is e...A switched linear quadratic（LQ） differential game over finite-horizon is investigated in this paper. The switching signal is regarded as a non-conventional player, afterwards the definition of Pareto efficiency is extended to dynamics switching situations to characterize the solutions of this multi-objective problem. Furthermore, the switched differential game is equivalently transformed into a family of parameterized single-objective optimal problems by introducing preference information and auxiliary variables. This transformation reduces the computing complexity such that the Pareto frontier of the switched LQ differential game can be constructed by dynamic programming. Finally, a numerical example is provided to illustrate the effectiveness.展开更多
The discussions on the development of an electricity market model for accommodating cross-border cooperation remains active in Europe.The main interest is the establishment of market couplings without curtailing the f...The discussions on the development of an electricity market model for accommodating cross-border cooperation remains active in Europe.The main interest is the establishment of market couplings without curtailing the fair use of the scarce transmission capacity.However,it is difficult to gain mutual consensus on this subject because of the absence of convincing simulation results for the entire region.To achieve that,researchers need a common grid model(CGM)which is a simplified representation of the detailed transmission model which comprises aggregated buses and transmission lines.A CGM should sufficiently represent the inter-area power flow characteristics.Generally,it is difficult to establish a standard CGM that represents the actual transmission network with a suf-ficient degree of exactness because it requires knowledge on the details of the transmission network,which are undisclosed.This paper addresses the issue and reviews the existing approaches in transmission network approximation,and their shortcomings.Then,it proposes a new approach called the adaptive CGM approximation(ACA)for serving the purpose.The ACA is a datadriven approach,developed based on the direct current power flow theory.It is able to construct a CGM based on the published power flow data between the inter-connected market areas.This is done by solving the issue as a non-linear model fitting problem.The method is validated using three case studies.展开更多
基金Supported by the National Fund of Natural Sciences.
文摘In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.
基金supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11231007,11301298,11471231,11401404,11371226,11071145 and 11231005)+2 种基金China Postdoctoral Science Foundation(Grant No.2014M562321)Foundation for Innovative Research Groups of National Natural Science Foundation of China(Grant No.11221061)the Program for Introducing Talents of Discipline to Universities(the National 111Project of China's Higher Education)(Grant No.B12023)
文摘This paper studies linear quadratic games problem for stochastic Volterra integral equations(SVIEs in short) where necessary and sufficient conditions for the existence of saddle points are derived in two different ways.As a consequence,the open problems raised by Chen and Yong(2007) are solved.To characterize the saddle points more clearly,coupled forward-backward stochastic Volterra integral equations and stochastic Fredholm-Volterra integral equations are introduced.Compared with deterministic game problems,some new terms arising from the procedure of deriving the later equations reflect well the essential nature of stochastic systems.Moreover,our representations and arguments are even new in the classical SDEs case.
基金supported by the National Natural Science Foundation of China under Grant No.61773098the 111 Project under Grant No.B16009
文摘A switched linear quadratic（LQ） differential game over finite-horizon is investigated in this paper. The switching signal is regarded as a non-conventional player, afterwards the definition of Pareto efficiency is extended to dynamics switching situations to characterize the solutions of this multi-objective problem. Furthermore, the switched differential game is equivalently transformed into a family of parameterized single-objective optimal problems by introducing preference information and auxiliary variables. This transformation reduces the computing complexity such that the Pareto frontier of the switched LQ differential game can be constructed by dynamic programming. Finally, a numerical example is provided to illustrate the effectiveness.
基金This work was funded by the Norwegian Centre of Offshore Wind Technologies(NOWITECH).
文摘The discussions on the development of an electricity market model for accommodating cross-border cooperation remains active in Europe.The main interest is the establishment of market couplings without curtailing the fair use of the scarce transmission capacity.However,it is difficult to gain mutual consensus on this subject because of the absence of convincing simulation results for the entire region.To achieve that,researchers need a common grid model(CGM)which is a simplified representation of the detailed transmission model which comprises aggregated buses and transmission lines.A CGM should sufficiently represent the inter-area power flow characteristics.Generally,it is difficult to establish a standard CGM that represents the actual transmission network with a suf-ficient degree of exactness because it requires knowledge on the details of the transmission network,which are undisclosed.This paper addresses the issue and reviews the existing approaches in transmission network approximation,and their shortcomings.Then,it proposes a new approach called the adaptive CGM approximation(ACA)for serving the purpose.The ACA is a datadriven approach,developed based on the direct current power flow theory.It is able to construct a CGM based on the published power flow data between the inter-connected market areas.This is done by solving the issue as a non-linear model fitting problem.The method is validated using three case studies.
