This paper explores the application of noncooperative game theory together with the concept of Nash equilibrium to the investigation of some basic problems on multi-scale structure, especially the meso-scale structure...This paper explores the application of noncooperative game theory together with the concept of Nash equilibrium to the investigation of some basic problems on multi-scale structure, especially the meso-scale structure in the multi-phase complex systems in chemical engineering. The basis of this work is the energy-minimization-multi-scale （EMMS） model proposed by Li and Kwauk （1994） and Li, et al. （2013） which identifies the multi-scale structure as a result of ＇compromise-in-competition between dominant mechanisms＇ and tries to solve a multi-objective optimization problem. However, the existing methods often integrate it into a problem of single objective optimization, which does not clearly reflect the ＇compromise-in-competition＇ mechanism and causes heavy computation burden as well as uncertainty in choosing suitable weighting factors. This paper will formulate the compromise in competition mechanism in EMMS model as a noncooperative game with constraints, and will describe the desired stable system state as a generalized Nash equilibrium. Then the authors will investigate the game theoretical approach for two typical systems in chemical engineering, the gas-solid fluidiza- tion （GSF） system and turbulent flow in pipe. Two different cases for generalized Nash equilibrinm in such systems will be well defined and distinguished. The generalize Nash equilibrium will be solved accurately for the GSF system and a feasible method will be given for turbulent flow in pipe. These results coincide with the existing computational results and show the feasibility of this approach, which overcomes the disadvantages of the existing methods and provides deep insight into the mechanisms of multi-scale structure in the multi-phase complex systems in chemical engineering.展开更多
In recent years,power saving problem has become more and more important in many fields and attracted a lot of research interests.In this paper,the authors consider the power saving problem in the virtualized computing...In recent years,power saving problem has become more and more important in many fields and attracted a lot of research interests.In this paper,the authors consider the power saving problem in the virtualized computing system.Since there are multiple objectives in the system as well as many factors influencing the objectives,the problem is complex and hard.The authors will formulate the problem as an optimization problem of power consumption with a prior requirement on performance,which is taken as the response time in the paper.To solve the problem,the authors design the adaptive controller based on least-square self-tuning regulator to dynamically regulate the computing resource so as to track a given reasonable reference performance and then minimize the power consumption using the tracking result supplied by the controller at each time.Simulation is implemented based on the data collected from real machines and the time delay of turning on/off the machine is included in the process.The results show that this method based on adaptive control theory can save power consumption greatly with satisfying the performance requirement at the same time,thus it is suitable and effective to solve the problem.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11688101,91634203,61304159by the National Center for Mathematics and Interdisciplinary Sciences
文摘This paper explores the application of noncooperative game theory together with the concept of Nash equilibrium to the investigation of some basic problems on multi-scale structure, especially the meso-scale structure in the multi-phase complex systems in chemical engineering. The basis of this work is the energy-minimization-multi-scale （EMMS） model proposed by Li and Kwauk （1994） and Li, et al. （2013） which identifies the multi-scale structure as a result of ＇compromise-in-competition between dominant mechanisms＇ and tries to solve a multi-objective optimization problem. However, the existing methods often integrate it into a problem of single objective optimization, which does not clearly reflect the ＇compromise-in-competition＇ mechanism and causes heavy computation burden as well as uncertainty in choosing suitable weighting factors. This paper will formulate the compromise in competition mechanism in EMMS model as a noncooperative game with constraints, and will describe the desired stable system state as a generalized Nash equilibrium. Then the authors will investigate the game theoretical approach for two typical systems in chemical engineering, the gas-solid fluidiza- tion （GSF） system and turbulent flow in pipe. Two different cases for generalized Nash equilibrinm in such systems will be well defined and distinguished. The generalize Nash equilibrium will be solved accurately for the GSF system and a feasible method will be given for turbulent flow in pipe. These results coincide with the existing computational results and show the feasibility of this approach, which overcomes the disadvantages of the existing methods and provides deep insight into the mechanisms of multi-scale structure in the multi-phase complex systems in chemical engineering.
基金supported by the National Natural Science Foundation of China under Grant No.61304159
文摘In recent years,power saving problem has become more and more important in many fields and attracted a lot of research interests.In this paper,the authors consider the power saving problem in the virtualized computing system.Since there are multiple objectives in the system as well as many factors influencing the objectives,the problem is complex and hard.The authors will formulate the problem as an optimization problem of power consumption with a prior requirement on performance,which is taken as the response time in the paper.To solve the problem,the authors design the adaptive controller based on least-square self-tuning regulator to dynamically regulate the computing resource so as to track a given reasonable reference performance and then minimize the power consumption using the tracking result supplied by the controller at each time.Simulation is implemented based on the data collected from real machines and the time delay of turning on/off the machine is included in the process.The results show that this method based on adaptive control theory can save power consumption greatly with satisfying the performance requirement at the same time,thus it is suitable and effective to solve the problem.
