This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a dis...This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points （extreme points） and the existing ones need to verify all points in the bounded polyhedron.展开更多
In heterogeneous network with hybrid energy supplies including green energy and on-grid energy, it is imperative to increase the utilization of green energy as well as to improve the utilities of users and networks. A...In heterogeneous network with hybrid energy supplies including green energy and on-grid energy, it is imperative to increase the utilization of green energy as well as to improve the utilities of users and networks. As the difference of hybrid energy source in stability and economy, thus, this paper focuses on the network with hybrid energy source, and design the utility of each user in the hybrid energy source system from the perspective of stability, economy and environment pollution. A dual power allocation algorithm based on Stackelberg game to maximize the utilities of users and networks is proposed. In addition, an iteration method is proposed which enables all players to reach the Stackelberg equilibrium(SE). Simulation results validate that players can reach the SE and the utilities of users and networks can be maximization, and the green energy can be efficiently used.展开更多
基金supported by National Science Foundation of China(11171221)Doctoral Program Foundation of Institutions of Higher Education of China(20123120110004)+2 种基金Natural Science Foundation of Shanghai(14ZR1429200)Innovation Program of Shanghai Municipal Education Commission(15ZZ073)Key Research Project Plan of Institutions of Higher of Henan Province(17A120010)
文摘This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points （extreme points） and the existing ones need to verify all points in the bounded polyhedron.
基金supported by the Beijing Natural Science Foundation (4142049)863 project No. 2014AA01A701the Fundamental Research Funds for Central Universities of China No. 2015XS07
文摘In heterogeneous network with hybrid energy supplies including green energy and on-grid energy, it is imperative to increase the utilization of green energy as well as to improve the utilities of users and networks. As the difference of hybrid energy source in stability and economy, thus, this paper focuses on the network with hybrid energy source, and design the utility of each user in the hybrid energy source system from the perspective of stability, economy and environment pollution. A dual power allocation algorithm based on Stackelberg game to maximize the utilities of users and networks is proposed. In addition, an iteration method is proposed which enables all players to reach the Stackelberg equilibrium(SE). Simulation results validate that players can reach the SE and the utilities of users and networks can be maximization, and the green energy can be efficiently used.
