Necessary and Sufficient Condition for Two-Player Stackelberg Strategy

被引：52

作者：

Xu, Juanjuan ^{[1
]}

Zhang, Huanshui ^{[1
]}

Chai, Tianyou ^{[2
]}

机构：

[1] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China

[2] Northeastern Univ, State Key Lab Synthet Automat Proc Ind, Shenyang 110004, Liaoning, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2015年 / 60卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Leader-follower; necessary and sufficient condition; Riccati equation; Stackelberg strategy; ZERO-SUM GAMES; DISCRETE-TIME; DIFFERENTIAL-GAMES; RICCATI-EQUATIONS; 2-PERSON; NASH;

D O I：

10.1109/TAC.2014.2346460

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This technical note revisits the open-loop Stackelberg strategy for a two-player game. By introducing a new costate, which captures the future information of the control input, we present a necessary and sufficient condition for the existence and uniqueness of the two-player game. The optimal strategy is designed in terms of three decoupled and symmetric Riccati equations which improves the existing results greatly on computation.

引用

页码：1356 / 1361

页数：6

共 50 条

[31] The convergence rate and necessary-and-sufficient condition for the consistency of isogeometric collocation method
Lin, Hong-wei
Xiong, Yun-yang
Hu, Hui
Yan, Jia-cong
Hu, Qian-qian
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2022, 37 (02) : 272 - 289
[32] A necessary and sufficient condition of existence of positive solutions for nonlinear singular differential systems
Zhang, Xinguang
Liu, Lishan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (01) : 400 - 414
[33] Necessary and sufficient condition for absolute exponential stability of a class of nonsymmetric neural networks
Liang, XB
Yamaguchi, T
IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS, 1997, E80D (08): : 802 - 807
[34] A necessary and sufficient condition for Hardy's operator in Lp(.)(0,1)
Mamedov, Farman I.
Mammadova, Firana M.
MATHEMATISCHE NACHRICHTEN, 2014, 287 (5-6) : 666 - 676
[35] The Necessary and Sufficient Condition of State Merging in Non-Deterministic Finite Automata
Zhang, Ming-ming
Tang, Rui-xue
PROCEEDINGS OF 2010 ASIA-PACIFIC YOUTH CONFERENCE ON COMMUNICATION, VOLS 1 AND 2, 2010, : 641 - 646
[36] A necessary and sufficient condition for the existence of large solutions to 'mixed' type elliptic systems
Zhang, Xinguang
APPLIED MATHEMATICS LETTERS, 2012, 25 (12) : 2359 - 2364
[37] Necessary and sufficient condition for the existence of positive solution to singular fractional differential equations
Wang, Yongqing
Liu, Lishan
ADVANCES IN DIFFERENCE EQUATIONS, 2015,
[38] Necessary and sufficient condition for the existence of positive solution to singular fractional differential equations
Yongqing Wang
Lishan Liu
Advances in Difference Equations, 2015
[39] The convergence rate and necessary-and-sufficient condition for the consistency of isogeometric collocation method
Hong-wei Lin
Yun-yang Xiong
Hui Hu
Jia-cong Yan
Qian-qian Hu
Applied Mathematics-A Journal of Chinese Universities, 2022, 37 : 272 - 289
[40] Necessary and sufficient condition for the comparison theorem of multidimensional anticipated backward stochastic differential equations
XiaoMing Xu
Science China Mathematics, 2011, 54 : 301 - 310

← 1 2 3 4 5 →