Nonlinear game problem with opponent restricted within circle

Cybernetics ◽  
1973 ◽  
Vol 6 (5) ◽  
pp. 685-689
Author(s):  
G. A. Belkin
Keyword(s):  
Game Problem ◽  
Nonlinear Game

Topsis Application to Fuzzy Game Problem

2019 ◽  
Vol 10 (7) ◽  
pp. 1426-1434
Author(s):  
M. Thirucheran ◽  
E. R. Meena Kumari
Keyword(s):  
Game Problem ◽  
Fuzzy Game

Graphical Minimax Game and Off-Policy Reinforcement Learning for Heterogeneous MASs with Spanning Tree Condition

2021 ◽  
pp. 2150011
Author(s):  
Wei Dong ◽  
Jianan Wang ◽  
Chunyan Wang ◽  
Zhenqiang Qi ◽  
Zhengtao Ding
Keyword(s):  
Reinforcement Learning ◽  
Spanning Tree ◽  
Learning Algorithm ◽  
Control Policy ◽  
Game Problem ◽  
Algebraic Riccati Equation ◽  
Multi Agent Systems ◽  
Rank Condition ◽  
Minimax Game ◽  
Tree Condition

In this paper, the optimal consensus control problem is investigated for heterogeneous linear multi-agent systems (MASs) with spanning tree condition based on game theory and reinforcement learning. First, the graphical minimax game algebraic Riccati equation (ARE) is derived by converting the consensus problem into a zero-sum game problem between each agent and its neighbors. The asymptotic stability and minimax validation of the closed-loop systems are proved theoretically. Then, a data-driven off-policy reinforcement learning algorithm is proposed to online learn the optimal control policy without the information of the system dynamics. A certain rank condition is established to guarantee the convergence of the proposed algorithm to the unique solution of the ARE. Finally, the effectiveness of the proposed method is demonstrated through a numerical simulation.

scholarly journals On pursuit-evasion differential game problem in a Hilbert space

2020 ◽  
Vol 5 (6) ◽  
pp. 7467-7479
Author(s):  
Jamilu Adamu ◽  
◽  
Kanikar Muangchoo ◽  
Abbas Ja’afaru Badakaya ◽  
Jewaidu Rilwan ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Game Problem ◽  
Pursuit Evasion

scholarly journals Two-Stage Pursuit Strategy for Incomplete-Information Impulsive Space Pursuit-Evasion Mission Using Reinforcement Learning

Aerospace ◽  
2021 ◽  
Vol 8 (10) ◽  
pp. 299
Author(s):  
Bin Yang ◽  
Pengxuan Liu ◽  
Jinglang Feng ◽  
Shuang Li
Keyword(s):  
Reinforcement Learning ◽  
Incomplete Information ◽  
Trajectory Optimization ◽  
Game Problem ◽  
Gradient Algorithm ◽  
Two Stage ◽  
Pursuit Evasion ◽  
Evasion Game ◽  
Close Distance ◽  
Pursuit Strategy

This paper presents a novel and robust two-stage pursuit strategy for the incomplete-information impulsive space pursuit-evasion missions considering the J2 perturbation. The strategy firstly models the impulsive pursuit-evasion game problem into a far-distance rendezvous stage and a close-distance game stage according to the perception range of the evader. For the far-distance rendezvous stage, it is transformed into a rendezvous trajectory optimization problem and a new objective function is proposed to obtain the pursuit trajectory with the optimal terminal pursuit capability. For the close-distance game stage, a closed-loop pursuit approach is proposed using one of the reinforcement learning algorithms, i.e., the deep deterministic policy gradient algorithm, to solve and update the pursuit trajectory for the incomplete-information impulsive pursuit-evasion missions. The feasibility of this novel strategy and its robustness to different initial states of the pursuer and evader and to the evasion strategies are demonstrated for the sun-synchronous orbit pursuit-evasion game scenarios. The results of the Monte Carlo tests show that the successful pursuit ratio of the proposed method is over 91% for all the given scenarios.

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