Sufficiency of Kalman's rank condition for the approximate boundary controllability on a spherical domain

2021 ◽  
Author(s):  
Chengxia Zu ◽  
Tatsien Li ◽  
Bopeng Rao
Keyword(s):  
Rank Condition ◽  
Boundary Controllability ◽  
Spherical Domain

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.

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