STATE SPACE REDUCTION METHOD FOR OPTIMAL CONTROL PROBLEM

2019 ◽  
Author(s):  
V. A. Bereznev ◽  
◽  
A. I. Diveev ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
State Space ◽  
Reduction Method ◽  
Space Reduction ◽  
State Space Reduction

scholarly journals Parrondo Games with Spatial Dependence, III

2015 ◽  
Vol 14 (04) ◽  
pp. 1550039 ◽  
Author(s):  
S. N. Ethier ◽  
Jiyeon Lee
Keyword(s):  
Computer Graphics ◽  
Markov Chains ◽  
State Space ◽  
Spatial Dependence ◽  
Reduction Method ◽  
One Dimensional ◽  
Space Reduction ◽  
State Space Reduction

We study Toral’s Parrondo games with [Formula: see text] players and one-dimensional spatial dependence as modified by Xie et al. Specifically, we use computer graphics to sketch the Parrondo and anti-Parrondo regions for [Formula: see text]. Our work was motivated by a recent paper of Li et al., who applied a state space reduction method to this model, reducing the number of states from [Formula: see text] to [Formula: see text]. We show that their reduced Markov chains are inconsistent with the model of Xie et al.

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