AN ANALYTICAL METHOD TO CALCULATE THE ERGODIC AND DIFFERENCE MATRICES OF THE DISCOUNTED MARKOV DECISION PROCESSES

P , it means, the control strategy should minimize quality coefficient if the factor
β is given.

These aspects mentioned above will be a subject area of next papers. It results
from analyses of MDP some conclusions:

1. Formula (19) allows to calculate in analytical way value of total reward
ν_∞^k (β) without difficult process of reverse of the matrix (I - βP). Reverse
of matrices using computer technology goes on in iterative way. The number
of iteration rises along with the size N of matrix rapidly. It leads to loss of
calculation’s accuracy.

2. Proposed analytical method of calculation of ergodic and difference matri-
ces gives us the possibility of selection of two components of total reward.
It increases the possibility of analysis of Discounted Markov Decision Pro-
cess.

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