An Application Of Infinite Dimensional Differential Game Policy For Distributed-lags System To River Control

In this paper, it is shown that the infinite dimensional differential game theory can be used to derive and implement the Nash policy for river quality control system when the concentration of BOD and DO (i.e. bio chemical oxygen demand and dissolved oxygen) in a reach of river is sufficient to describe the biochemical process which is modelled by distributed-lag equation. The necessary condition for the solution of the game system to exist is given. The lumped approximation method call ed "shifted-legendre polynomial approximation" is presented to solve the game strategy numerically. In order to illustrate the feasibility of our approach suggested, an example of 2-reach river game system is shown at the end of the paper.