optimization of a dynamic duoploy system using optimal control strategy

This paper, deals with the application of mathematical control theory techniques of optimization in an economics problem. here, we consider the optimizationproblem of a dynamic duopoly system that it’s model is stated by a first order ordinarydifferential equation. this system, consists of two agents such that each one has a distinct cost function that should be minimized. our purpose is to solve this minimizationproblem by means of control theory techniques. to that end, it is necessary to reformulate the economic model into a linear control model. so, at the first step, by introducingsuitable matrices, we reform the problem’s model into a standard model of linear controlsystem with quadratic cost functions. afterwards, by stating a theorem, we propose anoptimum control strategy to optimize the corresponding costs of the system and showthat the optimal control law is unique and obtains from solving hjb partial differentialequation.