OPTIMIZATION OF A DYNAMIC DUOPLOY SYSTEM USING OPTIMAL CONTROL STRATEGY

This paper, deals with the application of mathematical control theory tech niques of optimization in an economics problem. Here, we consider the optimization problem of a dynamic duopoly system that it’s model is stated by a first order ordinary differential equation. This system, consists of two agents such that each one has a dis tinct cost function that should be minimized. Our purpose is to solve this minimization problem by means of control theory techniques. To that end, it is necessary to reformu late the economic model into a linear control model. So, at the first step, by introducing suitable matrices, we reform the problem’s model into a standard model of linear control system with quadratic cost functions. Afterwards, by stating a theorem, we propose an optimum control strategy to optimize the corresponding costs of the system and show that the optimal control law is unique and obtains from solving HJB partial differential equation.