Robust H_∞ Control For Three Types Of Economic Systems Based On Differential Games

In recent years, the work of the economic system gradually takes the heat. Some researchers in China have begun to study some of the main features of economic models, that is, economic growth, employment, inflation (price index), international payments and foreign trade, and analyzed of the economic system to achieve certain results. During the past years, the instability of the international economic situation brought about tremendous impact to the economic. Facing the deteriorating international economic situation, the control strategy of how to face the uncertainty of the economic system which is under the condition of risk, is needed to be studied in depth. Here, the system comes down the uncertainty to noisy disturbance factors, and we use the h-infinity control theory to analyze and make decision for economic control system, so that we can set the economic system operate normally.Many economic phenomenon and behavior have been understood as game theory by economists. Game theory has been developed greatly, combining with the modern control theory. From the beginning of the 20th century 90's, differential game theory has been in the control of a wide range of applications.When we make use of differential games to solve the regulation problem, we can consider the h-infinity control problem as a minimax optimal control problem to design the controller to resist the worst-case disturbance. Firstly, the disturbance can be simulated as a signal, then we make a performance index, in which the controlling vector can be seen as minimizing the performance index, and the disturbance can be regarded as a party to maximize performance. And the existence of the controller can be linked to the existence of solutions of LQ differential game theory of algebraic Riccati equations. This paper studied the controlling of the economic system which is based on the idea of differential games. This article is mainly for the economic model of macroscopic, economic growth, as well as the characteristics of the input-output, so the main content is divided into three parts:the first part designs controllers of the macroeconomic system made against by Yu Jingyuan. In this part, the main result is finding the way to design the h-infinity controller of the macroeconomic control system under the disturbance. Then the second part is for the new classical model of economic growth, and gives the designing controller. Lastly, the third part aims at the Leontief dynamic input-output model, basing on input-output relationship, and the h-infinity optimal design is given.