Application Research On Game And Control Methods In The Economic Management

The economic system is an open system, it is easily affected by external environment. It is necessary to study on the problem of robust in the economic system when the economic system has some parameter perturbations and uncertain items. In order to solve the actual economic problem, the paper establishes the domestic macroeconomic system. Research the robust stochastic stabilization for jump system with time-delay. The price fluctuation of the international energy is regarded as the external disturbance in the system.Markov stochastic jump system has been paid close extensive attention because of the profound practical background. Though it formally extends the general linear system, it has more complicated structure. There are essential differences between the general linear system and Markov jump system. The system could describe numerous engineering and economic problems. Not only does it have important theoretical significance but also it has practical engineering value. Jump systems are a kind of complicated systems with two components in their vector states:the modes and the states. The mode is the dynamic process and described by a continuous Markovian process with a finite state space. The state is discrete variable. The state in each mode is represented by a system of differential equations.Firstly, this paper studies the problem of robust stochastic stability for the Markovian jump systems with time delay and guaranteed cost control in the domestic macroeconomic system. In order to solve the problem of robust stochastic stability of the stochastic system, a novel Lyapunov function is derived by delay partitioning approach. The paper uses the definition of the infinitesimal operator to differentiate Lyapunov function that has been derived along the system. Then applying the character of linear matrix inequalities (LMI), the sufficient condition of having the solution of the problem of the closed-loop system guaranteed cost control is given in the form of LMI and the robust guaranteed cost controller is designed. Illustrative example is provided to show the effectiveness.Secondly, this paper studies the problem of robustly stochastic stability of Ito stochastic systems with time-varying delays, where the system is subjected to both Brownian motion and Markovian parameter jumping. By using the method of free-weighting matrices, we get the sufficient condition of robust stochastic stabilization. The sufficient condition is transformed into solving some linear matrix inequalities. Put forward the concrete methods to design a state feedback controller such that, for all admissible uncertainties, the closed-loop system is robustly stochastically stable.Lastly, this paper applies the cooperate game theory in the economy to robust control theory. This article introduces the definition of income density and treat income density vector as system output, we study on the method of profit distribution in the system total income. Based on the definition of core, the author presents a formula for calculation when the core exists. When the core is an empty set, the paper also gives the method of how to get the profit distribution that can satisfy all the players. This article not only improves the theory of solving cooperate game but also contacts cooperate game with control system, so this theory has more practical value than before.