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Game economic management and control methods and applied research

Author: ZhouMingZuo
Tutor: LuoYueSheng
School: Harbin Engineering University
Course: Applied Mathematics
Keywords: Transition Delay Systems Robust stochastic stability Macroeconomic System LMI Core
CLC: O225
Type: Master's thesis
Year: 2011
Downloads: 104
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Abstract


Economic system is an open system, the external environment will inevitably be affected. When the economic system, there is a certain parameter perturbations and uncertain, the study of economic robustness of the system problem is essential. In this paper, the problem solving perspective of the real economy, the establishment of China's macro-system model, mainly studied the international energy price volatility as an external disturbance transition delay systems robust stochastic stability problems. Markov random hopping system, given its profound practical background received extensive attention in recent years. Although it is a general linear system in the form of promotion, but because its structure is more complex, and the general linear systems are essentially different. The system can be described in many engineering problems as well as economic issues, its research has not only theoretical significance, but also has a practical value of the work. Such complex transitions the system state vector containing the modal and the status of two parts. Modal represents the dynamic process is continuous variables, is defined by the finite state space in a continuous Markov process; the system state variables are discrete, each mode the system state is a set of differential equations. Firstly, in the context of China's macroeconomic system studied Markov jump delay systems robust stochastic stability and guaranteed cost control problem. In order to solve stochastic systems robust stochastic stability, delay-based decomposition method constructs a new Lyapunov function, the application of the definition of stochastic differential operators differentiate them by using linear matrix inequality (LMI) given the nature of such closed-loop system guaranteed cost controller sufficient conditions for existence, to design a robust guaranteed cost controller. A numerical example illustrates the effectiveness of the method. Then, still in the background of China's macro-system model to study the It6 type hopping delay systems robust stochastic stability problems. The system is subject to Brownian motion in both the items they contain Markov jump parameters. By adding this liberty matrix method has been robust stochastic stability of the system sufficient condition to solving a set of linear matrix into inequality problem, and proposes specific state feedback controller design method. The controller guarantees that for all admissible uncertainties, the resulting closed loop system is robust stochastic stability. Finally, the article economy cooperative game theory is applied to the robust control problem, the introduction of the concept of income density was studied in order to gain density vector as the system output, total revenue for the system to distribute the profits approach. Based on the core of the concept, the core exists when solving equations and when the core is not present all the participants how to make a satisfactory profit allocation method. This will not only be the core of this cooperative game theory is a perfect solution, but also cooperative game and control systems linked to more application value.

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Game theory ( game theory )
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