Optimal Control For Macro Economic System Based On Cobb-Douglas Production Function

Economy is the lifeblood of a country, economic development is a hotly concernby government, public and economists. It not only means the expansion of the scaleof national economy, but also means the improvement of the quality of life, economicand social. Economic system is a continuous evolution of complex system, and it hasthe multi-level and versatile structural features. It is the system which has someonetake part in, the function in the finally come down to production and consumption.In this sense it could regard a birth and death process.Firstly, the article put economic system as open complex huge system, using thetheories and ideas of scientific system, taking qualitative and quantitative methodto study the C-D production function which based on the macroeconomic system,put the dynamic development process of capital formation and operation as a birth-death process, introducing double variables continuous function, which consideringthe relationship between capital and time, and considering the years of capital, putcapital stock and consumption levels as the state variables of economic system, usingaccumulation control investment scale, established distributed parameter model ofmacro economic system, this paper reference the previous research results studymacro economic system control model which use Cobb-Douglas production functionas the feedback element, formed capital dynamic development closed-loop controlsystem, using the characteristic line method put the solution of original equationinto Volterra integral equation, proof the existence and uniqueness of solutions.Finally, put the initial boundary value problem of model into an abstract Cauchyproblem in Banach space, With functional analysis as a tool, in the conditions ofexistence and uniqueness of solution, optimal control problem is discussed.