The paper sees into the problem of bringing a certain macroeconomic system to the turnpike line of development along the trajectory, which, in terms of some quadratic quality criterion, approximates the proportions of gross output to optimal ones. Moreover, optimal proportions of gross output are considered to be the proportions of the turnpike economic system. A turnpike system is formed due to a selective control of the final demand vector, thanks to which the final demand vector becomes balanced. Optimal control of a developing microeconomic system allows achieving turnpike growth rates of a master system in the fastest way possible. The basis is an input–output dynamic model between the branches that was developed by Wassily Leontief. Selective control is based on interrelation of dynamic module secular equation roots and variable parameters, which are, in these terms, elements of the final demand vector. An objective of optimal control in this paper is formation of a linear-quadratic regulator, which can help to bring a certain microeconomic system on the trajectory of the already existing turnpike system. The use of qualitatively new principles of selective control in order to analyze and manage the balanced growth of gross output makes it possible to influence the specified movement components of dynamic macro-systems. Such inclusion of economic and mathematical methods in the objectives of state regulation of microeconomics is worth being considered as the most prospective.When applying methods of selective and optimal control of final demand and external investment effects on microeconomic systems it is possible to create and maintain turnpike growth rates of these systems, analyze and optimize temporary investment processes in the phase space of industries and provide financial and economic information about costs and investments for decision-makers in terms of optimal economic development.
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