Optimal control problem for the three-sector economic model of a cluster

The problem of optimal control for the three-sector economic model of a cluster is considered. Task statement is to determine the optimal distribution of investment and manpower in moving the system from a given initial state to desired final state. To solve the optimal control problem with finite-horizon planning, in case of fixed ends of trajectories, with box constraints, the method of Lagrange multipliers of a special type is used. This approach allows to represent the desired control in the form of synthesis control, depending on state of the system and current time. The results of numerical calculations for an instance of three-sector model of the economy show the effectiveness of the proposed method.