We present a new approach to finite horizon open-loop LQ-control problem with unknown dynamics under constraints on variable states in the form of equalities and on control impacts in the form of inequalities. The goal of optimal control is to find a control that minimizes a specified cost function to achieve a change in the state of the system that satisfies the imposed constraints and maximizes the value of the efficiency criterion (cost function). This algorithm finds a sequence of control impacts in the admissible cone on the horizon m minimizing the quadratic cost function on the vector input and vector output. The proposed approach will be very useful in solving real-world control problems in open-loop systems without measured input and output data. The dynamics matrix specifies only the law of transfer of influences between the factors of the model, and the input/output data are generated in the form of components of the conditional principal eigenvector on a given control horizon. This study has shown that the algorithm can efficiently solve problems of optimal planning of a control trajectory in a given direction of development under open-loop conditions with control constraints. Constraints can be imposed on the vector of control impacts depending on the available resources of the decision-maker. Existence of solution of the discrete optimal control problem under integral constraint and control constraints is proved by Theorem 1. Sufficient conditions for the convergence of the iterative process are established (Theorem 2).