The growth model for resource dependent economies requires for the control of stocks of exhaustible natural materials. This control carries a triple burden. Firstly, it ensures the availability of a reserve of resources to avoid their complete exhaustion in the expected period of time. The second role of the control parameter is to determine the amount of investments allocated for the development of the scientific and technological sector in order to create technologies that enable the use of renewable and/or recyclable resources in production. The third role of the regulator is to provide the maximum possible value of the quality functionality of the control problem, which describes the cumulative level of relative savings discounted over an infinite period of time. In this paper, the first two tasks of the regulator are considered in detail, and conditions are formulated under which the absence of risks of total resource exhaustion in long-term forecasts is guaranteed. The third role also becomes important in the case of non-uniqueness in the process of synthesizing a regulator based on solving the first two of these problems.