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Classic methods for determining the functional extrema can be successfully applied to solve a relatively narrow range of practical tasks. This is due to the fact that, in general, the quality of the studied output product in the process of movement varies. The traditional methods lose their main advantage associated with the assessment of the process quality at each step of the trajectory change. In this paper, we have used the example of identifying the process of batch liquid heating to illustrate the use of the devised efficiency criterion for practical determining the optimal control on the basis of experimental data and analytical determining of the value of the heating mechanism depreciation. Studies show that a necessary condition for finding a reliable optimality criterion is the account of technological equipment wear in situations where its impact on the assessment of efficiency is significant. The question of whether to consider or ignore the equipment depreciation (when searching the optimum) must be justified in each case. It was found that the maximum efficiency shifts relative to the minimum cost and maximum added value (profit in open systems) towards higher productivity. This is due to the fact that the growth rate of cost, in the vicinity of the minimum cost, is much lower than the decline in the rate of operation (productivity). Ultimately, this leads to an increase in the integral added value if the cyclic operations are handled more efficiently. The devised optimization criterion has a peculiar feature of its natural sensitivity to both the variation in the values of the system products’ cost and the operation time.

Identification of target system operations. 4. the practice of determining the optimal control