Theoretical Justification for the Solution of the Problem of Destabilization Energy-Saving Control of Multidimensional Technological Objects Operating in Variable Performance Conditions over a Long Time Interval

The solution of the so-called "destabilization optimization and destabilization control problems" is analyzed as applied to complex MIMO systems operating in variable performance modes according to the products manufactured over long time intervals. In relation to such problems, an additional economic benefit can be obtained as compared with the traditional method of solving them. Here it is essentially possible to improve the statics of the systems operation over the time interval by determination of such static modes corresponding to the jobs with varying performance so as to achieve the optimal effect in terms of minimizing energy or resources over the considered time interval. In the present paper the previously initiated study was continued, where a certain MIMO system with the load varying repeatedly over a given time interval was considered. There is an integral criterion characterizing the quality of the system operation over the time interval, while the integrand function is a linear parametric one that depends on additional control actions, as well as on the system performance as a parameter. The study is illustrated by the example of a local problem when there is one additional control and one additional state coordinate. The identical problem was derived from the previously formulated linear multi-level one-dimensional problem of destabilization optimization, called the primary problem, after its discussion. Its solution will allow to analyze the energy-saving control of MIMO systems, ensuring the construction and study of the existence domain of the problem solution and the determination of the function types for the optimal control

The study was supported by a RFBR grant (project no. 17-08-00457-а)

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