The theory of combined systems of extreme control, which is used in technical systems, was developed and adapted in socio-ecological-economic systems. For example, river basins are such systems. A combined extreme control system has been formalized to control the dilution of mineralized mine waters in river sections. A mathematical model of the distribution of water masses and pollution in river beds from point and diffuse sources is proposed on the basis of a system of difference balance equations under the influence of stochastic uncontrolled disturbances. With regard to such conditions as adequate instrumentation, a combined control system has been developed that uses decision-making according to environmental and economic criteria based on the analysis of input and output data simultaneously, identification and tracking of the optimum in conditions of displacement under the influence of the disturbances of extreme characteristics of the system. The structural and functional diagram is represented by the open-loop diagram, the identification of which is carried out on the basis of modeling the process of water dilution in various situations at a specific object. A closed part with a recognition system as a corrector provides feedback. Formalized mathematical models of the dynamics of water masses and pollution from point and diffuse sources are of a general nature and can be used for the basins of other rivers. The extreme control system can adapt to the hydrological conditions and water quality parameters of a particular river.
A mathematical model has been formalized for the combined extreme control of mine water dilution in the section of the Ingulets river. The water for dilution comes from a storage pond in the Svystunov gully. Regulatory actions that maintain water quality without exceeding the normative values of maximum permissible discharge are determined. At the same time, water consumption for dilution is minimized. The scenario analysis of the options showed a saving of up to 30% of water resources, namely 17.5 million m3, compared to the dilution carried out in February-March 2021 according to the existing individual regulations.
