Modeling Regulation of Economic Sustainability in Energy Systems with Diversified Resources

: The imperfection of theoretical and methodological approaches to regulate the jump process transition when combining differentiated energy resources is a pressing issue. The goal of this paper is to develop a theory and a method to regulate the integration-balancing processes of combining diversified resources. The concept of combining integration and balancing models has been substantiated by methods of transforming multidimensional space and approximating generalized functions that represent jump-like processes. Theoretical and operational-regulatory models of economic sustainability have been developed, substantiating new concepts, patterns, properties, dependencies and indicators of the dynamics of the processes of combination; the optimality conditions for the number of approximations of generalized functions, interpreting the effects of control functions of combining resources, are determined. New methods for solving problems have been developed: the organization of the energy technology complex of facilities for enhanced resource diversification and the Center for Sustainability, improving the quality of managing dynamic processes in terms of combining and diversifying resources.


Introduction
The urgency to improve the regulation of differentiated resource of systems and the effectiveness of the results of their evolutionary modernization and spasmodic development processes grow in conditions of instability and uncertainty. It is necessary to develop a special methodology for combining, integrating and replacing diversified resources and methods to allow for the convergence of target trajectories. We formulate the methodology as integration-convergent and organizational-technological since it determines the growing importance of the results of the unification of the totality of generally accepted scientific achievements in the theory of managing the processes of system formation and development. It determines the direction of actions to ensure sustainability in the long-term development of systems when combining differentiated resources. The processes of the first type correspond to the modernization of technologies with minor degrees of combination and diversification of resources mainly. Consequently, separate centralized and single-product production prevails on a constant technical-technological and organizational basis. The processes of the second kind are distinguished by the abrupt replacement of existing technologies and methods of organization. In this study, this means a transition to medium and high degrees of combination and diversification of resources by high-tech activities of interconnected facilities in multipurpose complexes of various types. The relevance of the economic justification for renewable energy development projects determines the need for new models and methods for project evaluation. Such energy consumes renewable energy resources (RERs). For example, the volume of solid household and industrial waste in the world is about 0.5 billion tons or 500 kg/person [1]. In the Russian Federation, an average of 63 million tons is produced, with 4%-6% of the total volume of useful use, according to various estimates, despite the fact that the climatic and geographical conditions of most of the territory of Russia and significant reserves of non-renewable resources do not contribute to an increase in the use of such natural renewable energy resources, as the energy of the sun, wind, tides, ocean currents, etc. Nevertheless, it is advisable to refer to the experience and forecasts of developed countries: in Germany by 2025 energy facilities consuming nuclear and coal fuels should be closed, and by 2035 the share of energy resources should be 8% [2]. The global scale of the problem of their insufficient use is associated with the expected depletion of non-renewable energy resources and the increasing importance of environmental protection in the concept of sustainable development. At the same time, the volumes of a new type of material resources with the energy potential of development-solid household waste (SHW) in the amount of about 0.5 billion tons or 500 kg/person are added every year [3,4]. This is aimed at improving the quality of life of the population and takes into account the rapid increase in the cost of traditional energy resources of a non-renewable type. The costs include the environmental component, since the norms of environmental activities must be strictly observed.

Literature Review/Background
The insufficient degree of scientific elaboration of the ecological and energy component of the research problem consists in the predominance of modernization approaches to the improvement of energy efficiency. This is exacerbated by the global scale problem of the irrational use of natural resources. With the depletion of primarily non-renewable energy and other material mineral resources, the importance of energy-saving and environmental protection activities in the concept of the sustainable development of the society of a post-industrial economy increases. At the same time, the volumes of a new type of anthropogenic resources with energy potential are growing in it. Such forecasts are substantiated by Topuzov and his co-authors in a multicriteria model. However, it does not show the methods for regulating the jump-like processes of transition to high-tech methods of energy saving. The advantage is the assessment of the use of hydrogen fuel, which is aimed at improving the quality of life of the population and takes into account the rapid increase in the cost of traditional energy resources of a non-renewable type. In the sentences of Razuvaev the environmental component is considered, but he justifies the technology only with a low degree of diversification of resources [3]. This reduces the potential for the full use of the potential of energy and resource conservation at the energy technology complexes scale (ETC). In official statistical forecasts [4], objects with the current low degree of combination and diversification of resources are more taken into account. It is not possible to predict the formation of multipurpose industries such as ETC in the presence of many optimization criteria.
Models and mechanisms for regulating combined diversified resources and integrating objects of the scientific-educational sphere, industry, traditional and renewable energy to achieve a compromise of their interests in the structures of complexes are not sufficiently perfect. The models and mechanisms do not correspond to the needs of the post-industrial economy in innovative methods for effectively solving the environmental problems of the post-carbon energy type. It determines, especially in developed European countries, the tendency of transition in the period up to 2025 to the preferential use of renewable energy sources. The impact of techno-technological and economic factor-challenges of the environment and competition of developed countries on the increase of energy and environmental efficiency of the Russian energy sector by high-tech innovative methods of combining resources is growing.
The type of energy aggregates suitable for different energy sources [5] proposed for scaling by Goldoliner et al. also has low possibilities for resource differentiation and cogeneration. At the same time, a regulated reduction in the imbalance of interests of traditional and renewable energy facilities is most effective if they have multipurpose opportunities for energy-saving development in the formation of ETC.
In Li et al. [6], using the example of the propagation of biological phenomena as an example, a model representing the zones of their stability and bifurcations is studied. It should be noted that the generalizations declared by them of the applicability of the model raise doubts about their application to technical and especially power systems. The proposal studied the nonlinear processes of the periodic development of such systems are more pronounced, more specifically, reflecting the specifics of this study of linear differential systems in proposals for estimating jump-like bifurcations of Euzébio [7]. However, in the three indicated works, the tasks of interaction of objects whose processes have a high degree of diversification of resources are not solved. To ensure positive synergy of interaction between different objects, it is necessary to combine the processes of evolutionary modernization of technologies, revolutionary (spasmodic) and bifurcation development as part of a multipurpose ETC. It is necessary to specify organizational methods for achieving practical results in regulating economic sustainability based on calculations of the entropy synergy results of combining resources of a high degree of diversification. This follows from the particular complexity of the processes of combining traditional resources and energy resources.
The policies in the post-carbon industrialization of the economy increased the need for tools to regulate economic sustainability of multipurpose energy systems with the inclusion of the so-called "smart" energy-saving and generating type facilities, hydrogen and other energy-efficient accumulators.
The singularity of technologies, as "breakthrough" innovative challenges of the post-industrial economy, is manifested in their exponential growth since the beginning of the 21st century. Indeed, many forecasts confirm the well-known methodological proposals of Adizes [8] that favor creating biosimilar management structures of "live" organizations. Sen and Lalu note that [9,10] holacratic flexible (agile) methods of creating self-governing teams of different profiles are effective. They correspond to the spiral dynamics model of the so-called "turquoise enterprises" [10]. Despite their practicality, they are more applicable in the design and engineering field. This narrows the applicability of such methods in the formation of ETC. More concrete forecasts for the development of intellectual resources forecasts by Frumin [11]: the increase in the number of digital and network companies such as "Amazon"; the expected growth by 2035 of the capabilities of computer systems and artificial intelligence in assessing their computing power (they will exceed the total analogous potential of the human biological system); and growth of high-tech and high-tech engineering services in the innovation ecosystem. In the modern conditions of the Russian Federation, universities of types 2.0 and 3.0 prevail, being drivers/challenges for the development of industry, mainly of industrial type. At the same time, the scale of their transformation into educational and scientific 4.0 complexes is growing with universities that are distinguished by a high degree of globalization of education and the use of new educational methods: on-line study and creative development along individual trajectories of students; the use of training digital simulators (doubles) in virtual or real cognitive technologies for solving practical problems of the post-industrial economy and energy.
In such a digital economy, it is necessary to use open educational platforms based on large databases. Especially they are necessary for analyzing the possibilities of advanced combination of resources based on the organization of ETC with the inclusion of objects of distributed energy, other multipurpose productions and participation in projects of such transformation of research and educational complexes of type 4.0. In the study of the impacts of knowledge management practices, the quality and competitiveness of the results of Azizi and co-authors [12] took into account only a part of the necessary organizational tools for the development of complex systems. Hoegl and Schulze [13], exploring the initial stage of creativity of the innovation cycle, and Liu and co-authors [14] in his empirical evaluations of correlations with product updates revealed the significance of process uncertainties. However, they have not solved many problems of modeling at the stages of self-organization of complex adaptive systems. This was complemented by the work of Lafond [15], McCarthy and co-authors [16]. At the same time, due to the specifics of their scientific research, they could not take into account the peculiarities of the interaction of energy technology objects of various purposes. Special methods are needed to regulate their interdependencies in the event of radical change in the results under the conditions of singularity of technologies.
Similar studies on solving complex problems of an organizational type were carried out by Kirsch [17]. Puschke [18] proposed multimodel approaches to the dynamic optimization of processes under parametric uncertainty. The promising methods of analytical modeling of the processes of management of differentiated innovations by Kim should be noted [19]. Taken together, their proposals justify the need to study the structure of complex systems, which are characterized by significant scales of exponential or abrupt growth of a number of "breakthrough" technologies: digital modeling of new products with optimization of all the necessary quality criteria of their designs and operating conditions; cross-sectoral technology transfer and reverse engineering for lowcost modernization of low or medium-level innovative technology; additive technologies with the possibility of simultaneous formation of the material and product design. The number of virtually distributed digital factories of global scale and operating digital counterparts of technologies and products are increasing. Such technologies should be taken into account in mathematical modeling of the sustainability of the processes of combining material expanded complex of resources (energy types under consideration, technological ones), non-material (competences of educational, research and design spheres). Such resources are proposed to be characterized by a high degree of diversification (HDD), justifying the integration of objects in the ETC.
The answer to the competitive challenges of the digital economy is to apply the methods of efficient polygeneration based on the combination of the resources of the HDD and the organization of a multipurpose ETC. In order to achieve positive synergy and energy savings, the interaction processes should take into account the principles of bio-and nature-similarity. They are based on the anthropic concept of the philosophy of ensuring the similarity of the complex material systems of the Universe, organizations and humans in an objectively existing space of all possible and interacting development options [20]. The possibilities of quantum mechanics and quantum computers will expand the scope of design of materials and processes with predetermined properties. Chandra made a significant contribution to the study of such revolutionary processes. [21] in terms of modeling processes of a periodic type. Approaching the objectives of this study in the proposals for strategies for managing the merger of radical innovations in nano-biotechnology was done by Maine [22]. Methods of Cunningham [23], according to the predictions of innovation brought to the practical training tasks, are taken into account in the methodology of this study.
The trends of post-industrial development and the challenges of the singularity of post-carbon energy technologies not only impact the imbalance of the goals of sustainability and the effectiveness of its development at certain stages of the innovation cycle, it is also necessary to take into account the aggravation of the conflict of interests of producers and consumers of decentralized and centralized types using only traditional renewable resources or when they are insufficiently combined with renewable energy resources. The complexity and diversity of existing market factors, the intensity of material and information flows and the dynamics of their growth in a highly competitive environment necessitate energy saving and diversification of energy supply technologies [2]. However, the proposed methods of theory and practice do not provide for the regulation of the processes. They do not take into account the integration of objects and the combination of the resources of the HDD in the extended range of their effective interaction.
An important factor in the sustainability of energy development processes due to the insufficiency of centralized generating capacity is the intensive development of low energy [4]. This is hampered by insufficient support from the state budget, the inertia of the thinking of supporters of traditional energy. It should also be noted their relatively low energy and economic efficiency of the use of renewable energy resources due to significant investments in the creation of power plants using renewable resources, and the relatively low cost and availability of traditional energy resources. The presence of a centralized dispatch control and a large potential for the development of alternative energy do not solve the existing problems of the Russian energy industry (Figure 1). The uneven localization of consumers of fuel resources and their deposits in different regions (deposits in the Eastern regions, consumers in the Western ones) is obvious. The energy intensity of the gross domestic product remains high (2.5 times higher than the average world level and 2.5-3 times higher than in developed countries) and the degree of depreciation of fixed assets of the fuel and energy are complex. For example, the degree of depreciation is 58% in the electric power industry and gas industry and 80% in the oil refining industry [24]. The underdeveloped infrastructure of the innovative modernization of the fuel and energy complex maintains the asymmetry in the supply of electricity to individual regions of the country: there is some surplus in the energy balance in the Urals and the Far East, and there is a shortage in the European part. The dependence of the energy industry on the supply of imported components and maintenance supplies remains [2,4].  At the same time, the fuel-substituting potential for the development of alternative energy in the Russian Federation is quite large, amounting to about 270 million tons of mercury equivalent, including solar energy, 12.5; wind power, 10; geothermal energy, 115; biomass energy, 35; energy of small rivers, 65; energy of low potential heat sources, 31.5. Historically, Russia lagged behind a number of developed countries in terms of the share of unconventional fuel in the overall structure of energy consumption. However, according to the forecasts of the Analytical Center under the Russian Government (Figure 1), their total use will increase 1.6-3.3 times, and their share in energy consumption will increase from 1% (in 2015) to 2%-3% by 2040. This is due to the lack of reasonable proposals for combining the resources of the HDD. Separate functioning of most of these energy facilities does not allow to regulate its sustainable development.
The insufficiency of the pace and scale of the transition to energy saving is confirmed by the fact that only 5% to 6% of industrial enterprises in developing countries have developed relevant technological innovations compared with 60% to 70% of developed ones. The lag in the pace of transition to industry 4.0 determines that the export of high-tech and high-tech products from Russia does not exceed 5% [2]. Nobel Prize winners Heckman and Schulz (1975) substantiated this discrepancy in their work on human capital arguing that the main contribution to labor productivity is related to the education, science and production facilities to what has been achieved and openness to the new, ensuring in developed countries up to 80% of its growth [25]. The significance of such an attitude can be confirmed by a number of statements from experience and forecasts: an exponential increase in the number of participants in scientific conferences from the beginning of the 21st century [16] and the number of freelancers; assumptions about the disappearance by 2025 of a greater number of jobs (especially intermediaries engaged in routine manual and cognitive labor) than their appearance [9,10]. Consequently, intellectual capital, which is characterized by the predominance of nonroutine, analytical and creative work based on interpersonal communications and holacratic methods of the spiral dynamics model by Lal and Robertson, should be the main focus [10]. Together with Schulz, they argue that investment in such capital should grow at a faster pace. At the same time, the characteristics of professional competencies prevalent in most domestic enterprises do not fully meet the requirements of the theory and methodology developed by the organization of hightech processes and methods for integrating objects into ETC for combining HDD.

Models of Combining Diversified Resources
The processes related to abrupt transitions require special attention. The incompleteness of the solution of the economic component of the problem is manifested in the absence of special models for ensuring sustainability based on minimizing the imbalance of interests of traditional and renewable energy with varying degrees of centralization of energy supply.
We present a model of the processes of combining diversified resources and technological processes. The model uses a cyclical sequence of processes and methods to organize energy technology production, which forms three interacting blocks: inputs of factor, target, and resource components; processes and methods; and outputs of components.
Block 1, the inputs, represents the initial level of combination and diversification of resources (natural, human-made and anthropogenic). Block 2 includes models for expanding cogeneration along the directions of trigeneration and polygeneration in the space of a complex of objects; the mechanism of organizing the interaction of objects in multipurpose energy technology complex (ETC). Block 3 contains outputs and tracks changes in the management practices to combine HDD resources.
This model introduces the authors' concept of extended cogeneration of thermal, electrical energy and other products using all types of traditional and renewable natural, human-made and anthropogenic resources. The composition of natural resources takes into account traditional nonrenewable (coal, gas, etc.) and renewable (solar energy, wind, etc.). Human-made resources include industrial and household waste, intellectual (objects of educational and scientific project activities) and fixed capital of objects (capabilities of the technical and technological base of production). Such a high degree of diversification of resources creates opportunities for obtaining a variety of products when organizing their joint activities in a multipurpose waste-free complex.
There is a need to take into account the imbalance of interests of traditional energy facilities and new ETC interests that use the processes of combining resources. This is due to the opposite of the goals of increasing the sustainability of such innovation processes and their effectiveness at some stages of the ETC life cycle. The opposite of goals is particularly evident in the high-tech processes of combining HDD resources with methods of organizing extended cogeneration, when multipurpose production of energy, industrial and other products is carried out. The sustainability of development at the beginning of the cycle often decreases, then gradual or intermittent increase is possible when regulating the factor indicators of energy, environmental and economic efficiency. This is explained by the discrepancy of staff competencies, insufficient consideration of the differences and capabilities of the cogeneration technology by the developers of projects for such a complex of facilities, the novelty and increased complexity of technologies for combining HDD, etc.
The need to study the formation of a multipurpose system of ETC objects using highly differentiated resources to ensure the sustainability of evolutionary and intermittent types of innovative development has determined the development of management theory and the development of a new methodology for managing the integration of resources according to indicators of integration and balance of opposing interests of sustainability and efficiency [20,25]. It provides for the possibility of achieving a minimum imbalance of goals expressing these interests and stabilizing their zone of compromise in the processes of combining the air traffic control resources organized in the structure of multipurpose, resource-saving, low-waste type systems. For example, these may be multipurpose, or multiproduct (target) ETCs, in which these objectives must be coordinated at the level of compromise of interests of traditional and renewable energy and other technologies for combining resources. For this purpose, it is necessary to regulate the convergence of the trajectories of the goals of sustainability and development efficiency in ETC of such objects using multipurpose production technologies (polygeneration).
Regulation is effective when applying a control mechanism based on an operational and integration model of the economic sustainability of the processes of combining air traffic control resources. Its special management functions should influence the application of methods of organizing the interaction of objects of different profiles in ETC by the criterion of minimizing the imbalance of their goals. Combining resources in such processes in combination with the methods of organizing trigeneration (ideally polygeneration) of heat, cold, electricity and other products provides a competitive differentiation of energy-saving results in terms of energy, environmental and economic efficiency. Improving the theory in the proposed formulation of the paradigm of systems development is possible in the concept of regulated stability of the processes of combining not only material energy, but also other resources of the HDD with methods of integrating relevant facilities for expanded polygeneration in organizing a multipurpose ETC. This will allow to take into account these factors and scientific achievements in our proposed theoretical model and operationalintegration model of methods for organizing the regulation of the relationship of objects in the complex. The provisions of the high-tech innovation management methodology [20] are based on the joint application of the systemic and holistic approaches to the study of a complex system as a complex of interacting objects of different profiles. The Authors' theoretical and methodological tools form an interdisciplinary approach to assessing their interaction and transformation (for example, metabolism using analogies and digital simulations of models of biological objects) of varying degrees of innovation and reproduction (replication). It corresponds to the well-known proposals of most modern management theorists. The improvements proposed in the article are aimed at their development and specification of the subject and objects of research on the interaction of ETC objects when combining the HDD resources.
The emergence and sustainable development of a post-industrial hybrid economy using resources of the HDD (intellectual, material, natural, man-made and anthropogenic types) is possible when they are combined in a cycle of evolutionary and revolutionary processes of systematic use of natural, labor and capital resources. For the sustainability of processes to ensure effective results with high added value, it is necessary to complement the integration of objects of different profiles, combine or replace resources (intangible and material) with the HDD for the organization of hightech balanced development of ETC. This justifies the idea of a unified methodology of integrationbalancing management (MIBM), combining theoretical models and methodologies for the integration and replacement of resources [20] with models and methodology for balanced development of systems in a dynamic environment [25]. On their basis, new methods have been developed in the concept of improving the quality of regulation of the economic sustainability of the processes of combining HDD resources during the integration of multipurpose ETC facilities. In order to implement the methods, in the second part of the article, a method and a mechanism for the regulated reduction of the imbalance of interests of objects, measured by the goals of sustainability and efficiency of innovative development in the context of the integration of objects in the ETC, are developed.
Joint research proved the possibility of using mathematical models of S.V. Alyukov for the interpretation of organizational and technological processes of integration and combining resources by the methods of approximation of stepwise and generalized functions in the simulation of dynamic processes based on the MIBM. The models allowed to quantify the evolutionary improvement in the quality of regulation of the economic sustainability of the processes of combining and changing the stepped form when organizing ETC structures by methods of enhanced integration of the resources of its facilities. A measurable assessment of the state and the processes of regulation of the imbalance of their interests was achieved, measured by the opposite objectives of the development of objects.
The theoretical and operational-regulatory models of economic sustainability form the basis of a unified methodology that provides the analytical ability to display the multicyclic expansion of the complex space and time of managerial influences. They are carried out by the functions and indicators of the effectiveness of the use of innovative technologies for combining resources and methods of organizing the indicator-property stability of evolutionary and spasmodic development processes. The existence of such possibilities is confirmed by the methods of geometric algebra of a multidimensional space, which studies computational approaches to compression and stretching as types of space transformation [26]. Subsequently, these approaches formed the mathematical foundations of quantum mechanics. For the first time, such algebra was proposed by William Clifford, the author of the term "divergence" and vector analysis (together with Gibbs and Heaviside) [27]. However, in these studies, purely mathematical problems were solved without practical application. Naturally, they were not specified on the subject and object of this study.
In mathematical and organizational research, we have identified opportunities for the development of geometric algebra based on the use of the toolkit of generalized functions, which makes it possible to describe singular variants and scenarios in relation to spasmodic processes of technological and organizational development. Such functions in many cases are of a purely abstract nature. They do not take into account the inertia property that precludes instant changes in the initial state of the object, which requires an infinitely large amount of energy.
For a better understanding of generalized functions solutions to such problems, Alyukov proposed a method for their approximation via analytic functions ( Figure 3) [28,29]. Figure 3a represents the delta function. Figure 3b shows how to use the delta function, taking into account the types of combination processes and organizational development of the system. The representation of the nature of generalized functions allowed using their features to describe the spasmodic processes of organizational behavior in assessing the sustainability of the effective development of the system The value x in this case is indicator to assess the levels of energy, environmental or economic efficiency (LE) of the factorial effects of technologies combining diversified resources and methods of organizing a multipurpose ETC that has a length in time t . In this study, it is the regulation of combining technologies by changing the degree of diversification of resources and the innovativeness of methods of organizing objects in ETC that affected the investigated property H efficiency (LE) in assessing the level of economic sustainability (LES) of the application of technologies for combining resources.
The specified ideal mathematical representation by Formula (1) of regulatory actions due to the specified reasons does not allow to reveal the real, practical content of cause-effect relationships (Figure 3a). To determine zones (surfaces or areas with a three-dimensional approach) of dynamic stability (Figure 3b) in the methodology of balanced development, it was proposed to choose methods that took into account known types of stability: for ETC technical systems-providing a return to their equilibrium state for any environmental disturbances; for the socio-economic systems of organizing joint activities of objects in ETC-affecting the return of actual indicators in the area of established goals for the integration of objects and the combination of resources in assessing the convergence of their trajectories, taking into account the compromise of interests of objects; unstable and uncertain state of bifurcation in the conditions of resource disintegration and trajectory divergence; spontaneously arising resistance at a certain stage of the cycle of ETC formation; absolute stability of a closed system while reducing stability and efficiency. To clarify the idea and concept of scientific work, a theoretical model of "4W" of economic sustainability of a multipurpose ETC-type system is proposed, based on spatial-temporal coordination in the integration-balancing cycle of diversified resources of combination technologies and methods of organizing interaction of objects. This takes into account changes in the imbalance of opposing goals of sustainability and effectiveness in the four stages of the life cycle of the formation and functioning of their complex. The initial letters of the words "Where-W1, When-W2, What-W3, Why-W4" correspond to the directionality of impacts and the content of cause-effect relationships (in assessments of target indicators of economic sustainability and efficiency of innovative development) of objects in space and time.
Taking into account the objectively positive direction of time changes along the x axis of the theoretical model (Figure 3), we will assume that the planes 2 and 3 interpret the processes of functioning of the ETC (the temporal measurement of the processes W2). The negative direction of changes in planes 1 and 4 corresponds to the processes of formation and divergence of cooperative relations of ETC objects (spatial dimension of the processes W1). It is proposed to regulate them with special management functions used in the new organizational structure of the Sustainable Development Center (SDC) ETC. Different directions of influences of processes and methods form the differences between the following types of processes of combining resources and organizational development in the life cycle of ETC in the following quadrant stages: 1, medium technological development by methods of separate functioning of objects (MTD processes) at the functionalevolutionary stage of development of control functions in the SDC the formation of ETC, leading to a decrease in LES; 2, combining the resources of the HDD at the structurally revolutionary (SR processes) stage of transition to new management structures (creation of SDCs and ETCs), which determines the abrupt growth of the LES index; 3, structural-evolutionary (SE processes) development with the inclusion of new objects in the ETC and the gradual growth of the LES; 4, low technology conservative self-organizing (CS processes) development by the methods of separate functioning of facilities or combining with a constant or low degree of diversification of resources (spontaneous processes of preserving the existing ETC structure and the achieved LES).
It can be determined that the plane of a two-dimensional representation of a theoretical model, in which the region of changes of the indicator-the property of economic sustainability of the LES = H-is vertically represented, and horizontally the changes of factor efficiency indicators over time form the life cycle field of the formation and development of ETC functions and structures. The field forms four zones and types of processes of combining resources and methods of organizing a complex of objects, the selection of which is advisable to carry out according to the results of ranking the extent of their impacts in statistical or expert assessments (for example, low, medium and high) indicators of sustainability and efficiency. Such differences in the characteristics of the cycle suggest the main hypothesis of a quantitative representation of the dynamics of economic sustainability levels when regulating the processes of combining resources and organization methods by the criterion of the minimum variability of its imbalance zone with efficiency in cycles of evolutionary and abrupt changes.
At the beginning of cycle 1 (corresponds to the measurement of processes of the type W1 in Figure 3), it is possible to observe phenomena in the ETC that are inherent in the opposites of the dynamics of the LES and LE indicators. It follows from the preemptive use of modernization measures at separate facilities (there is no minimal combination of resources, and there is no formation of ETC). The use of traditional technologies (for example, separate production, high centralization of activities, etc.) ensures high levels of LE and LES processes. However, for the above reasons, energy and environmental performance indicators are starting to decline. Therefore, scientific and project development of decisions on the formation of technologies for combining HDD resources and methods of integrating ETC objects is necessary to regulate the sustainability of processes. The analysis of the experience shows the possibility of stabilizing the LES in the zone of minimum values for the period of cycle 1 and the beginning of its evolutionary growth with the operation of individual energy-saving objects. The spasmodic increase in the level of innovation, determined by the moment of commissioning of polygeneration high-tech facilities in ETC, for a certain time reduces the indicator of LES for the above reasons. Then, when the staff develops the necessary competencies, it begins to gradually increase. Therefore, it can be assumed that by the end of cycle 1, the indicator of the LES will gradually grow ( Figure 3).
In cycle 2, in the case of new high-tech changes in the functioning of ETC, the considered processes should be repeated. At the same time, the indicator property (due to the stabilization of the compromise zone by the proposed methods of the LES and LE indicators) will not fall below the minimum values in cycle 1. Otherwise (the prevalence of modernization) there is a transition to zone 4.

Models of Regulation of Economic Sustainability
We use Ramsey′s growth model to confirm the main hypothesis of the dynamics of economic sustainability. The model of economic growth proposed by Ramsey and subsequently modernized by Cass, Kupmans and Alyukov [28,29] is used. It is adapted and specified by us as follows: where k and c are indicators to assess the economic sustainability of the ELS and the effectiveness of the LE type, respectively, governed by the following factors: This equilibrium position is asymptotically stable, since it satisfies the well-known transversality condition. It means that the solution of the problem of maximizing the level of process sustainability is achieved in the zone of compromise of subspaces of the vector functions of the innovative and economic goals of the development of the ETC system.
At first glance, the found equilibrium position in Formula (4) may seem strange, since the efficiency of applying the organizational method decreases to zero. On the other hand, given limited resources, as a rule, this equilibrium state is most consistent with the assumptions of hypotheses at the beginning of the periods of cycles 1 and 2.
We use the approximate analytical method of a small parameter. Having designated  Figure 4, where curve 1 corresponds to the variable k , and curve 2 corresponds to the variable c . The solid line is the numerical solution, the dotted line the analytical solutions. As seen in Figure   4, the differences in the solutions are minor. By the Lyapunov theorem on stability in the first approximation, all eigen values have negative real parts. Therefore, the resulting solution is asymptotically stable. This confirms the main hypothesis of the existence of a stable zone of indicators by the criteria of minimum variability of the compromise between the goals of sustainability of processes of innovative combining resources and the efficiency of structures of interaction of objects.
When modeling the dynamics of technologies and organizational methods of a singular type, mathematical tools are needed, shown by Formula (1). The meaning of such generalized functions is revealed in approximations, perceived as the limits of some approximating sequences of ordinary functions (for example, step functions). However, this does not allow to display the organizational behavior of a complex system of ETC objects in the space and time of the implementation of the jumplike processes of combining resources and the convergence of hopping trajectories by analytical functions. The problem is that step functions have break points at which they are not differentiable in the mathematical sense.
To overcome the problem and implement the research concept, we have specified the main hypothesis of the possibility of a quantitative assessment of the sustainability of the processes of abrupt transitions to the high-tech type of combining HDD resources and the organizational and structural specific set of embedded functions of their analytical approximation. At the same time, the number of functions describing transitions has been proposed to be interpreted by the number of types of integrated or combinable resources of the objects included in the ETC and the regulatory effects of the management functions of the SDC on the convergence of the trajectories of sustainable development goals.
It is proven that the quality of regulation of discontinuous processes is achievable with the elimination of the paradox of space and time compression peculiar to them. It is observed in the theoretically instantaneous period, and practically in the short duration of the jump-transition time.
For the analysis of the extended process zone, we will distinguish two areas of the theoretical model that determine the dynamics of development: MTD processes at the beginning of cycle 1 of the evolutionary development of additional regulatory functions and the formation of ETC; and the SR processes in cycle 2 of the abrupt transition to new SDC management structures and the processes of combining HDD resources (compare Figures 3 and 5). In the time ranges −0.15 ... 0 and 0 ... 0.15 rad cycles 1 and 2 of changes in the factors of innovation in the technical and technological base of the objects can be represented by a jump to a high LES based on the technology of combining HDD resources or a new organizational method of regulating the use of special management functions (Figure 4). We have found that such transitions are not sufficiently effective using only the basic standard control functions of separately functioning objects.
The increase in integration space of possible resources necessitates the estimator parameters for jump-transition singularity. They assess the possibility of reducing the influence of zero-length paradoxes of transition time and the unpredictability of the behavior of open-loop systems in Laplace. This led to the development of mathematically justified methods of "extending the time interval" for the implementation of short-term technological and organizational solutions of a jump type. A tangible extension value [29] is achieved by approximating a growing number of nested functions in the range A = (9,10,11). Figure 4 shows the graphs of the corresponding successive approximations obtained by Formula (6). The planar representation of the effect of space-time expansion is given in cycle 1 of medium-tech processes of the type MTD during the jump-to-cycle to cycle 2 and high-tech processes of the type SR (6). )))))))))) )))))))))) A In Figure 5, cycle 1 represents the zone of disintegration of resources and divergence of trajectories of development. Cycle 2 represents the zone of integration of trajectories of development. The graph illustrates the jump process in the range of ± 0.1 radians. The number of nested functions that provide the zone with the optimal values of the indicator of the LE, should correspond to the number of combined resources or additional SDC control functions displayed on the graph.
The change in the stability of the system under study ( H ) over time ( x ) in cycle 2 versus cycle 1 is also displayed. It can be determined by the ratio of the areas of the interaction zone of complex objects bounded by dashed lines. Moreover, Sc1 corresponds to zone 1 of the implementation of lowand medium-tech processes based on the use of evolutionarily added control functions, and Sc2 corresponds to zone 2 jumps to the high-tech level and zone 3 of evolutionary changes in the structures of the complex.

Results of Verification of Methods and Verification of Their Practical Implementation in a Real Development Project Based on Diversification of Resources
Possibilities of modeling the effect of the expansion of the process space with an increasing degree of combining resources and the time of making managerial decisions based on a theoretical model of "4W" of economic sustainability of a multipurpose ETC type system (Figure 3) are mathematically substantiated. We propose to implement in the methodology verification methods and verification of the results of regulation of economic stability according to static, dynamic and probabilistic criteria for ensuring the efficiency and stability of the processes of combining resources. Providing a stability zone in the range of 5-15 relative units in cycle 1 is simulated by the estimated dynamics of the levels of sustainability and efficiency of the processes of combining resources and organization in the formation cycle of a multipurpose energy technology complex model in Figure 4. This is possible by using additional control functions displayed by the system of Equation (6) and shown in Figure 5 in cycles 1 and 2, implemented using the methods of theoretical model "4W". The verification methodology should show that the basic theoretical representation of the four stages and methods of the cycle in Figure 3, modeled by functional analysis tools and shown in Figures 4 and 5, is reliably verified using criteria-based indicators according to Formulas (7)-(11) in mathematical modeling of organizational and technological processes. Verification is an analysis of the results of a real project, corresponding to the experience and directions of development of energy and resource conservation [31][32][33][34][35][36][37] for use of products in the formed energy technology complex combining objects and polygeneration (ETC) of solid, household and other waste (SHW-based products, in general, liquid for plasma-fire neutralization or biogas production). The result of the project may be the reduction of losses from the insufficient quality of energy-saving control processes, expressed in the under-utilization of the results: replacement of traditional energy resources; more types of energy products in terms of cogeneration, trigeneration and, in general, their polygeneration; diversification of energy production methods, increasing the reliability of energy supply in remote areas; increased processing of SHW to solve environmental problems; sale of waste to other countries.
Verification of the results includes the following steps of the methodology.
1. Static criteria made it possible to determine initial estimates of the level of imbalance of goals to increase the level of economic stability (LES = H) and efficiency over time (x = −0.2) at the beginning of the resource combination cycle in Figure 5 and verify their compliance with the methods of quadrant stages 4. Despite the application of control functions, efficiency decreases in the time range of 0-5 relative units (Figure 4). This can be estimated by the ratio of the area of the zone displaying the cycles. A static representation of the processes is sufficient to study the situation at the moment of the planning period, for example, with a slight combination of nondiversified resources. Modeling is carried out according to the criteria for improving the quality of efficiency regulation in final increments in Formula (7): The ratios of static areas (in the estimates of the products of efficiency and time) formed by dashed lines in Figure 5 made it possible to evaluate the results of improving the quality of regulation based on the effect of the expansion of space and decision time. Failure to comply with Formula (7) corresponds to the implementation of decisions on plans and projects for evolutionary modernization of technologies for combining resources of a low level of diversification and innovation using slow transformation methods. This is consistent with the methods of quadrant stages 4, low-technology conservative self-organizing (CS processes) development by the methods of separate functioning of facilities or combining with a constant or low degree of diversification of resources (spontaneous processes of preserving the existing ETC structure and the achieved LES). At the stage of diagnosis before the project situation, an unacceptable state of the orientation of actions in the region to preserve single-purpose facilities, the use of mainly renewable resources was revealed. Noncompliance with the criteria was confirmed by the calculation of cost indicators of insufficient efficiency (profitability, payback period below existing standards or industry average values). This confirmed the need to develop plans and projects for combining diversified resources for energy and resource conservation goals in cycle 1. It has been established that such domestic waste begins to emit a mixture of gases containing up to 50% of methane and hydrogen sulfide, and when burning waste, much more harmful gases occur. It is 20 times more harmful than carbon dioxide in creating the greenhouse effect [5][6][7][8][9][10][11][12]. In this case, it is possible to use functional mathematical models with dependences of a continuous type on time.
In the range of 0.0-0.1, the results of increasing the efficiency were revealed in terms of the intensity of application of high technologies, additional functions and indicators of stability control by changing their speed according to Formulas (8)- (10). At the time of commissioning of high-tech equipment, it was necessary to increase the intensity of the application of additional functions in the ETC Control Center. This corresponds to the methods of quadrant 2 of the theoretical modelcombining the resources of the HDD of high-tech equipment at the structurally revolutionary (SR processes) stage of transition to new management structures (creation of SDCs and ETCs), which determines the abrupt growth of the LES index. The regulation of such processes was simulated by increasing the number and intensity of application from 9 to 11 additional control functions in the previously identified optimality range according to the criterion of matching the number of embedded approximation functions according to Formula (6). At stage 2 of the cycle, a transition was made from the separate functioning of facilities to the organization of a radical increase in technical and technological capabilities based on combination and polygeneration. The structure-forming variant of energy-saving development is envisaged by the formation of ETC for the production of complementary or complementary types of energy and by-products using SHW as the main source of RER. This corresponds to the direction of ensuring the sustainable development of a transformable landfill (repository) or region over a cycle or several cycles of change. Ideally and over the decades, it is possible to create an industrial park of the Suzhou-Singapore type in a similar place with full reclamation of the occupied area and ensuring payback of the project.
The decrease in efficiency in cycle 2 determined the beginning of the development and implementation of plans and projects for scaling up innovations within the energy system. This corresponds to the quadrant 3 methods of the theoretical model structural-evolutionary (SE processes) development with the inclusion of new objects in the ETC and the gradual growth of the LES. For their implementation, measures were taken to implement projects at a number of enterprises in the system for training personnel in the elements of experience of foreign countries. The value of the initial investment resources was formed as the sum of one-time costs for the development of the project and the formation of the ETC or the park in terms of applied research. Basic research was not required, as there were all technical solutions and experience for any level of SHW processing: plants for degassing and flaring waste work in their centers or on the outskirts). In Japan, for example, it can be mentioned the company "Hitachi Zosen Inova". According to the project of this company, four such plants are built in the Moscow region using domestic metal-consuming parts of domestic production (pipes, boilers, etc.).
The growth of the innovation can be specified as an increase in the intensity of application of the functions and regulation of the structure of the ETC Project Management Center. This, for example, means an increase in the frequency and volume of requests for data on the characteristics of the processes of combination and polygeneration (by decision makers), the frequency and number of their communications over a certain period of time. The dominance of the strategy of evolutionary growth of efficiency in the short-term period of stage 1 was carried out by applying, mainly, the basic concrete and general management functions of separately working objects.
Management consulting was conducted in the areas of increasing economic sustainability and concretizing the factors of combining diversified resources and the formation of ETC, included in the structure of the system.
Using Formulas (8)-(10), the geography of expanding the space of objects in the sphere of combining diversified resources was modeled. Based on the results of evolutionary processes of applying high technologies and ETC formation methods, estimates of the stability of scaling the share of highly innovative ("breakthrough") transformations are obtained. Therefore, the points 0.05 and 0.05 radians, corresponding to the zero efficiency of innovation, determined the beginning of the selection of investment projects and the choice of objects of cooperation formed by ETC. A quantitative substantiation of the magnitude and possibilities of expanding the space-time zone at the stages of the singularity and scaling of technologies is used. For this, the values of dynamic areas (as the products of the rates of changes in efficiency and time) were estimated. They reflected the magnitude of the increase in efficiency over time from cycle 1 to cycle 2 in Figure 5, Formula (8), during the transition to the use of methods and processes of quadrants 2 and 3: Mathematically, the maximum value of S can be calculated using a certain integral. Estimating the derivative on the graph as the tangent of the angle of inclination on the tangent, one can notice that ) ( tan .  (10) is not met, the Center made decisions on enhancing the impact of the management functions by increasing the intensity of application of the relevant indicators (frequency of bringing to objects, converting planned indicators to normative, etc.). Modeling of this type and analysis of experience led to the conclusion that gaspiston type cogeneration plants are cost-effective at an installed capacity of approximately 1000 kW for SHW cities with a storage capacity of at least 1 million residents and waste storage period of 25-30 years. Therefore, the construction of a mini combined heat and power plant (HPP) of experimental designation based on the cogeneration of thermal and electrical energy using the above-mentioned renewable resources will create additional capacity.
The gas utilization system of this type of renewable sources will allow to regulate the production of thermal energy over a wide range. To do this, it is necessary to vary the gas supply using the storage of the appropriate type. This scheme allows you to provide simultaneously independent electrical and heat schedules of the station load can cover them without significant losses to transfer even heat, so many industrial and residential consumers are located within a radius of 1-5 km from the waste storage facility of a large city. With a greater installed capacity, a transition to gas turbine installations of HPP plants as part of ETC for the complete processing of SHW with the observance of environmental standards is necessary.
In the course of experimentation, the ranges of changes in the heat of combustion of a mixture of gases from an unconventional source such as a repository of waste of various types were identified. It is known that the majority of such domestic RER sources are characterized by excessive differences and uncertainties in the fractional composition of the stored components due to the SHW collection practices that are inappropriate to modern requirements. Therefore, it is necessary to introduce additional technical means of automation and temperature stability control over a larger range of changes in fuel consumption.
It should be noted that gas-piston units are able to work for a long time at partial loads (from 50% to 100% of nominal capacity) [5] without detriment to their resource indicators that meet existing environmental standards. This makes them reliable in the conditions under consideration. The optimal operating mode at the maximum power level (100%) is achievable provided the organization of the SHW separate collection system, their storage and processing in specially designed and constructed facilities according to the principles of combination and cogeneration or polygeneration.
It is practically established that in the conditions of trigeneration, maximum results are achieved when the useful use of the RER of the specified type reaches 80%-85%. In such a complex, standard conditions for the safety of personnel and the public and environmental standards can be better ensured. This follows from taking into account the location of many objects of the considered types of renewable waste (close to human settlements or even within the boundaries of a large city). 4. Regulation of the dynamic stability of processes and evaluation of development results, taking into account the entropy of the organizational behavior of the system as an additional indicator of efficiency [4][5][6]10]. The uncertainty of the dynamics results in the conditions of technology singularity determines the need to take probabilistic factors into account in assessing the positiveness of the synergy (SE) entropy as a criterion for achieving the goal of improving the quality of development management. For this, the Shannon formula [14] is used according to two assessment options (without using this technique, when the separate functioning of objects is analyzed without combining resources, with no or minimal integration in the complex) and with its application of Formula (11) where i p is the probability of the occurrence of the synergy of processes (determined on the basis of expert assessments when analyzing the results of joint projects or plans for high-tech resource combination under the conditions of an ETC); n is the number of such projects or plans. The positiveness of the indicator (SE ≥ 0) and the direction of its changes (SE↕) corresponds to the convergence (with a decrease in entropy) and divergence (with an increase in it) of the trajectories of target development in conditions of integration of objects and combination of resources and disintegration of objects and resources, respectively. When using the methods of quadrants 2 and 3, we determined the value of SE ≥ 0 and the fact of its decrease, which means an increase in the predictability of high-tech development processes. To ensure the positivity of the indicator (SE ≥ 0) and its stability during evolutionary bifurcation (SE ≈ const), additional functions are used to control the integration of objects and the combination of resources and indicators of their quality. As a result of regulating the number of functions and resources, the intensity of their application, the probability of successful implementation of projects and plans for combining resources in ETC was increased.

Conclusions
Below are the key findings.
1. An integration-convergent organizational-technological model is formulated to assess and regulate the development of a multipurpose energy technology type system. Mathematical methods to model evolutionary and spasmodic technological and organizational change are presented. Methods include the evaluation of indicators that differ with varying degrees of combining resources and integrating the interaction of objects in the energy technology complex. 2. The theoretical and operational-regulating models of spatial-temporal combination of resources and integration of complex facilities are specified, justifying methods for quantitative modeling of processes to improve the quality of managing economic sustainability by the criterion of minimizing imbalance with the goals. The concept of the organizational effect of expansion of the space and time of the jump-transition to a new level of technology is proposed. The regularity of the dynamics of the zone of maximum effect of the expansion in space and time of regulation of spasmodic development is revealed. The hypothesis of representing jump-transitions to hightech types of combined resources and integration methods of organizing the interaction of objects in a complex with a set of nested approximation functions corresponding to the number of types of integrable resources and objects is formulated. 3. Mathematical tools make it possible to model abrupt technological changes in complex systems. 4. Verification of theoretical models and methods was carried out on the basis of original criteria indicators, the use of which allowed us to draw conclusions about the theory′s compliance with the subject of research and the choice of specific tools to improve the quality of management by combining diversified resources. Verification of criteria based on relevant economic assessments of a real project for the formation of an energy technology complex increases the practical value of the study.
In sum, the research results will allow firms to improve the quality of managing economic sustainability of processes that combine resources with a high degree of diversification and multipurpose energy technology complexes with low-waste use. The addition of such mathematical and organizational tools will help improve the accuracy of analytical assessments and the speed of integration and balancing effects that increase the economic sustainability processes by combining the expanded number of technological energy development resources in the post-industrial economy.