Review of Models for and Socioeconomic Approaches to the Formation of Foresight Control Mechanisms: A Genesis

Abstract

The study of a genesis is determined by the needs when designing the processes of high-tech development. This is performed taking the knowledge-intensive factors of a large knowledge economy into account under conditions of environmental uncertainty. An increase in the number of publications on the regulation of imbalances in the goals of innovation and efficiency that objectively arise in the processes of such development has been revealed. Therefore, the purpose of this study is to analyze models and socioeconomic approaches for the integration of mechanisms for foreseeing and controlling the development goals of enterprises in the processes of their genesis. This led to the improvement of the theory and the development of new methodologies, models, and methods for improving the quality of the management of the innovative development of enterprises according to sustainability criteria. Therefore, an analysis of textual sources was carried out, as it is crucial to understand various text-processing approaches to optimize the forecasting of long-term goals. An attempt was made to apply methods for assessing the quality of proposals available in the literature by a number of authors to summarize and discuss the current text-based socioeconomic advances in the aspect of forming a unified mechanism for improving the quality of governance. The properties of the monitoring of the factors of the knowledge economy and the strategic planning of development goals were analyzed. The quality of proposals was assessed in a procedure, and a discussion of the strengths and weaknesses of scientific approaches was conducted. This made it possible to determine the correspondence of approaches to the development of theories and new methodologies for the integration–balancing management of the integration and combination of resources by using a foresight-controlling mechanism. Moreover, this study also determines the prospects of the analyzed areas of socioeconomic research and project development.

1. Introduction

The relevance of external factors for the increase in the efficiency of the high-tech development of systems (enterprises, organizations, and complex technologies) is determined by the needs of society in terms of the results achieved on the basis of the post-industrial resources of the knowledge economy. This has not been fully realized in developing countries [1,2,3] and has led to contradictions among the indicated factors, needs, and unsatisfactory results of economic development in terms of high-tech factors. The analysis of publications should show the need to improve the mechanisms for regulating the indicators of the quality of development management during the transition of enterprises to the 5th/6th modes of the post-industrial knowledge economy [4,5,6]. In socio-economic research, the general concept of a genesis is defined as the creation of a system of methods for integrating and combining the resources of enterprises with the potential objects of education and science. This concept is implemented by using the mechanism of foresight-controlling goals and the extended monitoring of environmental factors. It is necessary to take into account the internal factors and functions of organizational behavior in an environment of new production relations and the culture of post-industrial agglomeration. These are determined by the socio-humanitarian interactions of enterprises with the objects of a knowledge economy complex (in short, “tech-hume”). The contradiction that is revealed and the general goal of forming the socioeconomic part of this Special Issue determine the goal of the formation of models. It is necessary to develop the functions of the mechanism of the foresight and control of efficiency goals for the forecasting and strategic planning of the high-tech development of enterprises in the expanded space of joint activities. This determines the relevance of integrating and combining the foresight and controlling subsystems of enterprises in the processes of high-tech transformations by using the methods proposed in the years 2021 and 2022 [7,8,9].

The proposed toolkit can be described with the following keywords (search terms) from the improved theory and new methodology of integration-balancing management: “foresight”, “controlling”, “integration”, “combination”, “mechanism”, “function”, etc. These words describe the processes of developing a theory and methodology for the improvement of the quality of management by coordinating the interactions of enterprises with the objects of science and education. Interactions are organized as part of the emerging network structure of an agglomeration on an urban or regional scale. Overall, this study summarizes and discusses current descriptive approaches to unlocking the applicability of theoretical, methodological, and applied tools. In addition, this study evaluates the advantages and disadvantages of each socioeconomic approach.

2. Application of Approaches to the Development of the Theory and Methodology of Enterprise Development

2.1. General Mathematical Approaches to Assessing the Relationships of Complex Systems

In the period of 1948–2022, there has been and continues to be an increase in the number of publications on the quantitative assessment of the sustainability and effectiveness of the development of complex socioeconomic and technical systems. For their analysis, general mathematical models have been developed to represent the possibilities of modeling jump transformations [10,11,12,13,14]. At the same time, such models did not provide solutions to many problems of applied statistics and econometrics [15]. Therefore, methods have been developed for the representation of jump processes of changes in complex biological and technical systems [16,17,18,19,20,21,22,23,24,25,26,27,28]. Their weak side turned out to be the unresolved problems of regulating the relationships of the evolutionary and spasmodic economic processes inherent in cyclical changes in the innovative cycles of enterprise development. In addition, the impacts of environmental factors of the knowledge economy were not fully taken into account, and the insufficiency of existing standard management functions for ensuring the high-tech development of enterprises was revealed.

2.2. Applied Approaches to the Economic and Mathematical Analysis of Development Processes

Applied approaches were necessary for the formation of integrated structures of the centers of post-industrial agglomeration complexes, thus reducing the imbalances in the interests of objects of educational, scientific, and project activities with industrial enterprises. To reduce the imbalance between the goals of the efficiency and sustainability of an interaction, methods for increasing the reliability of assessments of quality indicators for the use of additional specific management functions (CFUs) turned out to be in demand. For this, subsystems of integrated continuous accounting of internal and external factors of the enterprise environment were proposed in the context of a relatively rapid transition to a knowledge economy. We propose the name of such a function of the expanded integration of environmental factors: “IVUCA + EVUCA-monitoring” of the development of the “tech-hume” socioeconomic methods and “high-tech” technologies.

Separately functioning subsystems for factor accounting are not quite effective and reliable in the long term [29,30,31,32,33,34,35,36,37,38,39,40,41]. The expediency of an integrated analysis of external (External) characteristics of EVUCA (“high-tech” type: variability (volatility), uncertainty (uncertainty), complexity of influencing factors (complexity), and ambiguity of influences (ambiguity)) with internal (Internal) denoted by IVUCA is substantiated. They characterize to a greater extent the environment of interaction of the enterprise subsystems of the “tech-hume” type: assessment by the staff of the goals of strategic development as part of the complex; understanding and acceptance by the staff of the vision of joint development in the complex (vision); understanding the goals of innovative development (understanding); clarity of representation of a situation of conflict of interest (clarity); and flexibility of decisions based on the continuous study of the possibilities of innovative development (agility). This made it possible to take into account the factors of efficiency and sustainability when expanding the space for regulating diversified objects in the ecology of post-industrial agglomeration. To ensure the consistency of developing management decisions using the resources of the knowledge economy, a multi-parameter approach was implemented to expert assessments of management quality indicators for the stages of the innovation cycle of each enterprise included in the complex [42,43,44]. New opportunities have appeared to deepen the analysis in terms of speed, economic, environmental, and energy (abbreviated 3-E) efficiency and sustainability of innovative transformations of enterprises [45,46,47,48,49,50,51,52,53].

At the same time, the problems of insufficient quality of managing the relationships between enterprises and objects of the knowledge economy in the agglomeration were revealed according to the criterion of inconsistency of socio-economic impacts on ensuring the efficiency of the triune 3-E. It was necessary to scale up the development of analog-to-digital approaches to the formation of analog-to-digital platforms that ensure the efficiency of management decisions.

2.3. Analog–Digital Approaches to Regulating the Balanced Development of Enterprises Based on Monitoring the Factors of the Knowledge Economy

In modern conditions, the importance of developing operational methods to improve the quality of management to ensure triune-balanced results of efficiency (3-E) and the corresponding sustainability criteria is growing. At the same time, the most common models accounted only for environmental sustainability factors [45,46,47]. In recent years, when creating centralized management structures for complexes and regional agglomerations, mathematical models with new analysis capabilities have appeared. We note the developments in Applied to Enterprise Organization and Industrial reduction Optimization. They allow the modeling of the behavior of technological systems when solving product problems using the theory of waiting in the queue. However, in this case, only evolutionary optimization processes with cost estimates by the Monte Carlo method in linear systems are displayed [48].

Of interest are the development of systems with properties of Thermal-Economic Optimization, providing modeling of 3-E efficiency. At the same time, the proposed optimization algorithms adequately reflect only evolutionary processes in the concept of particle swarm optimization, which does not allow reaching integration solutions according to the stability criteria of the system as a whole [49]. The problem was partially solved in a study based on Improved Clustering Algorithm for a Distribution Center Location Problem under Uncertainty [50].

Increasingly, environmental uncertainty factors are taken into account to increase economic efficiency in the formation of logistics clusters. However, the use of only natural indicators for assessing the quality of functions in the formation of these clusters does not allow us to use important characteristics of the organizational behavior of objects. The expansion of space determines the importance of the processes of regulating the speed of development of the Internet of Things (IoT), the development of technology for analyzing big data, and the possibilities of processes [38]. Valuation models bring industries closer to the goals of smart manufacturing. Data analysis is needed to develop an approach to the selection of energy saving projects. Therefore, a data shell analysis method was developed, that is, a mathematical tool based on linear programming models that can be used to measure the effectiveness of portfolio projects. However, the choice of projects was carried out in a model without feedback [39]. Proposals are known for improving the model using a mathematical program that maximizes the sum of the minimum ratios of production to the need for electricity and water at the right time [40]. At the same time, such an approach to the planning horizon does not meet the criteria for improving the quality of management according to the criteria for increasing the 3-E efficiency.

The need to regulate the effectiveness of the innovative processes of the functioning of an enterprise with the complex of objects of the knowledge economy has revealed the insufficiency of business models focused on making a profit. They were effective enough only in the processes of evolutionary transformations. The models for predicting the technological, structural, and cultural attributes of the organization of controlled activities of enterprises in a single mechanism of foresight-controlling are proposed as the basis for the implementation of new processes [7,8,9]. Direct and feedback links and the indicated monitoring subsystem provide an increase in the reliability of the forecasts and strategic plans of enterprises in terms of 3-E efficiency indicators and sustainability criteria. This increased the opportunities for improving the quality of management for the processes of their interaction with objects of knowledge economy complexes as part of regional, sectoral, country, or global agglomerations [54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70].

At the same time, we reveal the absence of a relationship between the considered methods of theory and practice in solving the problems of the imbalance in the high-tech development of enterprises. It is necessary to develop models of theory and methodology based on a systematic approach to the analysis of possible methods for strengthening interconnections in the ecology of post-industrial agglomeration. On their basis, it is necessary to improve the organizational structures and mechanisms for managing the interaction of enterprises based on the results of monitoring environmental factors.

2.4. Theoretical and Methodological Approaches to the Formation of the Mechanism of Foresight-Controlling of the Processes of the Regulation of High-Tech Development of Enterprises in the Post-Industrial Agglomeration

The multicomponent composition of the complex of objects of the knowledge economy determines the increase in the complexity of new theoretical models and methodology. They must possess the properties of natural biological development of structures and scales of activity. To include an enterprise and individual subsystems of foresight and controlling in the structure of the center of a complex or agglomeration, it is necessary to modernize the mathematical models for representing high-tech transformations based on the approximation of generalized functions [71,72]. This is necessary to display the relationship between socio-economic methods “tech-hume” and technologies “high-tech” factors of the future state of management systems in terms of 3-E efficiency [73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99].

The content of the study based on system analysis should be represented by the decomposition of the goal into subgoals, functions to identify the object of study for various purposes, and sectors of activity from the environment [100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116]. The element of mechanism decomposition in systems theory can include procedures for diagnosing the problems of insufficient efficiency, innovativeness, and sustainability of enterprises in the conditions of their separate functioning outside of stable links with agglomeration objects. Next, procedures should be defined for analyzing the possibilities of including enterprises in the complex on the basis of modernized mathematical models. Based on the simulation results, methods for the synthesis of a new system for monitoring processes and the functioning of an analog–digital model of the mechanism are implemented. It is advisable to organize the integration of the functionality of the controlling and foresight subsystems, advanced monitoring of the environment in the new structure of the Goal Coordination Center. It is proposed to implement the processes of improving the quality of management in digital simulators of regulators of the quality of management of a single mechanism, corresponding to the stages of the innovation cycle and a specialized criterion of stability [7,8,9].

In the period of 1948–2022, there was and continues to be an increase in the number of publications on the relationship of the rate of emergence of new methods for assessing the sustainability and effectiveness of the development of complex socio-economic and technical systems. The analysis and interrelation of methods are presented in the form of an operating model of the genesis of the type “input–process–output” (

Table 1. The operating model of the genesis models and socio-economic approaches to the development of the theory and methodology of the formation of the mechanisms of foresight-controlling and monitoring of management quality and efficiency.

Stages of Origin and Study of Theories, Methodologies and Methods, Main Authors, Sources, and Years of Publication	The Content of the Development Processes of Models and Approaches, the Advantages and Disadvantages of Applying Methods in Management Theory and Practice	Results of the Application of Methods in Theory and Practice to Improve the Efficiency and Sustainability of Innovative Development
1. Mathematical methods for modeling processes taking into account the uncertainty of the environment: Shannon, C.E., Paris, J., Harrington, L., Helmberg, G., Ayvazyan, S.A., Mkhitaryan, V.S., Bae, M.: 1948–2013.	Separate accounting of VUCA factors of the external and internal environment, ease of accounting, but the use of methods for controlling goals and foresight of indicators of innovativeness of high-tech development is not shown.	Evaluation of the effectiveness of short-term projects for the evolutionary development of enterprises outside the complexes and without coordinating interests with the objects of the knowledge economy of the agglomeration.
2. Mathematical methods for modeling static and dynamic processes based on generalized and step functions and methods for their approximation, Vladimirov, V., Meltzer, D., Alyukov, S.V.: 1979–2013.	Display of evolutionary and spasmodic processes, the possibility of modeling physical and technical processes that are radically different in speed, but lack economic and managerial applications of the methods.	Modeling of jump-like processes in the cycles of physical dynamics of natural phenomena, operation of technical devices, and representation of processes and technologies.
3. Economic and mathematical modeling of balanced development of enterprises in a dynamic environment: N. Glickman, N., Casti, J., Wiener, N., Akoff, A., Andersen, V.D., Ansoff, I., Nash, J., Kaplan, R., Norton, D., Rampersad, H., Arnold, V.I., Yu, S., Glaziev, L.D., Alabugin, A.A.:1980–2005.	Joint consideration of external and internal factors, the possibility of regulating efficiency according to the criteria of balance of interests and sustainability of the cyclical development of enterprises, but the coordination of its relationships with the objects of the knowledge economy according to the efficiency factors of high-tech development in the conditions of agglomeration and globalization is not modeled.	Models are developed for determining strategic plans for the long-term development of complex socio-economic and technical systems according to innovation factors and sustainability criteria within individual enterprises, their complex as part of a region and a country.
4. Regulation of innovative development of enterprises in the subsystems of trend foresight and goal controlling: Brummer, V., Meissner, D., Johnston, R., Belousov, D.R., Makarova, E.A., Calof, D.L., Makarov, S., Karayiannis, E., Perez-Vico, E., Cervantes, M., Unger, M., Bereznoy, A.V., Goetz, M., Magruk, A., Mainzer, K., Khudyakova, T.A., Alabugin, A.A.: 2010–2020.	Separate use of foresight and controlling subsystems of enterprise development trends, the possibility of using the criterion of sustainability of high-tech development in knowledge economy systems, but there are no specific functions for integrating and combining resources of knowledge economy objects consistent with standard enterprise management functions.	Mainly financial models of the evolutionary increase in the innovativeness of the enterprise development using the foresight resources of the “triangle of knowledge” or controlling strategic goals are developed, the principles of building a controlling system and evaluating its effectiveness are proposed.
5. Models and mechanisms of integration-balancing management of the efficiency of high-tech development of enterprises in the complex of objects of the knowledge economy: Drucker, P.F., Stubbs, W., Adizes, I.K., Johansen, B., Reefke, H., Seelos, S., Lalu, F., Velez-Perez, J.A., Li, J.H., Oreshkina, N.S., Alabugin, A.A.: 2008–2022.	The use of analog–digital models of cross-functional integration of enterprises with objects of the knowledge economy, the possibility of achieving stability in bifurcation processes of increasing the efficiency of high-tech development, but the control subsystem of enterprises and the complex becomes more complicated without a single mechanism.	A method of joint consideration of factors of the external and internal environment is proposed, which increase the creativity of the processes of innovative development. New specific functions for integrating and combining knowledge economy resources are implemented in a single foresight controlling mechanism.

Source: developed by the authors.

).

At stage 1 of the genesis of approaches (Table 1), the debatable aspects of assessing the insufficiency of existing mathematical methods were identified. They did not allow diagnosing the quality of management, which led to the insufficiency and imbalance of the triune provision of 3-E efficiency as simulation results. Its imbalance with the goals of the innovativeness of high technologies and management methods was unacceptably great in terms of the sustainability of enterprises under the conditions of their separate foresight and controlling. New methods of mathematical analysis and organizational possibilities were required for the inclusion of enterprises in the complex using a single mechanism.

At stage 2, methods for modeling static and dynamic processes based on generalized and step functions and methods for their approximation appeared. They turned out to be suitable for displaying jump-like processes in the cycles of the physical dynamics of natural phenomena, the operation of technical devices, and the presentation of processes and technologies. However, the lack of economic and managerial applications of methods determined the relevance of the specialization of economic and mathematical modeling to ensure the balanced development of enterprises in a dynamic environment.

At stage 3, a toolkit for integrated accounting of external and internal factors was developed with the ability to regulate 3-E efficiency according to the criteria for balancing interests and sustainability of the cyclical development of enterprises. At the same time, the processes of coordinating their relationships with the objects of the knowledge economy in terms of the efficiency factors of high-tech development were not modeled. This did not allow developing models of strategic planning for the long-term development of complex socio-economic and technical systems based on innovativeness factors and sustainability criteria within individual enterprises, their complex as part of a region and a country.

At stage 4, theoretical, methodological, and methodological approaches to regulating the innovative development of enterprises appeared in separate subsystems of trend foresight and goal controlling. New possibilities of using the criterion of the sustainability of high-tech development with a combination of resources in the complex of the knowledge economy turned out to be not quite realizable. There were no special specific functions for managing the integration and combination of resources of knowledge economy objects, consistent with the standard functions of enterprise management. Predominantly financial business models of the evolutionary increase in the innovativeness of the enterprise development prevailed. The use of foresight resources based on tools such as the “knowledge triangle” or controlling strategic goals implemented the principles of building a system for accounting for performance goals according to economic sustainability criteria with insufficient forecasting capabilities in the face of growing environmental uncertainty. Therefore, at stage 5 of the genesis of approaches, models and mechanisms of the integration–balancing management of quality improvement appeared based on the results of monitoring the efficiency indicators of innovative development of enterprises in the complex of objects of the post-industrial knowledge economy [2,3,4,5,6]. The use of analog–digital models of the cross-functional integration of enterprises with objects of the knowledge economy increases the possibility of achieving trend stability even in the bifurcation processes of increasing the efficiency of high-tech development. However, the control subsystem of the enterprise and the complex becomes more complicated. As a result, we develop and test procedures for modeling the processes of an organizational-digital model of a single foresight-controlling mechanism.

3. Discussion of Future Prospects

3.1. Aspect 1: Aspect-Based General Mathematical Approaches to the Development of Management Improvement Theory

When modeling processes (in Section 2.1 of the review) in systems with integration–balancing properties, approaches to the theory and methodology for analyzing abrupt processes of change, which are effective only in biological and technical systems, prevailed. This makes it possible to study the interrelationships of the corresponding evolutionary and jump processes. We substantiated their application for the analysis of cyclical processes of innovative changes in enterprises. Such approaches can be applied to organize effective interaction between enterprises in the extended space of the complex and regional agglomeration.

3.2. Aspect 2: Aspect-Based Applied Approaches to the Economic and Mathematical Analysis of Development Processes

Applied approaches to the theory and methodology of the formation and operation of a single mechanism for foresight-controlling in the Center for Coordinating the Interests of Objects take into account the interconnections of the emerging socio-economic system of the complex in the agglomeration. This increases the reliability of forecasts of the efficiency of innovative development, since the mechanism is regulated taking into account the expanded composition of external and internal environment factors. A single mechanism is distinguished by the greater efficiency of controlling processes and ensuring the consistency of the goals of the enterprise, the complex and the regional agglomeration according to the criteria of economic sustainability and the stability of their compromise. The integration of management functionalities and the combination of foresight and controlling subsystems in a single mechanism made it possible to speed up the development and decision-making processes in the organizational design system [22].

To reduce the delay in response to changes in the environment, it is proposed to use three additional key management functions to reconcile the interests of the enterprise and the objects of the complex: the speed of impacts of the functions of managing the integration and combination of resources; integration of resources for high-tech innovative development of enterprises in the complex; and combining innovative resources of the complex for high-tech development of enterprises. In the methods of the organizational design of the processes of functioning of the mechanism, usually developed in the methodological part of the study or project, we propose its digital simulator, which represents specialized regulators of the efficiency of enterprise development.

3.3. Aspect 3: Aspect-Based Analog-to-Digital Approaches to the Analysis of Resources for the Formation of a Mechanism for Foresight-Controlling and Monitoring the Processes of the Regulation of the High-Tech Development of Enterprises

It was revealed that the characteristics of management quality depend on the degree of formalization of organizational behavior. In the short term of development at the stages of the innovation cycle, they are provided by directive management with a strong formalization of structures. However, at the same time, the innovative activity of the personnel and its susceptibility to high-tech environmental factors are low. An analysis of the genesis of the theoretical and methodological foundations of similar studies made it possible to conclude that many of the scientists’ proposals were united by the mathematical theory of J. Nash, applied in the monograph [1]. It is based on the well-known principle of equilibrium, which determines the compromise between the goals of the long-term innovativeness of the development of the complex and its individual enterprises for three groups of environmental factors and the above types of sustainability: the dynamics of the needs of society as a whole; changes in engineering and technology; and the development of management science.

In the socio-economic part of the issue, the term “quality of management processes” should be referred to the object of study—the mechanism of foresight-controlling of the goals of enterprise development efficiency in innovation cycles and the composition of a complex socio-economic system of post-industrial agglomeration complexes. The most minimal reserves for improving the quality of control are provided by the theory of random transformations [15,16,17,18,19,20,21,22,23,24,25,26,27]. More effective are neo-institutional methods [29,30,31,32], which use a set of normative instructions of society and the state for the transfer of competencies and knowledge management in models of continuous convergent education. This is used in new indicators and functions for the formation and regulation of adaptive mechanisms [1,2], based on the theories of microeconomics [1]. It has been established that, over a long period of the innovation cycle, an enterprise can change all the above factors of production (in the general case, the main operating activity). Therefore, the choice of the theory of ecology of populations of organizations and its refinement in relation to the presentation of the hypothesis of the innovation cycle for improving the quality of regulation of the interaction of enterprises in the complex was justified. Therefore, the subject of socio-economic research should be the organizational and economic relations that arise in the processes of applying the methods of integration and combining the functionals of the foresight and controlling subsystems. A high-tech transformation requires a single mechanism for regulating the performance indicators of the innovative development of an enterprise in the space of the post-industrial agglomeration of objects of the knowledge economy.

To carry out the diagnostic procedure in the theoretical and methodological model, one should use an analysis of the dynamics of the market situation in the region where the complex being formed is located. With a low and stable over-time increase in the number of types of enterprises, unchanged innovativeness, their density, as a rule, grows. Therefore, the duration of the life cycle of existing enterprises tends to decrease. The decision to include an enterprise in the complex should be taken according to the criterion of exceeding the upward (due to the growth of sustainable development) and downward (due to the decrease in the efficiency of development) trends. Estimates of the number of (created and disintegrated) enterprises in the competitive sectors of the complex will make it possible to determine four boundaries of the stability zone for periods of cycles. It has been established that an increase in the criterion indicator leads to an increase in the number of enterprises in the region, and a decrease in efficiency in the long term leads to an increase in the number of their breakups.

It is proposed to evaluate changes in the levels of sustainability over the period of development, as the ratio of the number of these types of enterprises in the complex. The concept of the implementation of the main socio-economic approach is formulated as an opportunity to improve the quality of the regulation of the efficiency of the high-tech development of an enterprise by using additional CFU parameters for integrating and combining resources of the knowledge economy complex in the new mechanism according to the criterion of sustainability of the economic and organizational type.

Methods for approximating generalized functions simplify the existing computational approaches to estimating the processes of “compression and stretching” of the space of factors and the resulting properties of the system during its jump transformations [10]. It has been proven for physical and organizational processes that their maximum impact on the resulting property is achieved when they are approximated by a certain number of nested functions [72,73]. Subsequently, we applied such mathematical models according to the factors of the knowledge economy and the criterion of economic stability of processes based on their special interpretation [1,2,3,4,5,6,7,8,76,77,78,79,82]. The articles simulate the impact of factor indicators of additional key management functions and indicators of the quality of their regulation. They show the magnitude of the factor effects of the quality parameters of the regulation of processes that change over time. A number of studies have proved the tangible value of the conditional expansion of the function representation space when approximating by a growing number of nested functions in a certain range [1,2,3,4,5,6,7,8,9,72].

3.4. Aspect 4: Aspect-Based Theoretical and Methodological Approaches to Improving the Quality of High-Tech Development Management

An analysis of the genesis of the theoretical and methodological foundations for studying the processes of innovative development of enterprises revealed that until 2020 the approaches of separate controlling of the goals of regulation and foresight of the studied properties of efficiency and innovation prevailed. It has been established that high-tech development in a crisis is not sustainable when taking into account the standard VUCA factors of the environment. The integration of these characteristics of the external and internal environment is required for effective monitoring of the high-tech challenges of the knowledge economy. This is numerically confirmed by the correlation among managerial competencies, the quality of knowledge management, and creative thinking by modeling the processes of the effective functioning of knowledge networks [34,35,36,37,38]. Estimates of the foresight of future employment in the field of science, technology and innovation as a spiral of innovations for various configurations of the “knowledge triangle” were obtained [62,63,64,65,66,67,68,69,70]. They also note the lack of knowledge of such forms of organizing the interaction of science, education for the innovative functioning of the enterprise. The special role of higher education in the framework concept of the “triangle of knowledge” is determined to improve the efficiency of regulating reverse flows of knowledge as influencing the coordination of actors’ interests. The notions of such a triangle are being developed as a methodological basis for the integrated application of other concepts of high-tech development (“third mission”, “triple helix”, “four-link helix”, “entrepreneurial or socially oriented university”, “smart specialization”) [62,63,64,65]. However, these organizational structures do not provide for the implementation of a systematic approach to the integration and combination of knowledge economy resources.

The imperfection of models and methods for assessing the efficiency and speed of the transition of enterprises from the low-tech levels of the industrial economy to the level of the knowledge economy leads to the predominance of “creative destruction”-type scenarios. The processes of elimination of obsolete technologies or their minor modernization by individual VUCA factors prevail. Such regulation based on deviations and the results of only operational control reduces the circle of supporters of long-term scenario planning. Under the conditions of environmental uncertainty and crises, foresight methods are needed to predict the sustainable high-tech development of objects [54,55,56,57,58,59,60,61]. It is necessary to take into account risky complex alternatives aimed at radical changes in the complex of technologies. Therefore, the use of “technology mapping” methods as visual means of presenting development trends and normative forecasts is spreading [57]. The necessity of continuous correction of the existing mechanisms of strategic planning in terms of indicators of monitoring weak signals is substantiated [58]. This proposal is implemented in collaborative networks with the design of a successful foresight, corresponding to such an organization of developments.

However, these developments do not provide the centralization and efficiency of the effects of quality management functions. Therefore, we share proposals for improving control based on cyber-physical systems. Computer calculations using programming tools and artificial intelligence should substantiate the variety of options in a machine-to-machine way [76,77,78]. This allows the timely organization of the coordinated organizational and economic impacts of management subsystems on the economic sustainability of social and technological collaborations. Therefore, the importance of modernizing the mathematical approaches necessary for the development of digital simulators of the foresight-controlling mechanism is growing.

3.5. Aspect 5: Aspect-Based Approaches to Mathematical Modeling of the Functioning of the Mechanism of Foresight-Controlling of the Goals of Innovative Development of an Enterprise

The development of practical methods and research methodology should be based on the theoretical and methodological model outlined above. It substantiates the features, models, and new functions of the formation of the foresight-controlling mechanism. The mechanism is distinguished by the possibilities of providing four types of economic stability, described by special mathematical methods. They are applicable to the analysis of jump and step physical processes [72,73]. Their capabilities substantiate the modeling of the processes under study by an approximating sequence of analytical-nested functions that have derivatives of any order by a sequence of the resulting efficiency property depending on additional key control functions (KCF). These functions can be considered a digital simulator of the proposed new foresight-controlling mechanism in terms of the factorial parameters of the quality of their application, developed in the theoretical and methodological part of the study. The estimation of the first derivative makes it possible to simulate changes in the rate of influence of the quality parameters of the mechanism regulators on the indicator-property of the efficiency of the innovative development of an enterprise. The use of these functions simulates changes in four types of stability over periods of four stages of the cycle. A decrease in the stability of the functional and structural types in the initial cycle, when the experimental use of the new functions of the mechanism by the personnel, is revealed. The maximum rate of increase in the indicator-property at the stage of the subsequent cycle of a jump transition to technologies of the “high-tech” type is substantiated according to the maximum criterion of the bifurcation type. This means an increase in the variability of the effects of the quality parameters of the standard and additional functions of the foresight-controlling mechanism in the corresponding regulator. In the zone of organizational methods “tech-hume” and stabilization of the achieved level of technologies “high-tech” (stage 4), the maximum economic-organizational type of sustainability is provided. To assess the frequency and directivity of the impacts of the parameters, the maximum corrected value of the function is determined at the critical value of the factor variable of the quality parameters.

To justify the boundaries of the stages of the cycle, it is advisable to investigate the range of application of a certain number of approximations of nested functions. It can be shown by the dependences of the growth rate of the development efficiency indicator on innovativeness factors. It has been established that, with 18 functions, an ideal approximation of the function is achieved, corresponding to the ideal representation equation. However, it is not economical for practical use, as it overly complicates the management. Therefore, the criterion for providing an extended zone of the equilibrium state of the system determines the values of the approximating functions for three groups of functions in the controlled neighborhood of the abrupt development by factors at the critical point. The zones of minimum and maximum levels of efficiency of technologies and management methods are revealed, shown by the points of minimum and maximum efficiency. In a similar way, the boundaries of the zone of variability of the studied property of economic development regulated by the foresight-controlling mechanism are also established. An analysis of the dynamics of the processes of implementing a high-tech jump-transition based on high-tech technologies makes it possible to set target boundaries for the effectiveness of innovative development in assessing the levels of maximum and minimum losses in the range of their difference. The approximating trajectory of the innovative development of the enterprise shows that at the beginning of the development of high technologies and the mechanism, the level of efficiency of the enterprise falls. Accelerators of the mechanism provide the possibility of stabilizing the compromise zone of the goals of ensuring innovation and increasing efficiency in terms of economic sustainability.

The modeling of accelerators by derivatives of functions of higher orders of equations is substantiated. In organizational studies, it is practically sufficient to use successive approximations of four orders. This determines the processes of formation and application of a digital simulator of four types of regulators that affect the increase in the efficiency of the innovative development of an enterprise according to the criteria of four types of sustainability:

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The functional type models the processes of regulating the speed of processes at the initial stage of low-innovation modernization of enterprise technologies and the formation of a foresight-controlling mechanism. Modeling based on the first derivative of the approximation of the efficiency function of the innovative development of the enterprise estimates the increase in the resulting property, shown by the negative values of efficiency and innovation. This is explained by the low intensity of regulatory impacts of the additional key control function (KCF-1) of the integration of resources using the five corresponding quality parameters of the foresight-controlling mechanism. In the center of the complex, there is an experimental coordination of the intensity of their application with four similar indicators of the quality of the standard functions of the enterprise.

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The structural type is used to model the processes of acceleration of the impacts of a functional type. The second derivative interprets the acceleration of transformation by increasing the intensity of the use of standard functions in the new structure of the enterprise. The formation and the beginning of the application of additional key control function (KCF-2) of combining the innovative capabilities of the complex objects are represented by the efficiency function according to the factors of innovativeness of development with increased interaction according to the criterion of structural stability.

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The bifurcation type models options for jump processes of increasing efficiency based on the third derivative. This reflects the processes of the abrupt transition of high-tech transformations to the zone of positive efficiency. The maximum speed and degree of influence of the coefficients of integration and combination of additional key control functions (KCF-1,2) are required for the development of high technologies and a new management mechanism for innovative development of the “high-tech” type. The results of speed control are shown as a function of efficiency depending on the effects of an additional key control function (KCF-3). It affects the growth rate of key control functions when coordinating and using five additional and six standard quality parameters according to the criterion of bifurcation stability maximization.

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The economic-organizational type stabilizes the results of functioning of the regulators of the first three types and, therefore, is modeled by a system of corresponding equations. Development trends are displayed by corresponding curves of different enterprise development trajectories. They correspond to the results of applying technologies and management methods of increasing levels of innovation. The coordination of the functions of integration, combination of resources, and the speed of their impact when using the accelerators of the foresight-controlling mechanism contributes to the stabilization of efficiency. In the modernized system of equations, the speeds of individual key control functions (KCF-1,2,3) are modeled by estimating the first derivative approximations of functions. Modeling based on the fourth derivative interprets the processes of stabilization of the achieved level. A decrease in efficiency at one of the stages of the cycle requires the adjustment of the regulators of the mechanism by predominantly non-administrative organizational methods “tech-hume” according to the criterion of maximizing economic sustainability.

Approaches to the organizational design of the foresight controlling mechanism must be implemented in an analog model. As such, we consider the algorithm for the formation and functioning of the subsystems of the mechanism when integrating the foresight and monitoring functionals. In this view, the model can be defined as a twin (simulator) of the regulated “design” of the future state and development of objects in the post-industrial agglomeration. The particular complexity of their interconnections in the complex, the uncertainty of the results of monitoring the extended composition of the VUCA factors of the environment, determined the addition of the possibilities of using a large database (big data) and complex tools of the analog–digital type Data Science [76,77]. The cyclic application of the tools forms a mechanism for foresight-controlling the goals of forecasting and strategic management of the high-tech development of enterprises in the regulatory structure of the Center for Coordinating the Interests of the Complex. We identified the main stages of the inclusion of a new mechanism in the functions of the Center: the examination of the compliance of development with the goals and trend of high-tech and science-intensive development; forecasting the efficiency goals of enterprises in the controlling subsystem and real time based on learning neural networks of artificial intelligence; modernization or development of specialized analog and mathematical models of strategic planning or organizational design; assessment of the possibilities of using high technologies in core activities, management in the processes of developing scenarios that clarify the development trends of enterprises; and development or adaptation of computer programs based on the results of modeling to determine the target indicators of plans and strategies. For operational engineering solutions in the form of projects in the areas of high-tech development, it is advisable to use existing software products. Regression analysis and the considered mathematical models expand the possibilities of multivariate and multicriteria approaches in such a digital platform of the Center of the Complex without primary filtering of the source data.

The organizational design of the interaction of enterprises with the regulatory structures of the center of the complex should be carried out in accordance with the principles of centralization and decentralization of powers with enterprises. In the studies of socio-economic processes and systems, we developed procedures and operations for designing managerial decision making to improve the structure, coordination, and control of the processes of interaction between an enterprise and the objects of the knowledge economy of the complex. The structures of its center, using direct and feedback links, should regulate the processes of coordinating the interests of enterprises. We carried out an organizational design of the possibilities of innovative development of an enterprise—the object of study, which is at the initial stage of the cycle of high-tech transformations in the conditions of the 3rd–4th modes of the industrial-type economy [2,3,4,5,6]. It has an average number of employees and belongs to the machine-building industry. The production of products with high-added value, but insufficient innovation and science intensity, has exacerbated the problems of competitiveness and reduced demand. This determined the need for high-tech transformations according to the high-tech factors of the post-industrial knowledge economy of the 5th–6th modes.

To implement the indicated stages of the inclusion of a new mechanism in the functions of the center at enterprises, it is necessary to create temporary groups of experts, researchers, and project developers in its composition. External management consultants should propose and implement options for training processes for enterprise specialists to master new competencies. A significant increase in the complexity of the subsystems for integrated accounting of external and internal VUCA-environmental factors and KCF-1-3 and the system of quality indicators for their application, recommended by the Center of the complex, has been established. This necessitates their coordination with the standard functions and targets of enterprises. The integration of foresight and controlling functionality in a single mechanism of the Center at the initial stage of the innovation cycle determines the importance of studying its capabilities by specialists of enterprises. When enterprises operate outside the complex, it is advisable to use a digital simulator of the mechanism to assimilate the capabilities and achieve maximum stability in the target range of a compromise of interests. A large database, when using a multi-parameter approach to determine the output (resulting) variable of the effectiveness of the innovative development of an enterprise, led to a vector representation of the indicator-property. The numerical characteristics of the resulting indicator-property of the system are determined by the arguments (factorial indicators) of three additional KCF. They substantiate the coefficients for assessing the quality parameters of the regulation of the impact of input variables, or the parameters of the high-tech and science-intensive development of enterprises. The coefficients were established by ranges based on the generally accepted L. Harrington scale [28]. Experts evaluated the quality of regulation in terms of the degree of actual and planned impacts of each parameter based on the arithmetic mean estimates of specialists from the new structure of the Center of the Complex. Five intervals of fractions of a single segment were used, characterizing the very high (1–0.8), high (0.8–0.63), medium (0.63–0.37), low (0.37–0.2), and very low (0.2–0) degree of impact of the parameters in the specified verbal–numerical scale.

The objectivity of the estimates was tested on the basis of initial training recommendations to experts using pattern recognition methods in fuzzy sets and verified by numerical methods [29,30,31]. For approbation, the parameters of each additional control function that most affect the quality of regulation were used. The impact of the additional KCF-1 was assessed by the following coefficients-regulators: the degree of manifestation of the innovative competencies of researchers (project developers) of the objects of the complex and the flexibility of their structures. To regulate KCF-2, the following parameters were taken into account: the degree of awareness of researchers, developers about the possibilities of high-tech development of the object and the efficiency of establishing relationships in the space of the complex, taking into account environmental factors. The application of KCF-3 was evaluated according to other parameters: the degree of interest of business leaders in accelerating innovation, the efficiency of assessing the situation, taking into account environmental factors and the speed of perception by the staff of the object of vision and the prospects for high-tech development. We found that the new mechanism stabilizes the zone of compromise between the goals of ensuring innovation and ensuring economic efficiency according to the criterion of economic and organizational type of sustainability. This is provided by the regulators of the mechanism, which increase the reliability of predicting the normalized organizational-behavioral and economic indicators of the quality of the impact of the three management functions and their standard types on the economic development of the object.

Information on the number of established and liquidated enterprises in the complex was taken from official data on their state registration and bankruptcy. If the criterion of sustainability was not observed at certain stages of the cycle, a conclusion was made about an imbalance in the goals of efficiency and innovation. The effectiveness of the transition of the enterprise to high technologies was facilitated by the use of a new mechanism for regulating and adjusting indicators implemented on the basis of feedback. In a number of operations, the specialists of the Center made decisions to intensify the effects of the regulators of the mechanism that determine the increase in the quality parameters of additional KCF-1–KCF-3. This formed recommendations to the enterprises of the complex on adjusting the planned and target economic indicators aimed at increasing: the novelty of the technologies used, the share of costs for improving the competencies of personnel associated with the development, and use of information and communication technologies; and investments in new technologies and development of software tools to enhance interaction with suppliers and consumers of goods and services.

The methods of the organizational design of indicators of the quality of regulation have made it possible to increase the reliability of forecasts of the goals of strategies in assessing the effectiveness of high-tech development of enterprises. At the initial stage of the cycle, a strategy of controlled modernization is recommended, using mainly each enterprise’s own funds. Difficulties in obtaining investments and loans allowed only low-cost minor modernization projects to be implemented. The experience and competencies of generating creative ideas, increasing the innovative susceptibility of a part of the enterprise’s personnel based on the results of the implementation of the organizational project of external consultants, increased the dynamics of transformations in the complex of objects of the knowledge economy. In the next stage of the innovation cycle, an innovative strategy for the formation of a system of balanced indicators of the quality of enterprise management is recommended on the scale of the network dynamic structure of the complex. Such a system was previously known within individual enterprises. She substantiated the intensification of their regulated interaction with the objects of the knowledge economy and external consultants for modeling and designing organizational development processes. This made it possible to carry out an experimental application of the procedure for an enterprise’s abrupt transition to a high-tech development strategy with the functioning of a new management structure in the Center’s digital platform with a foresight-controlling mechanism. At the final stage of the innovation cycle, a strategy was applied to stabilize the results of improving the efficiency of innovation development.

While ensuring these results in subsequent innovation cycles, the recommended theoretical, methodological, and methodological approaches to improving the quality of high-tech development management help to ensure a compromise of interests. In assessing the goals of efficiency and sustainability of the processes of innovative development of enterprises in the complex of objects of the knowledge economy, the condition for a compromise is the combination of the capabilities of mechanistic and organic management structures of enterprises, consistent with the regulatory recommendations of the Center of the complex. The rationing of the management quality indicators in it helps to improve the quality of organizational design. We showed this in comparative assessments of target and threshold performance indicators [25] under conditions of different economic structures in two examples.

An enterprise of a medium-sized machine-building industry, as an object of application of a new mechanism, at the initial stage of transformation was in a low-tech economy of an industrial type. The production of products with high-added value but insufficient innovation exacerbates the problems of low competitiveness and reduced demand. This determined the need for high-tech transformations in terms of knowledge economy factors. The application of the theoretical and methodological model determined the development and implementation of methods for the functioning of the mechanism [9,117]. The operations of organizational design were implemented at the enterprise and in the Center for the Coordination of Interests of the Complex: a group of experts, researchers, and developers of the project for the formation and experimental functioning of the mechanism was created; external management consultants trained the company’s specialists in mastering the characteristics of extended accounting for VUCA environmental factors, and coordination with standard management functions when integrating foresight and controlling functionality. The use of a digital simulator of mechanism regulators according to the criterion of economic stability contributed to greater efficiency of its impact on the stability of the indicator-property in the target range of compromise of interests.

Continued research is expected in the areas of improving post-industrial ecosystems in complexes of organizational and energy-technological purposes [76]. The expanded monitoring of environmental factors will facilitate the combination of low-carbon green energy resources with alternative approaches to improve energy, environmental, and economic (3-E) efficiency. It is also aimed at the high-tech transformation of enterprises such as waste landfills as part of complexes into energy sources and carbon dioxide absorption zones. For this, the presently developed technological scheme, for which a new methodological framework is used for the purposes of the combination of technological systems based on organic fuel and renewable energy sources, is not uncommon. However, their combination in a single energy complex with a control and management system based on neural networks and micro-electric networks is used for the first time. In addition, the methodological base includes methods for approximating piecewise linear functions, which allow us to evaluate the effectiveness of technical solutions and optimize the process of choosing the most appropriate solution.

In crisis situations, for example, when renewable energy resources are insufficient, reserve capacities and technical means of traditional energy are needed. We assumed by the following types of main objects of the macro-network of the formed energy technology complex (ETC). These capacities make it possible to ensure the reliability of energy supply to the main consumers of objects of type I of the macro grid of the ETC: industries of the metallurgy type, engineering type, and other industrial objects. To regulate the economic, machine-to-machine, and physical relationships and interconnections in the micro-network of complementary objects and the macro-network of a single ETC, it is necessary to create a coordinating structure of the Center for Coordinating the Interests of Hybrid Network Objects.

The Center should make decisions on the organization and regulation of economic relations and physical relationships using objects control system for par allele operation of lines and control signal transmission lines for machine-readable interaction with the exchange of signals. Methodological support in infrastructure object is developed by structures such as research and educational centers for the development and sale of innovative products. It is necessary for the organization of a unified and high-tech approach to solving the problems of increasing 3-E efficiency while reducing the imbalance of interests of traditional and renewable energy facilities in the ETC.

An integrated approach to the organization of economic, machine-to-machine, and physical interaction of objects in accordance with the developed methodology provides a significant increase in reliability. Indeed, the tools of the control mechanism of the dynamic simulator of the mechanism for combining methods of joint energy generation, the Internet of Energy and Things provide advanced diagnostics of equipment failures and opportunities for author supervision during its life cycle. This significantly increases the 3-E efficiency of the joint operation of micro-network objects. In absolute terms, for example, the gains in energy and environmental efficiency are determined as follows (the results of the calculations are summarized).

4. Conclusions

This review surveyed noteworthy research on socio-economic processes. They confirmed the practice of increasing the resulting efficiency indicator as the goals of enterprise development in the complex of objects of the knowledge economy, determined by the vision of ideal prospects. However, a study of the genesis of models and socio-economic approaches to ensuring the sustainability of the effective state showed that such results were not fully achieved in the period of 1948–2021. The analysis of scientific and practical proposals on models and approaches to improve the efficiency of sustainable development of enterprises showed that the separate functioning of the subsystems of controlling and foresight of enterprises without constant interaction with the objects of education and science of the complex leads to an increase in the conflict of interest. In the processes of high-tech transformations and the uncertainty of the goals of enterprises, there are imbalances in the goals of ensuring their 3-E efficiency and sustainability of development. Therefore, it is necessary to create a system for the IVUCA + EVUCA monitoring of environmental factors in the digital platform of the Center for Regulating the Interests of the Complex. The complexity of the application of new subsystems required the improvement of organizational design procedures and the functioning of a single foresight-controlling mechanism. The scientific and practical results of the application of the new mechanism were first published in 2022. Three main conclusions can be drawn from the results of the review. First, the study reviewed different approaches in forecasting and categorized them in terms of the formation of foresight-controlling mechanisms in approaches to the development of management theory, the methodology of integration-balancing management, analog–digital and mathematical models for various purposes, in socio-economic, technical, and energy management systems.

Afterwards, the study discussed the strength and weakness of each approach, compared their differences, and discussed their suitable application. Finally, the study highlighted the future research direction in applying the aspect-based review. The review will be useful to people from different backgrounds to easily understand the corresponding approaches to introduce new approaches into scientific practice.