Viktor Tsvetkov, Center for Strategic Analysis and Development Research and Design Institute for Information Technology, Signalling and Telecommunications in Railway Transportation, Moscow, Russia, firstname.lastname@example.org
Sergey Shaytura, Department of Geodesy, Navigation and Geographic Information Systems Russian University of Transport (MIIT), Moscow, Russia, email@example.com
Alexsandra Bayandurova, Department of Geodesy, Navigation and Geographic Information Systems, Russian University of Transport (MIIT), Moscow, Russia, firstname.lastname@example.org
Alexey Nedelkin, Department of Informatics Plekhanov Russian University of Economics, Moscow, Russia, email@example.com
Vasiliy Matchin, Department of Informatics and Information Systems, MIREA – Russian Technological University, Moscow, Russia, firstname.lastname@example.org
Vyacheslav Barbasov, Syemka S Vozdukha, LLC, Moscow, Russia, email@example.com
Abstract — A cyber-physical system can be considered as a distributed system controlled by a computer and closely integrated with the other systems. The purpose of the work is to develop methods, providing modernization of the life cycle of specialized computing systems for cyber-physical systems. In the context of the modern cyber-physical systems, solution of the problem of maintaining control and support of the life cycle of the cyber physical system within the conditions of external actions is not well studied. Object of study are specialized models, providing life cycle support of the cyber physical systems. These models improves its operational opportunities and efficiency of use. Basic concept of work is to increase the life cycle of cyber-physical systems through the use of the ideas of complementarity, regeneration and subsidiarity.
Keywords: cyber-physical system, digital control, social cybernetics, specialized computing systems, life cycle, redundancy, modeling, digital economy, resource approach
© The Authors, published by CULTURAL-EDUCATIONAL CENTER, LLC, 2020
This work is licensed under Attribution-NonCommercial 4.0 International
The cyber-physical system (CPS) is broadly defined as a complex distributed information and communication system managed with calculator and tightly integrated with the Internet. In CPS physical and software components are closely interconnected. Each component can work at the different time scales. Together, the components reflect many different technological modalities and cooperate with each other in many other ways, depending on the contextual and external information situation. Examples of CPS are: “smart grid”, autonomous car systems, medical monitoring systems process control, robotic systems (RS) and avionics . CPS usually uses transdisciplinary approaches, including: cybernetics theory, distributed control methods, methods mechatronics, life cycle theory, information theory interactions, the theory of multiagent systems. Management in CPS and with the help of CPS is often realized with the embedded systems (embedded systems) . In these systems, the emphasis is mostly often made on the computing elements and less on the strong connection between computing and physical elements. CPS is a derivative of Internet of Things (IoT) technology. Both systems use a similar underlying architecture. However, the IoT is more technological system, and CPS is more physical system and rather represents combination between the physical. communication and computing elements . Distinctive features of cyber-physical systems are: computational integration, digital distributed communication, allowable parallelism of processes, the presence of descending, ascending and regulatory flows. An important stage in CPS design is the development of a conceptual description or its information design . An important characteristic of CPS is its life cycle associated with survivability and adaptability. CPS has an analogue with software because they have the ability to increase life cycle. This is especially noticed in the software. For example, the development and application of the new operating system, without changing software itself, can increase in certain situations software life cycle. This is an example of software lifecycle support.
Howeverit is not always possible, but only under certain conditions. Therefore study of the life cycle and methods of its support is an actual problem for CPS, software and technological systems, including control systems and information systems (IS).
II. Research Methodology
The basis for research is cybernetic analysis, structural analysis, comparative analysis and qualitative analysis. As materials used are publications in the field of social cybernetics, cyber-physical systems, special computers, as well as materials on Internet technologies of things.
III. Research Results
A. Life Cycle Model
The Life Cycle model is used in the different application and scientific areas: economics, biology, CPS, politics, modeling, computing, computer science, IoT, military, manufacturing, construction, etc. The content of the life cycle is that it reflects the sequence of the time periods during the each one object shows itself in the different ways.
The life cycle (LC) have most of the existing systems, models, processes and objects. Therefore, it is necessary to note the diversity of life cycles. One can introduce the notion carrier life cycle carrier.
One can denote life cycle carrier asl an entity: an object, process, system or another entity for which the concept of a life cycle is applicable and which has life cycle. One of the first concepts of life cycle is associated with the development and life of the organisms. The life cycle of living organisms is a set of phases of development. Alive organism, having gone through all phases, gives rise to the next generation, closing the life cycle itself. In this example, we can conclude that the life cycle serves as the basis for cyclical development. From the life cycle of organisms is different from life cycle of innovation.
Innovation Life Cycle — the period of time from the rise of the innovative product till its replacement by a more perfect and efficient product. The life cycle of an innovative product depends heavily on diffusion of innovation and dissipation of the product during operation. It is natural process. The life cycle of an innovative product also depends from market conditions and from competitors’ products.
It is not deterministic process. In a competitive environment, the life cycle is shorter. In a monopoly life cycle increases. In this example, we can conclude that the life cycle depends not only on the resources of the object, but also on the state the external environment. In a competitive environment, the product life cycle is natural. In the process of replacement of the obsolete products or systems naturally new product or system appears. Abstract and applied systems have a life cycle.
The system life cycle is divided into natural and competitive. Natural system life cycle is the time period during which the system effectively functions in relation to the selected criterion for assessing effectiveness without taking into account the influence of the environment or other systems. Competitive system life cycle is the time period during which the system is effective functions taking into account interaction or reaction with others systems. For example, on average, software has conditional life cycle of 2–3 years. However, a viral attack as an environmental impact can interrupt the life cycle of a software system much earlier.
On this example we can conclude that the life cycle of the system in the environment is significantly depends on the environment and therefore requires media protection mechanisms of the life cycle. The examined three examples are related to the objects — life cycle carriers, the life cycle of which depends on their own resources and environmental impact. In practice, there are standards that have a life cycle themselves. and set the life cycle for other objects or processes. In this case such products and systems are not carriers of the life cycle, they are indicators.
The carrier of the life cycle for such products is standard and the person behind this standard. Standard life cycle is  the time period during which these documents are suitable as tool to improve the quality of production and products. By virtue of this regulatory documents applied after the end of their life cycle, become the cause of inefficient and uncompetitive production. The peculiarity of this type of LC is that it is determined not by the carrier — standard, but those objects to which the standard is applied.
The other feature of the standard life cycle is that it is specified directive from above. Thus, the standard life cycle is determined the effectiveness of the product on the one hand and the arbitrariness of the person taking decision on the other hand. Figure 1 shows the triad of interaction of the medium (E) and the product (Pr), life cycle (LC) and human (H).
Figure 1. Life cycle formation triad when standard is used.
For products and systems — carriers of the life cycle, LC is determined by interaction pattern
Pr ∧ E → LC (1)
In the presence of a normative normative LC is determined by a more complex pattern
Pr ∧ E → In (2)
In → H (3)
H ∧ IS ∧ A → LC (4)
Expression (2) suggests that the interaction of the environment and the product gives an indication signal (In). Expression (3) suggests that an indication signal is sent to senior management (H).
Expression (4) says that the person (H) examines the situation (IS), makes an analysis (A) and on basis of it, decides to change the life cycle standard for this object. Lifecycle chain without application norm (1) is more operational than the chain (2–3–4) of the life cycle formed with the help of the norm. It is possible to talk about natural life cycle in expression (1). It is possible to talk about artificial life cycle, which describes the expression (2), (3), (4).
In the Project Management Methodology Project Life Cycle has 5 phases: Initialization; Planning Execution Control and monitoring (Controlling and Monitoring); Closing.
Business Process Life Cycle is a set of the successive phases of BP used for implementation business processes, their control and management. In all these cases, the life cycle determines the effectiveness operation of the facility. The relationship of the effectiveness of the operation of the object with life cycle (LC) determines the importance of supporting the life cycle for any system and project.
Lifecycle support can be external and internal. Internal Lifecycle support is focused on functioning system and the elimination of contradictions between its components. External Life cycle support is aimed at the reflecting external threats from the environment or competitors. Internal life cycle support uses internal resources. External life cycle support uses external resources.
The life cycle of a complex system can be a complex model, depending on a number of independent factors: system performance criteria; a causal relationship between the environment and system performance; market factors affecting the system; design models life cycle, systems modernization and life cycle models. To analyse the support of the life cycle, we examine several standard models of the life cycle. Thus, the sigmoid naturally describes the three phases of life cycle
This refers to the operational efficiency of the facility. Efficiency object link with a life cycle (LC) determines the importance life cycle support for any system and project. Support life cycle can be external and internal. Life Support aimed at the functioning of the system and the elimination of contradictions between its components. The internal support of the life cycle is aimed at reflecting external threats from the environment or competitors. It is necessary to distinguish different life cycles of the different objects and systems.
The project life cycle  is different from the product life cycle. The project life cycle also differs from the life cycle of a complex technical system. The life cycle of an information system is different from the life cycle technical system. Life Cycle System Analysis is connected with research of the important parameters: life cycle criterion, causal a corollary of the existence of a life cycle, design model life cycle. In order to examine the support of the life cycle, we go into several typical life cycle models.
The most common simple LC model is trapezoidal. The model includes 4 phases. More complex is the life cycle model, that is known as a quality loop including 11 phases. These models arestatic. In design and in dynamic systems, there are cascade model of LC and spiral model of LC. The cascade model relies on additional external resources that increase the duration life cycle. The spiral model is based on the development of additional resource in the process of functioning of a system or object. These models of the LC are dynamic. In fact, these models perform functions of the reintegration and regeneration . In this model, a resource model of the life cycle is proposed. , that is based on the fact that the amount of resources and speed of their consumption determines the life cycle of a system or object.
The equation describing the process of state changing of the system due to resource consumption is called the logistic equation. Logistic the equation, is also known as the Verhulst equation (Pitrre Francois Verhulst), which initially appeared during considering the growth model . Denote by P state (effectiveness) of the system, after t time. This model comes down to differential equation:
Most records of this equation do not consider the quantity of δ. This quantity is not a variable but it serves as indicator that has two opposition quantities +1 and –1. With equality, it is omitted. The positive meaning of the indicator corresponds to the growth of the system due to the resource consumption and accumulation of own resource by the system.
Negative meaning of the indicator corresponds to the degradation of the system due to the own resources consumption and system resource loss. In this entry, the parameter r characterizes the rate of resource consumption, and K is the circumference potential that is, the maximum possible capacity of system resources. The exact solution of the equation (1) is a logistic function, S-shaped curve, (logistic curve):
For which there is a limit
You can simplify the solution of the logistic equation to a simple form, which is used in the one-parameter Rasch model
Such a curve is shown in Fig. 1 is known in mathematics and belongs to the class sigmoid. Sigmoid is a smooth monotone nonlinear S-shape increasing function that is used to reflect the accumulation process and process limits. Quantity a makes a shift from the the origin of coordinates to the right. This solution has the form in Fig. 1. Sigmoid S1 shows birth, growth. Saturation or the maturity of the cyber-physical system indicates a horizontal segment of Pcon.
Figure 2. Three phases of the life cycle at δ = 1.
Thus, the sigmoid naturally describes the three phases of the life cycle. If the degradation of the system begins, then the indicator δ takes the quantity –1. This is equivalent to the fact that the argument t changes sign and the quantity of a will be replaced by the quantity of b, which makes the shift to the left. As a result, for the degradation process we obtain equation (7).
The solution for equation (2) has the form shown in Fig. 3.
Figure 3. Two phases of the life cycle at δ = –1.
Figure 2 shows the three phases of the life cycle. Figure 2 shows two life cycle phases. The “maturity” phase is common in both figures, that gives reason to describe this life cycle model (Fig. 2, Fig. 3) as trapezoidal, having four phases. Separate demonstration of the life cycle on Fig. 2 and Fig. 3 suggests that the growth and birth of an object or system are independent from its possible subsequent dissipation or degradation. And vice versa, degradation of the system does not depend on previous phases of birth and growth.
Figure 3 shows the maturity process and S2 degradation process. Process S2 degradation is also called dissipation process. Degradation time (dissipation) is denoted by θ. Total life cycle of the cyber-physical system (LC CPS) is determined as
In order to support the life cycle of the CPS, it is necessary to prevent degradation S2. For this, an additional resource S1 * has been taken from the reserve on which condition S1 * = – S2 is imposed. As a result, the new resource neutralizes S2 degradation and maturity increase.
Degradation occurs due to internal failures or external impacts. With the appearance of the new reasons for degradation S2*i, the use of new resources S2*i+1 is necessary. Recursive use of expression (9) allows us to increase CPS life cycle as long as resources are available to suppress degradation or dissipation.
B. Management in CPS
Management in modern cyber-physical systems (CPS) is carried out with the help of specialized computing systems (SCS), which have a network architecture. Under conditions of increase of complexity in the information situation surrounding the CPS, more often principles of decentralized and stochastic management are used. Researches in the field of SCS are conducted in many scientific centers. Development of the opportunities of the Internet of things and cyber-physical technologies systems allows you to create computing systems for CPS, with intellectual capabilities. One important problem of the computing CPS complexes, that is equipped with a decentralized management system, is the life cycle system growth.
In practice, CPS with the elements of the artificial intelligence is often represented by a group of SCS, that work with the help of decentralized algorithms. Swarm systems serve as their replacement in nature. They can be represented with a multilevel network. In a cyber physical environment SCS functionalize conditionally autonomously, coordinating information and intellectual interactions between themselves through network. In turn, CPS operate autonomously and combine into complexes. A striking example are swarms of robots [9, 10]. Complexes СPS are one of the most promising directions for the development means of computing and adapting to external influences.
C. Failures in the CPS
• Distinctive feature of any CPS or distributed system is the availability of the possible failures. These failures create delays in operation, especially under condition of insufficient redundancy protection in the system. It can result in the partial loss of interaction between SCS. The reasons for failures can be internal functional software failures or hardware failures under the influence of external factors. Such failures can occur comprehensively in different subsystems and due to different influencing factors at the same time, that is why there is a question of adapting existing survivability methods to a complex of failures for realization possibility of the continuation of the work of CPS computing systems with partial permissible loss of effectiveness. Elimination of the complex of failures can be realized by means of the specialized computing CPS complexes, that are capable of reconfiguration .
Therefore, the problem of creation the structure of such computing complexes CPS, providing the duration of the life cycle in the presence of external impacts is very actual. As a result, the solution of this problem makes influence on the creation and improvement of the theoretical and technical base of the specialized computer systems and CPS, aimed at solving important applied tasks. Many organizations both in Russia and in China, the USA and Europe are involved in the process of creation specialized computing systems for CPS There are results in the development of scientific methods, algorithms and programs monitoring, diagnostics and life cycle of CPS systems. They are represented in the form of centralized and multi-agent systems . Many works are devoted to the problem of providing long life cycle of the CPS, most of which are based redundancy.
D. Specialized Calculators as the Core of CPS
In practice, CPS is represented by a group of heterogeneous systems, each of which has at least one calculator. Sometimes the term calculator replaced by the term specialized computing systems (SCS). Each CPS has at least one calculator or SCS. If the number of calculators on the CPS is more than one, then they are combined into redundant internal network. So, combining SCS into a network creates a resource ZhC CPS. SCS function autonomously, coordinating its actions between themselves through an external network.
The model admits failures, that result in complete or partial loss of communication between the SCS and the full or partial failure of calculators. Figure 3 shows the model CPS complex, taking into account the reservation of life cycle. SCS operates on the basis of the double algorithm, coordinating interactions with each other. In this case, failures in one of SCS redistribute its tasks to the whole complex. Network interaction serves as resource. Such a resource is possible with the implementation of the reconfiguration mechanism CPS computing systems, taking into account peculiarities of the considered CPS models.
Figure 4 shows the complex, conditionally consisting of three CPS. CPS1 has three SCS, CPS2 has two SCS, CPS3 has three SCS. All SCS are connected inside CPS. CPS are interconnected by local networks, which means intercomplex communication. CPS have an external connection through an external high-speed network and additional backup network.
Figure 4. Structure of a typical CPS complex.
It is noteworthy that the triad of objects is minimal redundant system. The presence of three bonds provides a link between three components if one of the links breaks. On this basis, CPS1 and CPS3 have internal redundancy, but CPS2 does not. Therefore CPS2 backup is possible only when connected to the complex.
In complex all CPS are connected with the help of local computing network (LCN) according to the principle “each other with each other”. In the CPS complex in the case of failure one connection between the SCS due to additional connections the connection in the system will be maintained and the complex will function. In the CPS complex in the case of failure one of SCS its functions will be redistributed between the remaining SCS and the complex will function. Three (or more) related CPS create a reserve for each of the systems of the complex. Reserve for external communications creates a backup network. The basic idea of redundancy is to create triangles of connected systems. A line can be interrupted, and the interruption of the network will be more difficult.
The developed method of support of the life cycle of CPS complexes is divided into following parts: reservation of computers, CPS Reservation, reservation of communication channels at the physical level, life cycle support due to the additional resources.
The support model is as follows. Heterogeneous complex CPS can be in many states Z, each of which can be represented by the processes of S1i growth and S2i degradation. Each state Zi depends on the interaction between the resource and the process of dissipation. During operation the CPS complex passes from one state to another Si. Transition between states of the computer complex CPS occurs under the influence of external factors and internal events.
The proposed method of adaptive response on the dissipation processes includes creating a reactive response system on the impacts that initiates the connection of a resource to neutralize another dissipation. The essence of the method of reintegration of CPS complexes is to create redundant architecture of the complex and the use of software controller reacting (indicating) external influence or internal loss of complementarity of system actions.. The method allows reintegrate the CPS complex after the failure of one of the components and continue the execution of the functional process.
The general algorithm for the reintegration of CPS complexes in case of failure consists of the following steps: indication of failure, assessment of the consequences of failure, or transfer tasks to another CPS, or suppression of interference due to internal resources. Exception of the failed device from the information exchange network. Exclusion of communications with the failed device. Attempt to restore failed device. The proposed methods are different from existing one, which take into account the peculiarities of the formation of the life cycle of the CPS complex for consumption and resource consumption account.
IV. Discussion of the Results
One should distinguish between dissipation  and degradation  of CPS, although the results from these processes are the same. Degradation means violation of the internal consistency and complementarity of the components of the CPS. Dissipation means a change in the state of the CPS apart from purpose with internal consistency system components. In the first case, resources are aimed at the recovery, because it is always required. In the second case, they sent to reflect threats and self-healing, if required. There are a number of limitations to the use of this technology. Main the limitation is that each CPS must have at least three SCS.
Basic link in the technology should be a triad. On the one hand, it provides reservation, but on the other hand, parasitic reverse connections appear in the system communications that reduce the internal stability of the CPS complex and individual CPS with a large number of SCS. An increase in the number of SCS results in the increase of complexity systems exponentially. An increase in the number of SCS results in the increase of complexity synchronization problems. The use of an indicative indicator in the logistic equation is caused by the need to reflect the nature of the two opposite processes. In most works, these processes are considered whatever.
Wide use of cyber-physical systems in application areas contributes to the formation of a new direction of social cybernetics. Modern CPS are widely used in solving dynamic problems, for example, when driving. This led to create specialized transport cyber physical systems that come to replace intelligent transport systems. The conclusion about the need for rational reservation of computing resources. An adaptive redundancy method is proposed to ensure redundancy in depending on the operating mode of the robot based on distributed management.
Adaptive redundancy is defined as a function dependent from the operating mode. The results obtained indicate that to ensure stable and reliable operation of the CPS complex, it should be modeled on basis of the base model of the triad. The criterion for the formation of life CPS cycle, which allows you to create a recursive mechanism for its support. The proposed reservation model can be applied in management private transport in digital rail technology , as well as in other tasks of the spatial economy [16, 17, 18]. The results obtained allow us to solve practical problems of support life cycle of cyber-physical systems. Fundamentally this work shows the direction of research and creates a perspective for new analytical research.
 Khaitan, et al. Design Techniques and Applications of Cyber Physical Systems: A Survey, in IEEE Systems Journal, 2014
 Lee, E. A., and Seshia, S. A. Introduction to Embedded Systems, A Cyber-Physical Systems Approach. LeeSeshia.org, 2011
 Rad, C.-R., Hancu, O., Takacs, I.-Al., and Olteanu, G. Smart Monitoring of Potato Crop: A Cyber-Physical System Architecture Model in the Field of Precision Agriculture, in Conference Agriculture for Life, Life for Agriculture, 2015, vol. 6, pp. 73–79
 Tsvetkov, V. Ya. Information Constructions, in European Journal of Technology and Design, 2014, no. 3 (5), pp. 447–152
 Muravyova, Ya. I. Project life cycle, in Economics and Society, 2016, no. 3 (22), pp. 22–25
 Matchin, V. T. Regeneration of airborne databases, in Science and Technology railways, 2019, no. 4 (12), pp. 20–29
 Tsvetkov, V. Ya. Resource Method of Information System Life Cycle Estimation, in European Journal of Technology and Design, 2014, no. 2 (4), pp. 86–91
 Verhulst, P. F. Notice sur la loi que la population poursuit dans son accroissement, dans Correspondance mathématique et physique, 1838, vol. 10, pp. 113–121.
 Ferrer, E. C. The blockchain: a new framework for robotic swarm systems, in Proceedings of the future technologies conference, Springer, Cham, 2018, pp. 1037–1058
 Xi, J., Shi, Z. and Zhong, Y. Output consensus analysis and design for high-order linear swarm systems: Partial stability method, in Automatica, 2012, vol. 48, no. 9, pp. 2335–2343
 Perepelkin, D. A. Mathematical and software adaptive routing and balancing data flows in software configurable networks to ensure the quality of network services, Dis. Doctor of Technical Sciences specialty: 05.13.11, Ryazan, RGRU, 2018, 443 p.
 Tsvetkov, V. Ya. Management using cyber physical systems, Prospects for science and education, 2017, no. 3 (27), pp. 55–60
 Kawai, R., Parrondo, J. M. R., and Broeck Van den, C. Dissipation: The phase-space perspective, in Physical review letters, 2007, vol. 98, no. 8, p. 080602
 Singh, B. and Sharma, N. Mechanistic implications of plastic degradation, in Polymer Degradation and Stability, 2008, vol. 93, no. 3, pp. 561–584
 Tsvetkov, V. Ya., Shaytura, S. V., and Ordov, K. V. Digital management railway, in Advances in Economics, Business and Management Research, vol. 105. 1st International Scientific and Practical Conference on Digital Economy (ISCDE2019), pp. 181–185
 Shaitura, S. V., Minitaeva, A. M., Ordov, K. V. and Shaparenko, V. V. Virtual enterprises in a spatial economy, in International Journal of Recent Technology and Engineering (IJRTE), 2019, vol. 7. no. 6, pp. 719–724
 Shaitura, S. V., Ordov, K. V., Lesnichaya, I. G., Romanova, Yu. D. and Khachaturova, S. S. Services and mechanisms of competitive intelligence on the internet, in Espacios, 2018, vol. 39, no. 45, p. 24; Shaitura, S. V., Kozhaev, Yu. P., Ordov, K. V., Vintova, T. A., Minitaeva, A. M., and Feoktistova, V. M. Geoinformation services in a spatial economy, in International Journal of Civil Engineering and Technology, 2018, vol. 9, no. 2,pp. 829–841
 Tsvetkov, V. Ya., Shaitura, S. V., Minitaeva, A. M., Feoktistova, V. M., Kozhaev, Yu. P., and Belyu, L. P. Metamodelling in the information field, in Amazonia Investiga, 2020, vol. 9, no. 25, pp. 395–402