Cyber-Physical Systems: Modelling and Intelligent Control

A mathematical model of a smooth irregular line with distributed parameters is considered, on which ultra-wideband information is recorded in the form of a change in wave parameters. The numerical solution of the differential equation makes it possible to determine the law of this change. As a result, when an ultra-wideband signal is input to such a line, the reflected signal carries the recorded information.

The applicability of the statistical method for determining the significant homogeneity of binary sequences under probabilistic moments of any finite order for solving problems of mathematical modeling of stochastic objects is proved. Approaches to the construction of the homogeneity criterion in the framework of various ways of setting probabilistic moments are described. Significant differences between the Central probabilistic moments’ initial decompositions for systems of random events of homogeneous character and digital models of processes are revealed. Brief theses of methods for finding the critical length of samples within which binary sequences have significant homogeneity over the specified raw or central probabilistic moments are presented. Areas of application of the concept of homogeneity of random sequences in classical simulation and creation of objects of cyber-physical systems are noted.

A new principle of mathematical models creation for the technical and other objects which are characterized by essential nonlinearity of interdependence of variables is substantiated. It is shown that the use of special analytical functions with a number of unique properties for the multiplicative transformation of fragmented mathematical models that approximate certain parts of the modeled dependencies allows us to obtain new functions that are analytically isolated in their domain of definition. The analyticity of these functions makes it possible additively to combine them into a single analytical function that approximates the simulated dependence in the entire area of its description. In this case, the total approximation error of the mathematical model of the studied object does not exceed the largest error of fragmentary approximating functions. The unique properties of multiplicatively isolating functions provide an almost “seamless” additive union of fragments. This chapter is dedicated to the study and proof of these properties, which are illustrated by examples.

The chapter considers an approach to numerical integration of the second kind nonlinear coupled Schrödinger equation system, written taking into account second-order dispersion and Raman scattering, which differs from the often-used approach based on the method of splitting into physical processes. The main advantages of the proposed method are its absolute stability through the use of an implicit computing scheme, an integrated mechanism for refining the solution at each step; automatic selection of integration step. Besides, there is a noticeable performance gain (or time resolution) up to three or more orders of magnitude because there is no need to produce direct and inverse Fourier transforms at each integration step, as is required in the method of splitting according to physical processes, which is very important for cyber-physical systems with minimum time response requirement. An additional advantage of the proposed method is the ability to calculate the interaction with an arbitrary number of propagation modes in the fiber.

We consider the boundary value problem for an inhomogeneous biharmonic equation and extend the problem in a variational form. Also, we carry out the discretization of the considered problem by the finite element method. The continued problems, is presented in matrix form. An iterative process is formulated for an approximate solution to the original problem. The problem in matrix form is solved by method of fictitious components. Estimates of the convergence of the iterative process are given. Research of the problem being solved is reduced to a cyber-physical system. The estimates of the convergence of the absolute error do not depend on the grid steps. An algorithm is formulated for solving the investigated computer problem. To process information in the algorithm, a variation method is used. The steepest descent method is used to control computations in the iterative process. The software implementation of the algorithm uses certain elements of artificial intelligence.

The separation of granular materials into specific fractions by size on sieve classifiers is a large and complex system both in terms of the separation process and hardware design. The separation process depends on many design and operating parameters, the shape and size of the sieve cells, the number of sieves, as well as the fractional composition, shape and particle size of the material to be separated, i.e. is a cyber-physical system (CPS). The key to CPS is the mathematical model of the separation process, which is used in the control system. A mathematical model of the process of separation of granular materials on sieve classifiers based on the theory of random processes is developed. As a random process, the linear particle density of the considered fractions on the sieve surface is considered and a system of stochastic differential equations is constructed for its determination. The obtained solutions allow us to determine the recovery coefficient and evaluate the separation efficiency. Based on the constructed mathematical model, the design and operational parameters of the classifier were optimized. The performance criteria and separation efficiency are considered as optimization criteria. All this allows us to control the process of separation of granular materials by determining the optimal values of the operating parameters of the classifier depending on the fractional composition, shape and size of the particles of the original material to be separated and its other characteristics.

We focus on forecast evaluation techniques that comply with the design principles of Industry 4.0 (or I4.0). The I4.0 concept refers to trends and principles attributed to the 4th industrial revolution and, in particular, assumes the following capabilities of automated systems: interoperability, decentralization, real-time processing, and service-orientation. Generally, effective forecast evaluation requires us to store both actuals and forecasts. We look at how to handle rolling-origin forecasts produced for many series over multiple horizons. This setup is met both in research (e.g., in forecasting competitions or when proposing a new method) and in practice (when tracking/reporting forecasting performance). We show how to ensure access to all the variables required for exploratory analysis and performance measurement. We propose flexible yet simple and effective data schemas allowing the storage and exchange of actuals, forecasts, and any additional relevant info. We show how to construct various tools for forecast exploration and evaluation using the schemas proposed. In particular, we present our implementation of a prediction-realization diagram showing forecasts from different methods on one plot. We propose special tools for measuring the quality of point and interval rolling-origin predictions across many time series and over multiple horizons. The workflow for using techniques proposed is illustrated using R codes.

The cascade architecture of neural networks, providing multichannel information processing as a part of a cyber-physical system, is presented. The architecture contains a hybrid network for aggregation of intermediate results obtained by an ensemble of deep recurrent neural networks based on fuzzy logic methods. The structure of the software which implements the presented architecture and being developed for conducting simulation experiments is described, their results are given.

The problem of eliminating the redundancy of knowledge bases formed based on fuzzy neural networks is considered. To solve this problem, fuzzy rules reduction technology based on the principles of knowledge taxonomy and genetic optimization was proposed. A technique for clustering fuzzy rules in the initial knowledge base has been developed with obtaining an intermediate knowledge base. To minimize the number of fuzzy rules in the intermediate knowledge base and obtain the required knowledge base, a genetic algorithm has been developed. A software package was developed on the basis of the proposed mathematical methods. The research carried out based on the software complex showed the effectiveness of the technology of fuzzy rules reduction and the possibility of its practical use.

Tasks, opportunities and prospects of converting the significantly nonlinear mathematical models, obtained for technical objects by the method of fragmentary, multiplicative-isolating approximation, to the Jordan controlled form are investigated. The equations of nonlinear objects in the Jordan controlled form and the algorithm of the analytical solution of the designing problem of the stabilizing control law on the basis of this model are considered. It is shown that the mathematical models of many significantly nonlinear objects can be obtained in the fragmentary form, but not in the analytical one. It is also shown that the method of Cut-Glue approximation allows us to provide these models with analytical properties. This gives a possibility for the analytical design of the nonlinear control laws with the property of “analytical adaptation” on the basis of the CGA models. The effectiveness of this approach is illustrated by the example of the analytical design of the nonlinear control system for the object with the fragmentary and considerably changing static characteristic on the base of the Jordan controlled form.

In accordance with the topic of the chapter, to ensure the management and operation of archives of design work, a comparative analysis of information support algorithms was carried out, allowing you to choose flexible manufacturing systems (FMS), their standard elements, production modules, layout schemes and a set of information about their parameters or location of documents. The task was set and the model for creating algorithmic support based on the frame modeling for the effective search and selection of FMS, its production modules, and active elements by the scope of production and the purpose of each technical unit was implemented. To ensure the reliable functioning of the FMS automatic control system, an algorithm is proposed for the search for sensors based on frame slots and the values of the achievable positioning error of industrial robots and technological equipment. An algorithm for searching for sensors and controlling the active elements of the FMS production module is proposed. The software of an expert system of a frame type with fuzzy control of the shaft processing of a cylindrical gearbox for landing gear and bearings on a lathe in a flexible manufacturing module has been developed.

A synthesis technique of an autonomous multidimensional robust stabilization system based on a new structure for compensating cross-links of a multiply connected technological control object with delays in direct and cross-links is considered, which allows obtaining a physically realizable structure of the compensator for any relations between the values of delays indirect and reciprocal relationships and for any transfer functions inertial elements, which ensures the robustness of the system to the parametric uncertainty of the object and lag values in the presence of disturbances.

This chapter dwells upon the control of groups of autonomous cyber-physical robotic cleaners designed for wet cleaning of rooms in large public or commercial buildings. It presents various strategies to control the movements of a robot group or those of robots within a group. It also discusses the factors affecting the intragroup behavior of robots. The author offers a method for building robot formations, which is based on using the wet trails of the leading robot. To control groups of cyber-physical robotic cleaners, the chapter proposes an algorithm that combines a global strategy based on the bees search algorithm with elements of swarm intelligence, and a local formation-building method for orientation to the leading robot and its neighbors. The author has simulated some robot group control and formation tasks in NetLogo. The results can be used to solve other similar problems, such as harvesting, deactivating the area from radioactive substances, disinfecting the area from viruses and others.

Compaction of hot mix asphalt (HMA) is one of the most important processes in the construction of road surfaces. The technologies of continuous compaction control (CCC) and intelligent compaction (IC) are based on algorithmic and software–technical means for processing informative signals and presenting the results of determining material compaction indicators. One of the possible reserves for increasing the efficiency of compaction is an increase in the compaction coefficient by the working bodies of stackers. The most effective management of road construction in real-time is carried out when asphalt pavers and road rollers interact as part of the existing cyber-physical system. In this chapter, using the state space method, a mathematical model of the HMA compaction process with a highly efficient stacker working body as an object of continuous nondestructive compaction control is obtained. The use of the state space method provided a clear formalization and automation of computational procedures, increasing the efficiency of theoretical research of the object using modern software. The model takes into account the design elements of the working body and the properties of the compacted material. The output parameters of the object model are intended for process dynamics analysis, continuous compaction monitoring, measurement, and control automation. The chapter presents a computer model of the object in the MATLAB/Simulink and the results of a computational experiment to model the workflow of the research object. The development of cyber-physical systems helps to increase the efficiency of managing sets of automated compacting machines at a construction site.

Currently, at NASA significant attention is paid to the development of an initiative on simulating and studying cyber-physical systems (CPS) (Cyber-Physical Systems Modeling and Analysis (CPSMA) Initiative, https://​www.​nasa.​gov/​centers/​ames/​cct/​office/​studies/​cyber-physical_​systems.​html). CPS are a new class of physical systems describing the complex models of the behavior of spacecrafts equipped with high-performance software complexes of control and navigation (DRAFT Modeling, Simulation, Information Technology & Processing Roadmap Technology Area 11, https://​www.​nasa.​gov/​pdf/​501321main_​TA11-MSITP-DRAFT-Nov2010-A1.​pdf). CPS could therefore be characterized as both hybrid systems combining software and hardware and mechatronic complexes containing electronic and mechanic components. In particular, when implementing space missions, CPS include systems for transforming coordinates and algorithms of spatial navigation referencing that have competitive advantages in the accuracy of parameters, the stability of the interaction between various components of CPS, and the possibility of adaptation to the change in dynamic behavior (DRAFT Robotics, Tele-Robotics and Autonomous Systems Roadmap Technology Area 04, https://​www.​nasa.​gov/​pdf/​501622main_​TA04-Robotics-DRAFT-Nov2010-A.​pdf). The creation of simulation models for space navigation that could be used further in CPS is an important and relevant task. This chapter considers the development of the navigation simulation model for the lunar space satellite (LSS) referencing the dynamic reference selenocentric system on the basis of coordinates transformation using the regression modeling. The transformation process includes the generation of a photogrammetrically corrected image and referencing the observed lunar objects to the ones included in the digital maps of the Moon. By the coordinate position of an object observed by the LSS and using the software developed by the authors one calculates and compares altimetry parameters of the given point in relation to known selenocentric reference objects.

The chapter presents an information technology concept for integrating aircraft computing resources into the physical processes of personalized informing passengers of civil aviation aircraft about the potential danger of an emergency in high-altitude flight, based on the calculation of estimates of the reserve time of consciousness preservation by a person in real time using technologies of the fourth industrial revolution.

This chapter considers a method for investigating the topographic model of the Moon’s surface based on harmonic multi-parameter analysis and fractal geometry. The data from the “Clementine”, “Kaguya” and “LRO” satellite space missions were used as observational material. The Russian plans include carrying out works that will provide referencing of the lunar surface images to the selenographic coordinate system. The implementation of those plans may bring selenodesy to a level comparable to the Earth’s geodesy. At the same time, data analysis in the projects mentioned above put increased demands on the description of the complex dynamic and gravity model of the Moon’s structure. The observations produced at space missions refer to the so-called quasi-dynamic system whose origin coincides with the lunar center of mass, but axes have a shift concerning the lunar axes of inertia. Many lunar maps have a quasi-dynamic system. The main purposes of this work are related to the construction of theoretical models of the physical surface based on modern satellite measurements. An analysis of fractal dimensions and self-similarity coefficients of both individual local zones and the global model of the entire lunar sphere was conducted. As a result, similar zones of the lunar surface formed at the same physical processes were determined. These results are significant for constructing a theory of the Moon’s evolution.

Many natural processes in space may be simulated and controlled by a computer using the corresponding methods and approaches. These processes include: geophysical phenomena, gravitational interactions, celestial bodies mechanics, and astrophysical events. In these cases, computer simulation directly interacts with physical systems. As it is well known, those models refer to cyber-physical systems (CPS). In the case of geophysical processes, there is the interaction between computer algorithms and complex physical systems, whose models are hard to develop and control. The practice of analyzing geophysical processes has shown one is able to control the behavior of such systems using the computer adaptive regression modeling which also allows performing prediction actions. The construction of the prediction dynamics of a physically complex system has a crucial value for the quality of processing geophysical information. At the same time, CPS could be complex, especially when it is necessary to combine cyber-physical systems. The application of adaptive regression modeling for analyzing geophysical parameters is considered. In this chapter, the variations of the Earth’s pole position are investigated. Based on time series of observations of the Earth’s pole an adaptive regression model (ARM) describing the pole’s dynamics over 30 years is developed. Similar models were created earlier by other authors but their capabilities were limited for prediction. The ARM approach has provided a more accurate combination of observational and model parameters. As a result, the use of ARM has allowed constructing the predictive curve of the change in the Earth’s pole motion and comparing the produced results with observations. The comparison shows a rather good agreement between the model parameters and the observations data.

Currently, cyber-physical systems and technologies are successfully used while implementing space missions and creating coordinate and time reference systems. To solve the problems of spatial orientation and to apply on-board sight cameras and goniometers for this purpose, it is necessary to implement referencing to the visible limb of a celestial body and determine dynamic parameters from the long-term series of observations containing large data array and also erroneous measurements. In this process, the use of robust methods for assessing produced values of the desired parameters plays an important role. This chapter suggests a noise-immune Huber’s method (Huber M estimator method—HMEM) for estimating selenographic and lunar libration parameters. In the investigations, we used positional observations of Mösting A crater concerning the lunar limb. Such observations represent unequal observations depending on the Moon’s optical librations and conditions of observations. Such time series are therefore described by the complex system of conditional equations of desired parameters whose solution by the classic least squares method cannot eliminate erroneous observations from the processing. It is more plausible to estimate long-term observational series using HMEM. As a result, the values of lunar characteristics are obtained with high accuracy of their estimation.

The methodological support for the collection and processing of information in a cyber-physical system for evaluating the linear resolution of digital аerophotographic systems on the ground using the modulation transfer function is presented, which ensures the determination of the modulation transfer function according to the results of a flight experiment in an automated mode.

The presented conceptual solution enables the design of a complex system configuration and risk analysis using the example of a cargo port. A formal description of Petri net configuration graphs is presented. The sequential construction of risk scenarios, L-models, and B-models for each strategic goal is shown. The solution is based on the formal technique of goals definition, logical management of the sequence of operations, selection and issuance of management decisions, formalization of risk scenarios, and their interpretation based on the results of simulation modeling. The simulation model will make it possible to obtain a reasonable quantitative assessment of the risk of failure to achieve a strategic goal for making management decisions.

Coalitions of robots equipped with a set of special sensors and actuators can be used for rescuing injured people in emergency situations. These sets will vary depending on the type of emergency and the activity of the environment, which, in turn, also affects the options for the interaction of robots and their tasks. In this chapter, the use of cyber-physical systems concept is proposed to form a common information-physical space in which robots will perform joint actions for eliminating the consequences of an emergency. Each robot in the coalition takes into account the specific of the emergency and the developing situation at the emergency site. Robots consider parameters of developing situations through their ontological description. The total functionality of the coalition covers the requirements of the tasks. Monitoring a developing situation allows making a timely decision on changing the composition of the coalition if the conditions change in such a way that the current composition becomes ineffective. The interaction of robots and the implementation of the rules for changing the coalition is carried out through smart contracts in a distributed ledger. This provides the opportunity to control the actions of the coalition and reduce the likelihood of being incorporated into the coalition in order to disrupt the coherence of the actions of its individual members.

The chapter presents the concept of aircraft flight safety management, which is based on a certain system of principles. The principles proposed by the author (intelligence, information, speed, safety), as well as methods and algorithms for their implementation, are a methodology for managing the flight safety of an aircraft. The chapter presents a new class of control object, an intelligent aviation system, which belongs to the class of cyber-physical systems and is characterized by the presence in its structure of the aircraft flight safety control subsystem, on the basis of which the proposed concept is implemented. In addition, the chapter shows a study of the efficiency of the algorithm for supporting decision-making by the crew to parry the threat of an aviation accident, which can be implemented based on the aircraft flight safety management system.

The chapter provides a description of the bubble energy during its stochastic movement under conditions of hydrodynamic cavitation in the flow part of a direct-flow valve with a turn of the external shut-off shell depending on the throughput of the device from the standpoint of the energy method. The results of this description form the basis of stochastic modeling of the formation of the macrosystem of bubbles in this region and rely on the formalism of cyber-physical systems.

A duopoly model with a linear demand function and non-linear cost functions of agents is considered. We study a game with multi-level Stackelberg leadership. This game arises in the case of an oligopoly in the telecommunications market that connects consumers, services supply equipment, and management of the telecom operators, therefore, the market is related to cyber-physical systems. In this case, the decision-making mechanism of the management is based on the analysis of mutual assumptions of the operators about the possible strategies of competitors, taking into account the technical characteristics of the equipment. Conjectural variations (i.e., changes in the counterparty’s actions assumed by the agent that optimize a utility function of the latter) are analyzed. Formulas for calculating the conjectural variations of agents are derived. Signs and boundaries of the variations for an arbitrary Stackelberg leadership level are investigated.

The study considers the flaws of the process of technical maintenance of boiler units of thermal power plants carried out with the use of non-specialized software and conducted as part of a set of engineering measures called an integrated logistics support. The results of the analysis of scientific and technical literature and regulatory and technical documentation governing the technical maintenance procedures of boiler units are presented. It is shown that it is possible to eliminate the flaws of the technical maintenance process by developing and applying a problem-oriented cyber-physical system. The goal and objectives of the study, necessary to automate the technical maintenance procedures of boiler units, including the intelligent decision-making procedures, are presented. A functional model is developed that formalizes the formation of individual metal control programs of boiler units as an organizational and technological process and describes the interconnections between the procedures of this process and the regulatory and technical requirements for its implementation.

A statistical approach to the construction of Precision-Recall curves is proposed for analyzing the quality of algorithms for detecting objects in images. Statistical Precision-Recall curves, unlike traditional ones, are guaranteed to be monotonously non-increasing. At the same time, the statistical average accuracy of object detection algorithms on small test data sets turns out to be less than the traditional average accuracy. On relatively large test image sets, these differences are smoothed out.

The use of the YOLOv3 and YOLOv5 algorithms for apple detection in fruit-harvesting robots are compared. It is shown that the YOLOv5 algorithm could detect apples in orchards without additional pre- and post-processing with 97.8% Recall (fruit detection rate), and 3.5% False Positive Rate (FPR). It is much better than YOLOv3 that gives 90.8% Recall and 7.8 FPR when combined with special pre- and post-processing procedures, and then 9.1% Recall and 10.0% FPR without pre- and post-processing.