We study a boundary problem of optimal control, described by a system of second-order hyperbolic equations with Goursat boundary conditions. A necessary optimality condition of the Pontryagin maximum principle type is established under the usual smoothness conditions for such problems. For the proof we use an analog of the scheme proposed in [8].

Keywords: boundary problem of optimal control, Goursat – Darboux system, quality functional increment, Pontryagin maximum principle, Lagrange multiplier.

Kamil B. Mansimov (Baku, Azerbaijan Republic) – Dr. Habil. in Physics and Mathematics, Professor, Head of the Mathematical Cybernetics Chair, Baku State University, Head of the laboratory of control in complex dynamic systems, Institute of Control Systems of ANAS (Baku, Az1141, B. Vahabzade st., 68, e-mail: kamilbmansimov@gmail.com).

Vusalya A. Suleymanova (Sumgait, Azerbaijan Republic) – Assistant, Department of Mathematics and its Teaching metothods, Sumgait State University (43rd block, Sumgait, Azerbaijan, Az5008, e-mail: vusalevusale16@gmail.com).

1. Yegorov A.I. Ob optimal'nom upravleniii protsessami v nekotorykh sistemakh s raspredelennymi parametrami [On optimal control of processes in some systems with distributed parameters]. Automation and Remote Control, 1965, no. 5, pp. 613-623.
2. Yegorov A.I. Optimal'nyye protsessy v sistemakh s raspredelennymi parametrami i nekotoryye zadachi teorii invariantnosti [Optimal processes in distributed parameter systems and certain problems in invariance theory]. Izv. Akad. Nauk SSSR, Ser. Mat., 1965, no. 29 pp.1205-1260.
3. Egorov A.I. Neobkhodimyye usloviya optimal'nosti dlya sistem s raspredelennym parametrami [Necessary optimality conditions for distributed-parameter systems]. Mathematics of the USSR, Sbornik, 1966, Vol. 69(111), no. 3, pp. 371-421.
4. Plotnikov V.I., Sumin V.I. Optimizatsiya ob’yektov s raspredelennymi parametrami opisyvayemykh sistemami Gursa-Darbu [The optimization of objects with distributed parameters, described by Goursat-Darboux systems] USSR Computational Mathematics and Mathematical Physics, 1972, vol. 12, iss. 1, pp.73–92, DOI: 10.1016/0041-5553(72)90066-3
5. Sumin V.I. Optimizatsiya upravlyayemykh obobshchennykh vol'terrovykh system [Optimization of controlled generalized Volterra systems]. Abstract of Ph. D. thesis. Gorkiy, 1975, 16 p.
6. Akhiyev S.S. Nekotoryye voprosy teorii optimal'nogo upravleniya [Some questions of the theory of optimal control]. Abstract of Ph. D. thesis. Baku, 1973, 16 p.
7. Akhmedov K.T. Akhiyev S.S. Neobkhodimyye usloviyaoptimal'nosti dlya nekotorykh zadach teorii optimal'nogo upravleniya [Necessary conditions of optimality for some problems of optimal control theory].  Doklady akademii nauk azerbajdzhanskoj SSR, 1972, vol. 28, no. 5, pp. 12-16.
8. Akhiyev S.S. Sposob razdeleniya mnozhitelya Lagranzha na slagayemyye [A method of dividing the Lagrange multiplier into terms]. Doklady akademii nauk azerbajdzhanskoj SSR, 1976, vol. 31, no. 5. pp. 3-6.
9. Vasil'yev O.V. Srochko V.A., Terletskiy V.A. Metody optimizatsii i ikh  prilozhenniya [Optimization methods and their applications]. Novosibirsk, Nauka, 1990, 151 p.
10.  Srochko V.A.Variatsionnyy printsip maksimuma i metody linearizatsii v zadachakh optimal'nogo upravleniya [Variational maximum principle and linearization methods in optimal control problems]. Irkutsk, Irkutskij universitet, 1989, 154 p.
11. Vasilyev F.P. Cislenniye metodi resheniya ekstremalnix zadach [Numerical methods for solving extremal problems]. Moscow, Nauka, 1988, 520 p.

The purpose of this work is to provide decision support for the management of software development information systems. The novelty of the results is determined by the fact that the developed models and algorithms for managing the process of developing information systems software provide an increase in the quality of management decisions by ensuring the accounting of uncertainty in the estimates of experts at the initial stage of the project, automated calculation of the volume of changes as a proportion of requirements implemented in the previous stages/iterations and affected by the implementation of new requirements, based on the calculated relationships between the elements of the project and the automated calculation of estimates of the complexity and timing of software development based on fuzzy inference systems, dynamically adjusted as retrospective data are accumulated.

Keywords: software, information systems, control process, software systems, automated system.

Sergei S. Gusev (Moscow, Russian Federation) – Ph.D. Student, V.A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences (65, Profsouznaya st., Moscow, 117997, Russian Federation, e-mail: gs-serg@mail.ru).

1. Guide to the Software Engineering Body of Knowledge, Version 3.0. Washington D.C., IEEE Computer Society, 2013. 355 p.
2. Davis A. Just Enough Requirements Management: Where Software Development Meets Marketing. New York, Dorset House, 2005. 240 p.
3. Vigers K., Bitti D. Razrabotka trebovanij k programmnomu obespe­­cheniyu [Software requirements development]. Moscow: Russkaya redakciya, 2014. 736 p.
4. Gol'fand I.Yа., Hlebutin P.S. Ocenka trudozatrat razrabotki programmnoj komponenty [Evaluation of labor costs of software component deve­lopment] Trudy ISA RAN. 2005. Vol. 15. pp. 125-135.
5. Fauler M. Arhitektura korporativnyh programmnyh prilozhenij [Enterprise software application architecture]. Moscow, Vil'yams, 2006. 544 p.
6. Desyatoe ezhegodnoe issledovanie Rossijskoj industrii eksportnoj razrabotki programmnogo obespecheniya [Tenth annual survey of the Russian export software development industry]. Moscow, Russoft. 2013. 183 p.
7. Lars Mieritz Gartner Survey Shows Why Projects Fail, 2012, available at: http://thisiswhatgoodlookslike.com/2012/06/10/gartner-survey-shows-why-projects-fail/.
8. Rupinder K., Sengupta J. Software Process Models and Analysis on Failure of Software Development Projects. International Journal of Scientific & Engineering Research. 2011, iss. 2, vol. 2, pp. 1-4.
9. Stanish Group Chaos report 2014. available at: http://www.projectsmart. co.uk/docs/chaos-report.pdf (accessed 02.05.2019).
10. Royce W. Managing the Development of Large Software Systems TRW. 1970, pp. 328-338.
11. Bogomolov A.V., Zueva T.V., CHikova S.S., Golosovskij M.S. Ekspertno-analiticheskoe obosnovanie prioritetnyh napravlenij sovershenstvo­va­niya sistemy preduprezhdeniya biologicheskih terroristicheskih aktov [Expert-analytical substantiation of priority directions of improving the system of prevention of biological terrorist acts]. Informatika i sistemy upravleniya. 2009, iss. 4 (22), pp. 134-136.

Methods are described that make it possible to increase the efficiency of using neural network systems used in areas for which it is difficult to collect a large amount of data to form a training set: a method for detecting anomalous observations in a variety of empirical data, a method for calculating the informativeness of the input parameters of a neural network model, a method for tuning the sensitivity of learning algorithms to errors first and second kind and two methods to improve the accuracy of forecasting the development of complex processes in time using neural networks models.

Keywords: abnormal observations, outliers, binary classification error, process development forecasting, informativeness, diagnostic system, neural network, neural network model.

Fedor M. Cherepanov (Perm, Russian Federation) – Senior Lecturer, Department of Applied Informatics, Information Systems and Technologies, Perm State Humanitarian Pedagogical University (614990, 24, Sibirskaya st., Perm, Russian Federation, e-mail: fe-c@yandex.ru).

1. Eliseeva I. et al. Biznes-statistika [Business statistics]. Moscow, Iurait, 2018, 411 p.
2. Smoliak S.A. Titarenko B.P.  Ustoichivye metody otsenivaniia: statisticheskaia obrabotka neodnorodnykh sovokupnostei [Stable estimation methods: statistical processing of heterogeneous sets]. Moscow, Statistika, 1980, 206 p.
3. Grubbs F.E. Sample criteria for testing outlying observations, University of Michigan, 1949, 71 p.
4. Katkovnik V.Ia. Neparametricheskaia identifikatsiia i sglazhivanie dannykh: metod lokal'noi approksimatsii [Nonparametric identification and data smoothing: local approximation method]. Moscow, Nauka, 1985, 336 p.
5. Freund R.J., Wilson W.J., Sa P. Regression analysis, Elsevier Science, 2006. 480 p.
6. Weiner I.B. et al. Handbook of psychology, Research Methods in Psychology. Wiley, 2003. 736 p.
7. Tsaregorodtsev V.G. Robastnaia tselevaia funktsiia s dopuskom na tochnost' resheniia dlia neiroseti-prediktora [Robust objective function with accuracy tolerance solution for neural network predictor]. Neirokomp'iutery: razrabotka, primenenie, 2003, vol. 13, 5 p.
8. Beliakov G., Kelarev A., Yearwood J. Derivative-free optimization and neural networks for robust regression. Optimization, 2012, vol. 61, iss. 12, pp. 1467–1490.
9. Vankeerberghen P., Smeyers-Verbeke J., Leardi R., Karr C.L., Massart D.L. Robust regression and outlier detection for non-linear models using genetic algorithms. Chemometrics and Intelligent Laboratory Systems, 1995, vol. 28, iss. 1, pp. 73–87, DOI: 10.1016/0169-7439(95)80041-7
10. Cherepanov F.M. Iasnitskii L.N. Neirosetevoi fil'tr dlia iskliucheniia vybrosov v statisticheskoi informatsii [The neural filter for exception of emissions in the statistical information]. Vestnik Permskogo universiteta. Matematika. Mekhanika. Informatika, 2008, vol. 4, no. 20, pp. 151–155.
11. Cherepanov F.M. Vyiavlenie anomal'nykh nabliudenii v obuchaiushchem mnozhestve posredstvom neirosetevoi modeli [Detection of anomalous observations in the training set by means of the neural network model], Problemy informatiki v obrazovanii, upravlenii, ekonomike i tekhnike: materialy mezhdunar. nauch.-tekhn. konf (Problems of computer science in education, management, economics and technology: proceedings of the International scientific conference). Penza, Privolzhskii Dom Znanii, 2014, pp. 210–213.
12. Yasnitsky L.N. Vvedenie v iskusstvennyi intellekt [Introduction to the artificial intelligence]. Moscow, Akademiia, 2005. 176 p.
13. Tsaregorodtsev V.G. Prosteishii sposob vychisleniia pokazatelei znachimosti pervogo poriadka dlia setei obratnogo rasprostraneniia [The simplest way to calculate first-order significance indicators for backpropagation networks] Nejroinformatika i ee prilozheniya: materialy 10 Vserossijskogo seminara (Neuroinformatics and its applications: Proceedings of the 10th All-Russian Seminar), Krasnoyarsk, 2002, pp. 153–156.
14. Engelbrecht A.P., Cloete I., Zurada J.M. Determining the significance of input parameters using sensitivity analysis. From Natural to Artificial Neural Computation,  IWANN 1995. Lecture Notes in Computer Science, 1995, vol. 930. pp. 382–388. DOI: 10.1007/3-540-59497-3_199
15. Sung A.H. Ranking importance of input parameters of neural networks. Expert Systems with Applications, 1998, vol. 15, iss. 3–4, pp. 405–411, DOI: 10.1016/S0957-4174%2898%2900041-4
16. Olden J.D., Joy M.K., Death R.G. An accurate comparison of methods for quantifying variable importance in artificial neural networks using simulated data Ecological Modelling, 2004, vol. 178, iss. 3–4, pp. 389–397, DOI: 10.1016/j.ecolmodel.2004.03.013
17. Kemp S.J., Kemp S. J., Zaradic P., Hansen F. An approach for determining relative input parameter importance and significance in artificial neural networks. Ecological Modelling, 2007, vol. 204, iss. 3–4, pp. 326–334, DOI: 10.1016/j.ecolmodel.2007.01.009
18. Mustafaev A.G. Primenenie iskusstvennykh neironnykh setei dlia rannei diagnostiki zabolevaniia sakharnym diabetom [Application of artificial neural networks for the early diagnosis of diabetes]. Kibernetika i programmirovanie, 2016, vol. 2, no. 2, pp. 1–7, DOI: 10.7256/2306-4196.2016.2.17904
19. Chen J. A et al. Comparison of Four Data Mining Models: Bayes, Neural Network, SVM and Decision Trees in Identifying Syndromes in Coronary Heart Disease, Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol. 4491. – Berlin, Heidelberg: Springer, 2007. P. 1274-1279. DOI: https://doi.org/1274–1279. 10.1007/978-3-540-72383-7_148
20. Kalyan K., Jakhia B., Lele R.D., Joshi M., Chowdhary A. Artificial neural network application in the diagnosis of disease conditions with liver ultrasound images. Advances in Bioinformatics, 2014, vol. 2014, pp. 1–14, DOI: 10.1155/2014/708279
21. Raji C.G., Vinod Chandra S.S. Graft survival prediction in liver transplantation using artificial neural network models. Journal of Computational Science, 2016, vol. 16, pp. 72–78, DOI: 10.1016/j.jocs.2016.05.005
22. Stralen K.J., Stel V.S., Reitsma J.B., Dekker F.W., Zoccali C., Jager K.J. Diagnostic methods I: sensitivity, specificity, and other measures of accuracy. Kidney International, 2009, vol. 75, iss. 12, pp. 1257–1263, DOI: 10.1038/ki.2009.92
23. Takayama T., Okamoto S., Hisamatsu T., Naganuma M., Matsuoka K., Mizuno S., Bessho R., Hibi T., Kanai T. Computer-Aided Prediction of Long-term prognosis of patients with ulcerative colitis after cytoapheresis therapy.  PLoS One, 2015, vol. 10, 9 p., DOI: 10.1371/journal.pone.0131197
24. Baxt W.G. Improving the accuracy of an artificial neural network using multiple differently trained networks. Neural Computation, 1992, vol. 4, iss. 5, pp. 772–780. DOI: 10.1162/neco.1992.4.5.772
25. Cherepanov F.M. Sposob nastroiki chuvstvitel'nosti k oshibkam pervogo i vtorogo roda dlia algoritmov obucheniia neironnykh setei [The method of setting the sensitivity to errors of the first and second kind for neural network learning algorithms]. Iskusstvennyj intellekt v reshenii aktual'nyh social'nyh i ekono­mi­che­skih problem XXI veka,  Perm, Perm University Press, 2016, pp. 187–192.
26. Conroy R.M., Pyörälä K., Fitzgerald A.P. [et al.] Estimation of ten-year risk of fatal cardiovascular disease in Europe: the SCORE project. European Heart Journal, 2003, vol. 24, iss. 11, pp. 987–1003.
27. Yasnitsky L.N., Dumler A.A., Bogdanov K.V., Poleschuk A.N., Cherepanov F.M., Makurina T.V., Chugaynov S.V. Diagnosis and prognosis of cardiovascular diseases on the basis of neural networks. Biomedical Engineering, 2013, vol. 47, iss. 3, pp. 160–163, DOI: 10.1007/s10527-013-9359-0
28. Yasnitsky L.N., Dumler A.A., Cherepanov F.M. The capabilities of artificial intelligence to simulate the emergence and development of diseases, optimize prevention and treatment thereof, and identify new medical knowledge. Journal of Pharmaceutical Sciences and Research, 2018, vol. 10, iss. 9, pp. 2192–2200.
29. Vafaeipour M., Rahbari O., Rosen M.A., Fazelpour F., Ansarirad P. Application of sliding window technique for prediction of wind velocity time series. International Journal of Energy and Environmental Engineering, 2014, vol. 5, iss. 2, p. 105, DOI: 10.1007/s40095-014-0105-5
30. Yasnitsky L.N., Dumler A.A., Cherepanov F.M. Dynamic Artificial Neural Networks as Basis for Medicine Revolution. Advances in Intelligent Systems and Computing, 2018, vol. 850, pp. 351-358, DOI: 10.1007/978-3-030-02351-5_40
31. Yasnitsky L.N., Dumler A.A., Cherepanov F.M. Novye vozmozhnosti primeneniia metodov iskusstvennogo intellekta dlia modelirovaniia poiavleniia i razvitiia zabolevanii i optimizatsii ikh profilaktiki i lecheniia [New possibilities of artificial intelligence method applications for to simulate the occurrence and development of diseases and optimize their prevention and treatment]. Terapiia, 2018, vol. 1, iss. 19, pp. 109–118.

The goal of implementing autopilot system into vehicle is the automation of its movement on a dynamic landscape. Vehicle movement task can be considered as a particular case of a classification task, because the problem of every autopilot system is an optimal set of agent actions selection depending on the vehicle state. Over the recent years a great success has been achieved in self-driving vehicles learning. This article is about current approaches to implementation of autopilot system with the focus on portable vehicles. Particularly, it covers neural networks’ algorithms, appropriate for such project, and analyses them between each other according to available state-of-the-art reference sources. Work quality, learning speed, convergence guarantee and AI tasks stack coverage extent were chosen as the comparative characteristics. As a result, DQN (Deep Q-Learning) algorithm was chosen as the best option for implementation in terms of both virtual and real portable self-driving vehicles. This research paper also contains basic details about useful software solutions: virtual platforms and frameworks.

Keywords: neural network, autopilot, autonomous control, cyber-physical systems, portable vehicles, deep learning, virtual platforms, frameworks.

Artem I. Meyer (Perm, Russian Federation) – Bachelor, National Research University Higher School of Economics, Perm Branch (38, Studencheskaya st., Perm, 614070, Russian Federation, e-mail: meyer59@mail.ru).

1. Bhutani S. MIT 6.S094: Deep Learning for Self-Driving Cars 2018 Lecture 1 Notes, available at: https://hackernoon.com/mit-6-s094-deep-learning-for-self-driving-cars-2018-lecture-1-notes-807be1a50893 (date of access: 01.05.2019).
2. Golovinov A.O., Klimova E.N. The advantages of neural networks over traditional algorithms, Experimentalniye i teoreticheskiye issledovaniya v sovremennoy nauke: sb. st. po mater. V mezhdunar. nauch.-prakt. konf. № 5(5), Novosibirsk, 2017, рр. 11–15 (in Russian).
3. Setlak G. The use of artificial neural networks to solve classification tasks in management field, Radioelektronika, informatika, upravlenye, 2004, № 1, р. 127–135 (in Russian).
4. Nekipelov N. Introduction to RBF networks, available at: https://basegroup.ru/community/articles/rbf (date of access: 01.05.2019).
5. V. Mnih, K. Kavukcuoglu, D. Silver et al. Playing Atari with Deep Reinforcement Learning, NIPS Deep Learning Workshop, Lake Tahoe, USA, 2013.
6. Russell S., Norvig P. Iskustvennii Intellekt. Sovremennii podhod (Artificial Intelligence: A Modern Approach), Moscow, Williams Publishing, 2007, 1408 p. (in Russian).
7. Korobov D.A., Belyaev S.A. Modern training approaches of intelligent agents inside Atari environment, Programmnye produkty i systemy, 2018, Vol. 31, № 2, P. 284–290 (in Russian).
8. Bhutani S. MIT 6.S094: Deep Learning for Self-Driving Cars 2018 Lecture 3 Notes: Deep Reinforcement Learning, available at: https://hackernoon.com/mit-6-s094-deep-learning-for-self-driving-cars-2018-lecture-3-notes-deep-reinforcement-learning-fe9a8592e14a (date of access: 01.05.2019).
9. Irpan A. Deep Reinforcement Learning Doesn't Work Yet, available at: https://www.alexirpan.com/2018/02/14/rl-hard.html (date of access: 01.05.2019).
10. Hessel M., Modayil J., Schaul T. et al. Rainbow: Combining Improvements in Deep Reinforcement Learning, AAAI, 2018, р. 3215–3222.
11. Schaul T., Quan J., Antonoglou I., Silver D. Prioritized experience replay, ICLR, Hilton, San Juan, Puerto Rico, 2016.
12. Schulze C., Schulze M. ViZDoom: DRQN with Prioritized Experience Replay, Double-Q Learning, & Snapshot Ensembling, available at: https://arxiv.org/pdf/1801.01000 (date of access: 01.05.2019).
13. StatSoft, Inc. Electronic textbook on statistics, available at: http://www.statsoft.ru/home/textbook/default.htm (date of access: 01.05.2019) (in Russian).
14. Soldatova O.P., Garshin A.A. The use of convolutional neural network for handwritten digits recognition, Komputernaya optika, 2010, Vol. 34, № 2, рр. 252–259 (in Russian).
15. Rumelhart D., McClelland J. Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations – MIT Press Cambridge, 1986 – 547 p.
16. Sug H. Performance Comparison of RBF networks and MLPs for Classification, Proceedings of the 9th WSEAS International Conference on applied Informatics and Communications (AIC ’09), 2009, P. 450–454.
17. Kayri M. An Intelligent Approach to Educational Data: Performance Comparison of the Multilayer Perceptron and the Radial Basis Function Artificial Neural Networks, Educational Sciences: Theory & Practice, 2015, Vol. 15, № 5, рр. 1247–1255.
18. Wild S., Shoemaker C. Global Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms // SIAM J. Optim, 2011, Vol. 21, № 3, рр. 761–781.
19. Devillers J. Endocrine Disruption Modeling. – CRC Press, 2017. – 424 p.
20. Gil D., Johnsson M. Supervised SOM Based Architecture versus Multilayer Perceptron and RBF Networks, Linköping Electron Conf, 2010, рр. 15–24.
21. Benjamin O. A convergence criterion for self-organizing maps // Dissertations and Master's Theses (Campus Access). – 2012. – Paper AAI1508312.
22. Seif G. Deep Learning vs Classical Machine Learning, available at: https://towardsdatascience.com/deep-learning-vs-classical-machine-learning-9a42c6d48aa (date of access: 01.05.2019).
23. Collobert R., Kavukcuoglu K., Farabet C. Torch7: A Matlab-like Environment for Machine Learning, BigLearn, NIPS Workshop, 2011.
24. Gordon M. Deep Q-Network Training, available at: https:// github.com/soumith/cvpr2015/blob/master/DQN%20Training%20iTorch.ipynb (date of access: 01.05.2019).
25. Gloria Bueno García, Oscar Deniz Suarez, José Luis Espinosa Aranda et al. Obrabotka izobrazheniy s pomoshyu OpenCV (Learning Image Processing with OpenCV), Moscow, DMK Press Publishing, 2016, 210 p. (in Russian).
26. Dosovitskiy A., Ros G., Codevilla F. et al. CARLA: An Open Urban Driving Simulator, CoRL, Mountain View, California, 2017, рр. 11–16.
27. Kato S., Tokunaga S., Maruyama Y. et al. Autoware on Board: Enabling Autonomous Vehicles with Embedded Systems, ICCPS, Porto, Portugal, 2018, р. 287–296.
28. Shah S., Dey D., Lovett C., Kapoor A. AirSim: High-Fidelity Visual and Physical Simulation for Autonomous Vehicles, FSR, Zürich, Switzerland, 2017, рр. 2149–2154.
29. Koenig N., Howard A. Design and Use Paradigms for Gazebo, An Open-Source Multi-Robot Simulator, IROS, Sendai, Japan, 2004.
30. Comiskey C. The Very Best Euro Truck Simulator 2 Mods, available at: https://www.geforce.com/whats-new/articles/the-very-best-euro-truck-simulator-2-mods (date of access: 01.05.2019).
31. Moss R. Why A Million People Still Play Multiplayer Grand Theft Auto: San Andreas Every Month, available at: https://www.rockpapershotgun.com/ 2016/09/15/why-a-million-people-still-play-multiplayer-grand-theft-auto-san-andreas- every-month/ (date of access: 01.05.2019).
32. Lentin J. Robot Operating System (ROS) for Absolute Beginners: Robotics Programming Made Easy, Apress, 2018, 282 p.
33. Bhutani S. A Self Driving New Year #1, available at: https://hackernoon.com/a-self-driving-new-year-33284e592f35 (date of access: 01.05.2019).
34. Bhutani S. A Self Driving New Year #2, available at: https://hackernoon.com/a-self-driving-new-year-2-d1bbc5a83570 (date of access: 01.05.2019).
35. Bhutani S. A Self Driving and Flying (New) Year #3, available at: https://hackernoon.com/a-self-driving-and-flying-new-year-3-30d5ecd375e8 (date of access: 01.05.2019).
36. Zelenkovsky D. A ROS/ROS2 Multi-robot Simulator for Autonomous Vehicles, available at: https://github.com/lgsvl/simulator/blob/master/README.md (date of access: 01.05.2019).
37. Harrison K. Reading game frames in Python with OpenCV - Python Plays GTA V, available at: https://pythonprogramming.net/game-frames-open-cv-python-plays-gta-v/ (date of access: 01.05.2019).

The paper proposes a method of short-term forecasting based on the identification of the spanning algebraic sequence c using evolutionary algorithms. This method is especially effective in the case of short time series. When there is not enough data for training standard models, the developed method still allows to extract the maximum available information on the process behavior in order to extrapolate it to future points in time.

Keywords: time series forecasting, short-term forecasting, spanning algebraic sequence, evolutionary algorithms, additive noise.

Mikhail V. Danilov (Izhevsk, Russian Federation) – Ph.D. in engeeniring, doctoral student of the Department of Industrial and civil construction of the Izhevsk state technical university named after M.T. Kalashnikov (7, Studencheskaya St., Izhevsk, the Udmurt Republic, 426069, e-mail: danilovmih@gmail.com).

1. Christiaanse W.R. Short term load forecasting using general exponential smoothing, IEEE Transactions on Power Apparatus and Systems, 1971, no. 90, pp. 900-911.

2. Satpathy H.P., Liew A.C. A real-time short-term peak and average load forecasting system using a self-organasing fuzzy neural network, Engineering Applications of Artificial Intelligence, 1998, no. 11 (2), pp. 307-316.

3. Liu D., Niu D.X., Xing M. Day-ahead price forecast with genetic-algorithm-optimized support vector machines based on GARCH error calibration, Automation of Electric Power Systems, 2007, no. 31 (11), pp. 31-34.

4. Vahidinasab V., Jadid S., Kazemi A. Day-ahead price forecasting in restructured power systems using artificial neural networks, Electric Power Systems Research, 2008, no. 78 (8), pp. 1332-1342.

5. Arciniegas A.L., Rueda I.E. A. Forecasting short-term power prices in the Ontario Electricity Market (OEM) with a fuzzy logic based inference system, Utilities Policy, 2008, no. 16, pp. 39-48.

6. Kim H., Sin K. A hybrid approach based on neural networks and genetic algorithms is used for detecting temporal patterns in stock markets, Applied Soft Computing, 2007, no. 7 (2), pp. 569-576.

7. Xue J., Shi Z. Short-time traffic flow prediction based on chaos time series theory, Journal of Transportation Systems Engineering and Information Technology, 2008, 8 (5), pp. 68-72.

8. Lee C.M., Ko C.N. Time series prediction using RBF neural networks with a nonlinear time-varying evolution PSO algorithm, Neurocomputing, 2009, no. 73 (1-3), pp. 449-460.

9. Bashir Z.A., El-Hawary M.E. Applying wavelets to short-term load forecasting using PSO-based neural networks, IEEE Transactions on Power Systems, 2009, no. 24 (1), pp. 20-27.

10. Casolari S., Colajanni M. Short-term prediction models for server management in Internet-based contexts, Decision Support Systems, 2009, no. 48(1), pp. 212-223.

11. Niu D.X., Liu D., Xing M. Electricity price forecasting using
generalized regression neural network based on principal component analysis, Journal of Central South University of Technology, 2009, no. 15 (s2),
pp. 316-320.

12. Dongxiao Niu, Da Liu, Desheng Dash Wu, A soft computing system for a day-ahead electricity price forecasting, Applied Soft Computing, 2010, 10 (3), pp. 868-875.

13. Haupt R.L., Haupt S.E. Practical Genetic Algorithms, John Wiley & Sons, Inc., Hoboken, New Jersey, 2004, 272 p.

14. Holland J.H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Application to Biology, Control, and Artificial Intelligence,
The MIT Press, 1992, 225 p.

15. Lukoseviciute K., Ragulskis M., Evolutionary algorithms for the selection of time lags for time series forecasting by fuzzy inference systems, Neurocomputing, 2010, no. 73, pp. 2077-2088.

16. Herrere F., Lozano M., Verdegay J.L. Tackling real-coded genetic algorithms: operators and tools for behavioural analysis, Artificial Intelligence Review, 1998, no. 12 (4), pp. 265–319.

17. Navickas Z., Bikulciene L., Ragulskis M. Generalization of Exp-function and other standard function methods, Applied Mathematics and Computation, 2010, no. 216, pp. 2380-2393.

18. Whitley D. A genetic algorithm tutorial, Statistics and Computing, 1994, no. 4 (2), pp. 65-85.

19. Time Series Data Library | Rob J Hyndman, available at: http://robjhyndman.com/TSDL/

20. Box G.E.P., Jenkins G.M., Reinsel G.C. Time series analysis: forecasting and control, Englewood Cliff, New Jersey: Prentice-Hall, 1994, 614 p.

Statement of the rating and control of complex objects problem under uncertainty is formulated. Seven methods are presented for assessing the state of individual properties of a complex object, designed for various conditions of uncertainty. The source of uncertainty can serve as objective tools of control, that is, estimates of particular properties of an object can be either exact values ​​on a set of real numbers or interval estimates, in addition to this, the state of individual properties can have a probability distribution about the possible state of an object. The qualitatively described properties of an object are subject to uncertainty, the source of which is the subjectivity of the judgments of experts involved in their evaluation. It is important that experts can also evaluate quantitative indicators, for example, in cases where the tools of objective control are not available, that is, subjective input methods are applicable not only to qualitative indicators, but also quantitative ones. In order to aggregate information about private properties, it is proposed to use the matrix mechanisms of complex assessment that are known and obtained by the author. The defined matrix mechanisms of complex evaluation are as follows: the tree fuzzy rating mechanism with an additive-multiplicative approach and two max-min approaches to set theoretic operations, as well as two continuous complex evaluation mechanisms. Six model examples demonstrate procedures of aggregating two criteria with accurate real values, as well as with different uncertainty such as interval values, fuzzy values and F-Fuzzy values.

Keywords: complex objects, aggregation, rating and control mechanism, mechanism design, uncertainty.

Alexander O. Alekseev (Perm, Russian Federation) – Ph.D. in Economics, Associate Professor, Department of Construction engineering and material
sciences, Perm National Research Polytechnic University (614990, 29, Komsomolsky av., Perm, Russian Federation, e-mail: alekseev@cems.pstu.ru).

1. Bossert W., Peters H. Multi-attribute decision-making in individual and social choice. Mathematical social sciences. 2000, vol. 40, iss. 3, pp. 327-339.
2. Chankong, V., Haimes, Y.Y. Multiobjective decision making: theory and methodology, North-Holland. 1983, 213 p.
3. Sabaei D., Erkoyuncu J., Roy R. A review of multi-criteria decision making methods for enhanced maintenance delivery. Procedia CIRP 37. 2015, pp. 30- 35.
4. William Ho, Xiaowei Xu, Prasanta K. Dey  Multi-criteria decision making approaches for supplier evaluation and selection: A literature review. European journal of operational research. 2010, no. 202, pp. 16-24.
5. Mendoza G.A., Martins H. Multi-criteria decision analysis in natural resource management: A critical review of methods and new modelling paradigms. Forest Ecology and Management. 2016, vol. 230, iss. 1-3, pp. 1-22, doi: https://doi.org/10,1016/j.foreco.2006.03.023
6. Hassanzadeh S., Cheng K. Suppliers selection in manufacturing industries and associated multi-objective decision making methods: past, present and the future. European Scientific Journal. 2016, vol. 12, no. 1, pp. 93-113, doi: 10,19044/esj.2016.v12n1p93
7. Novikov D. Theory of Control in Organizations. New York, Nova Science Publishers, 2013, 341 p.
8. Burkov V.N., Goubko M.V., Korgin N.A., Novikov D.A. Mechanisms of Organizational Behavior Control: A Survey. Advances in Systems Science and Application. 2013, vol. 13, no. 1, pp. 1-20.
9. Glotov V.A., Pavelyev V.V. Vector stratification. Moscow, Nauka, 1984, 132 p.
10. Anohin A.M. Gusev V.B. Pavelyev V.V. Complex evaluation and optimization on models of multidimensional objects. Moscow, Institute of Control Sciences of Russian Academy of Science, 2003, 79 p.
11. Novikov D.A., Suhanov A.L. Fuzzy network systems of complex evaluation. Modeling of innovation processes and economic dynamics. Vol. 6. Moscow, Lenand, 2006, iss. 6, pp. 279-292.
12. Kharitonov V.A., Belyh A.A. Technologies of contemporary management. Under scientific edition by prof. V.A. Kharitonov. Perm, Publ. of  Perm state technical university, 2007, 190 p.
13. Alekseev A.O., Alekseeva I.E. Fuzzy integrated assessment procedures. 12th Control Sciences All-Russian Meeting, Moscow, June, 16-19, 2014. Moscow, Institute of Control Sciences of Russian Academy of Sciences, 2014. pp. 7884-7893.
14. Alekseev A.O., Kalentyeva A.S., Vychegzhanin A.V., Klimets D.A. Algorithmic basics of fuzzy procedure of integrated assessment of different nature objects. Fundamental researches. 2014, no. 3, (part 3), pp. 469-474.
15. Alekseev A.O. Research of alternative approaches to theoretic-multiple opertions under fuzzy sets in the procedure of fuzzy intagrated assessement. Applied Matehmatics and Control Sciences. 2015, no. 1, pp. 60-72.
16. Alekseev A.O. Classification of integrated assessment mechanisms for complex objects. Information and mathematical technologies in science and management. 2018, no. 2 (10), pp 106-120.
17. Burkov V.N. Novikov D.A. How to project management? Moscow, SINTEG. 1997, 190 p.
18. Alekseev A.O. Fuzzy and F-Fuzzy integrated assessment of complex objects. Control of Lafrge-scale Systems – 2018. All-Rusian school conferences of young scientists. Voronegh. 2018, pp. 16-23.
19. Alekseev A.O., Gureev K.A., Kharitonov V.A. Intellectual Modelling Technologies of Investment Market. Applied Mathematical Sciences. 2013, vol. 7, no. 137, pp. 6825-6848.
20. Alekseev A.O., Gureev K.A., Kharitonov V.A. Intelligent technologies in modelling the investment preferences of market participants. Actual Problems of Economics. 2014, vol. 152, iss. 2, pp. 435-449.
21. Gureev K.A., Chernyi S.A., Kharitonov V.A. Models of socioeconomic system strukture: their development and use. Actual Problems of Economics. 2014, vol. 159, iss. 9. pp. 475-487.
22. Spirina V.S., Alekseev A.O. Forecasting the attendance of retail real estate based on estimation of its attractiveness to consumers. Actual Problems of Economics. 2014, vol. 160, iss. 10, pp. 513-526.
23. Kharitonov V.A., Alekseeva I.E., Alekseev A.O.  Grounding the Control Premium or Discount for Lack of Control in the Investment Value at Mergers and Acquisitions. Actual Problems of Economics. 2015, vol. 164, iss. 2, pp. 461-473.
24. Alekseev A.O., Koskova K.S., Galiaskarov E.R. Technologies of Deve­lopment Decisions Making in Residential Civil Engineering. IOP Conference Series: Materials Science and Engineering. 2019, Vol. 481, no. 1, art. 012059, doi: 10,1088/1757-899X/481/1/012059

An importance of tourism study and forecasting for the near future is proved. A criteria and factors affecting the object are choose from a set of publicly available annual series of selected private. The choice is justified. Normalized values of criteria and factors are calculated. A general criterion for assessing the quality of the object under study on the basis of private ones is compiled. The mutual correlation of factors is investigated. A linear multifactor model is built. It was proved that it cannot be used for prediction because of its poor predictive properties. A regression-differential model of the second order is constructed. An optimal combination of interpolation factors is selected. The forecast of factors and dynamics of changes in the object is calculated for the next three years. The influence of changes in controlled and uncontrollable factors on the object is investigated. The possibility of influencing an object under conditions of negative environmental effects is investigated. Recommendations for compensating of the negative impact are given as a decision support.

Keywords: economics, tourism, Turkey, forecasting, mathematical modeling, regression-differential model, linear multifactor model.

Andrey V. Zatonskiy (Berezniki, Russian Federation) – Dr. Habil. in Engineering, Professor, Head of the Department of Automation of Technological Pro­cesses, Berezniki branch of Perm National Research Polytechnic University (618404, 7, Thalmann st., Berezniki, Perm region, Russian Federation, e-mail: zxenon@narod.ru).

Larisa G. Tugashova (Almetievsk, Russian Federation) – Senior Lecturer, department of automation and information technologies, Almetyevsk State Oil Institute (423450, 2, Lenin st., Almetievsk, Tatarstan, Russian Federation, e-mail: tugashowa.agni@yandex.ru).

Anastasya E. Barova (Berezniki, Russian Federation) – master student of the Department of Information Technologies and Automation Systems, Berezniki branch of Perm National Research Polytechnic University (618404, 7, Thalmann street, Berezniki, Perm region, Russian Federation, e-mail: nastya_barova@list.ru).

1. Rol' turizma v mirovoj jekonomike [The role of tourism in the global economy] available at: http://tourlib.net/books_tourism/artemova4-1.htm
2. Jekonomika Turcii [Turkish economy] available at: http://www.webeconomy.ru/index.php?newsid=1392&page=cat&type=news
3. Geraskina I.N., Petrov A.A., Zatonskiy A.V. Modeling of the investment and construction trend in Russia. International Journal of Civil Engineering and Technology. 2017. vol. 8. no. 10. pp. 1432-1447.
4. Institut statistiki Turcii [Turkish Statistical Institute] available at: http://www.turkstat.gov.tr
5. Pokazateli razvitija turizma [Indicators of tourism development] available at: http://www.kukiani.ru/index.php?page=content&subpage=s&r=7&p=18&s=63
6. Asanova I.M., Trofimova R.V., Semuhina E.V. Faktory, sposobstvujushhie razvitiju vnutrennego i viezdnogo turizma v Rossii [Factors contributing to the development of domestic and inbound tourism in Russia] – Nauchno-metodicheskij jelektronnyj zhurnal «Koncept». 2015. pp. 131-135. available at: http://e-koncept.ru/2015/95586.htm.
7. Vsemirnyj bank: krizis 2008 g ne zakonchilsja, on prodolzhaet uglubljat'sja [World Bank: 2008 crisis is not over, it continues to deepen] available at: https://ria.ru/20150116/1042864724.html
8. Orlov A.I. Nechislovaja statistika [Non-numeric statistics]. Moscow, MZ-Press Publ., 2004. 513 p.
9. Zatonzkiy A.V., Safyanova T.V. Control of the regional social resource dynamic based on the regression-differential simulation // Vestnik Juzhno-Ural'skogo gosudarstvennogo universiteta. Serija: Komp'juternye tehnologii, upravlenie, radiojelektronika. 2016. T. 16. No. 2. pp. 101-115.
10. Grigalashvili A.S., Koksharova L.F., Zueva I.O. O primenimosti korreljacionnogo analiza dlja iskljuchenija faktorov v regressionno-differencial'nyh modeljah [Application of Correlation Analysis to Exclude Factors from Regression-Differential Models] – Vestnik Tambovskogo gosudarstvennogo tehnicheskogo universiteta. 2016. No. 1. pp. 35-44.
11. Myshkis A.D. Jelementy teorii matematicheskih modelej [Elements of the theory of mathematical models]. Moscow, Komkniga Publ, 2007. 192 p.
12. Sirotina N.A., Janchenko T.V., Zatonskiy A.V. Ob approksimacii faktorov differencial'noj modeli social'no–jekonomicheskoj sistemy [About approximation of factors in development’s differential model for agriculture of Perm region] Sovremennye issledovanija social'nyh problem (jelektronnyj nauchnyj zhurnal). 2012. No. 11 (19). URL: http://sisp.nkras.ru/e-ru/issues/2012/11/sirotina.pdf.
13. Zatonskiy A.V., Janchenko T.V. Metod upravlenija razvitiem social'nogo resursa regiona na osnove regressionno-differencial'nogo modelirovanija [Regional social potential management based on second order regression-differential model] Upravlenie bol'shimi sistemami: sbornik trudov. 2015. No. 54. pp. 86-113.
14. Janchenko T.V., Zatonskiy A.V. Opredelenie optimal'noj ranzhirovki chastnyh kriteriev ocenki kraevogo social'nogo resursa [Regional social potential management based on second order regression-differential model] Jekonomika i menedzhment sistem upravlenija. 2013. No. 4. pp. 99-104.
15. Zatonskiy A.V., Sirotina N.A. Preimushhestva differencial'noj modeli slozhnoj jekonomicheskoj sistemy [Advantages of a differential model of a complex economic system] Obrazovanie. Nauka. Nauchnye kadry. 2012. No. 8. pp. 98-102.