Analysis and algebraic­symbolic determination of conditions forsafe motion of a vessel in a non­stationary environment




effective safety, conditions for preventing collisions, system of adaptive motion, positioning dynamics


We have proposed a method for the algebraic formalization of predicativedetermining of zones for safe and dangerous areas of navigation for the criterion "Computational stability – continuity".

It is not possible tobuild effective mathematical models for all cases of direct application of integrated and differential equations that describe statistical correlation functions of the space-time continuum. At the same time, there are always significant difficulties in operative processing of large volumes of information. Numerical results determine known long-time delays in the work of computers in the systems of navigation and operational control over the motion of a vessel.

We have analyzed and obtainedconditions for the effective technology of structuring a safemaneuvering trajectorybased on typical sequences of formalized symbolic elementary zones. Briefpredicative fragments describe effective steps to maneuver in a safe area of navigation. Analytical description of the structural processes that transformthe input informational situational parameters into controlled effective parts and integrated modelsmakes it possible to increase technological speed of operational decision-making. Situational symbolic control over the qualities of adequate safe motion of a vessel is executedunder specific non-stationary changes in theinfluence from a dynamic external environment.

Actual effects of the influencefrom external factors in a non-stationary environment that surrounds the hull of a moving vessel were symbolically formulated. In this case, typical estimates of degrees in thenon-stationary environment are algebraically collapsed into integrated safety criteria. We have established the target effect of modeling in terms of computational dynamics of processes for operational rapid control over motion of the vessel. In this case,vector regularized parameters ofevents are continuously entered in real time as corrections for initial data. We have solved the problem on predictive modeling of maneuvering variants for the criteria that guarantee current safety of motion along a planned strategic route.

To effectively solve the taskon stable safety of motion, numerical methods to solve integral-differential nonlinear dynamic systems are typically employed. However, they are effective only for the substantiation of strategic routes. Delays in time at these stages are significant and accepted.

It is proposed to manage and control algorithmic processes in real time by using alternative methods of symbolic algebra. The modelsproposed would make it possibleto find variants that are guaranteed to be adaptive to a specific current situation based on the transversal trajectory of a vessel motion.

It is proven that in the areas where there may occur situations of conflict and risk, local rules that guarantee a safe motion trajectory areimplemented by connecting the boundary conditions for safe navigation area taking into account the presence of adjacent zones with threats, perturbations, obstacles.

Author Biographies

Illya Tykhonov, State University of Infrastructure and Technologies Kyrylivska str., 9, Kyiv, Ukraine, 04071

PhD, Associate Professor

Department of Navigation and Ships’ Management

Georgy Baranov, National Transport University Omelianovycha-Pavlenka str., 1, Kyiv, Ukraine, 01010

Doctor of Technical Sciences, Professor

Department of Information Systems and Technologies

Volodymyr Doronin, State University of Infrastructure and Technologies Kyrylivska str., 9, Kyiv, Ukraine, 04071

PhD, Associate Professor

Department of Technical Systems and Control Processes in Navigation

Andrii Nosovskyi, Kyiv Center for Maritime Transport Specialists' Training, Training, Retraining and Refreshing Competence Olenivska str., 25, Kyiv, Ukraine, 04070

PhD, Associate Professor


  1. Aisjah, A. S. (2010). An Analysis Nomoto Gain and Norbin Parameter on Ship Turning Maneuver. IPTEK The Journal for Technology and Science, 21 (2). doi: 10.12962/j20882033.v21i2.31
  2. Bremer, R. H., Cleophas, P. L. H., Fitski, H. J., Keus, D. (2007). Unmanned surface and underwater vehicles. TNO report. TNO-DV 2006 A455. Netherlands, 126.
  3. Cândido, J. J., Justino, P. A. P. S. (2011). Modelling, control and Pontryagin Maximum Principle for a two-body wave energy device. Renewable Energy, 36 (5), 1545–1557. doi: 10.1016/j.renene.2010.11.013
  4. Roberts, G. N. (2008). Trends in marine control systems. Annual Reviews in Control, 32 (2), 263–269. doi: 10.1016/j.arcontrol.2008.08.002
  5. Baranov, G. L., Tykhonov, I. V. (2010). Effictiveness of of integraned navigation and vessel traffic control system intellectualization. Systemy upravlinnia, navihatsiyi ta zviazku, 1, 13–20.
  6. Fossen, T. I. (2011). Handbook of Marine Craft Hydrodynamics and Motion Control. John Wiley & Sons, 582. doi: 10.1002/9781119994138
  7. Guidelines for Voyage Planning. International Maritime Organization. Available at:
  8. Gudkov, D. M., Tykhonov, I. V. (2016). Problem about subjects movement in inhomogeneous environment and the ways to solve operation of water transport. Scientific Works of Kharkiv National Air Force University, 1 (46), 112–115.
  9. Stern, F., Yang, J., Wang, Z., Sadat-Hosseini, H., Mousaviraad, M., Bhushan, S., Xing, T. (2013). Computational ship hydrodynamics: nowadays and way forward. International Shipbuilding Progress, 60, 3–105.
  10. Ohsawa, T. (2015). Contact geometry of the Pontryagin maximum principle. Automatica, 55, 1–5. doi: 10.1016/j.automatica.2015.02.015
  11. Onori, S., Tribioli, L. (2015). Adaptive Pontryagin’s Minimum Principle supervisory controller design for the plug-in hybrid GM Chevrolet Volt. Applied Energy, 147, 224–234. doi: 10.1016/j.apenergy.2015.01.021
  12. Ozatay, E., Ozguner, U., Filev, D. (2017). Velocity profile optimization of on road vehicles: Pontryagin's Maximum Principle based approach. Control Engineering Practice, 61, 244–254. doi: 10.1016/j.conengprac.2016.09.006
  13. Saerens, B., Van den Bulck, E. (2013). Calculation of the minimum-fuel driving control based on Pontryagin’s maximum principle. Transportation Research Part D: Transport and Environment, 24, 89–97. doi: 10.1016/j.trd.2013.05.004
  14. Baranov, G. L., Mironova, V. L., Tykhonov, I. V. (2012). Axiomatic of the algorithmic converting into the intellectual of navigation and ships traffic control systems. Automation of ship technical equipments, 18, 3–12.
  15. Convention on the International Regulations for Preventing Collisions at Sea, 1972 (COLREG) (2004). International Maritime Organization. London: IMO, 45.
  16. Costa Concordia owner faces $2 billion in costs. Disaster at Sea. Available at:
  17. General provisions on ships' routeing. Available at:
  18. New Ships' Routeing. 2015 edition (adopted on 95th session of the IMO Maritime Safety Committee June 2015) (2015). London: International Maritime Organization, 68.
  19. Safety and Shipping Review 2015. Allianz Global Corporate & Specialty. Available at:
  20. Casualty Statistic. Global Integrated Shipping Information of International Maritime Organization. Available at:
  21. Chu, Z., Zhu, D., Eu Jan, G. (2016). Observer-based adaptive neural network control for a class of remotely operated vehicles. Ocean Engineering, 127, 82–89. doi: 10.1016/j.oceaneng.2016.09.038
  22. Tykhonov, I. V. (2016). Navigation without collisions and catastrophes during sailing on high risk aquatorias. Nauchnye trudy Azerbaydzhanskoy Gosudarstvennoy Morskoy Akademii, 2, 61–68.
  23. SOLAS (2009). International Maritime Organization.
  24. Carriage Requirements for Shipborne Navigational Systems and Equipment. Resolution MSC.282 (86) adopted on 5 June 2009. Available at:
  25. Baranov, G. L., Tykhonov, I. V., Sobolevskyi, G. G. (2014). Structural analysis of the difficult dynamic systems of vessel trajectory motion. Water Transport, 1, 71–79.
  26. Scherer, R. (2012). Relational Modular Fuzzy Systems. Studies in Fuzziness and Soft Computing, 39–50. doi: 10.1007/978-3-642-30604-4_4
  27. IEC 31010:2009. Risk Management – Risk Assessment Techniques (2009). International Organization for Standardization, 176.
  28. Yang, M.-S., Lin, T.-S. (2002). Fuzzy least-squares linear regression analysis for fuzzy input–output data. Fuzzy Sets and Systems, 126 (3), 389–399. doi: 10.1016/s0165-0114(01)00066-5
  29. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8 (3), 338–353. doi: 10.1016/s0019-9958(65)90241-x
  30. Anderson, T. (1994). The Statistical Analysis of Time Series. Wiley-Interscience, 704.
  31. Tykhonov, I. V. (2011). Efficiency evaluation of the operating plan stages during ships’ navigation of ships in a limited gabarites. Systemy upravlinnia, navihatsiyi ta zviazku, 3 (19), 19–21.
  32. Rusu, R. B., Cousins, S. (2011). 3D is here: Point Cloud Library (PCL). 2011 IEEE International Conference on Robotics and Automation. doi: 10.1109/icra.2011.5980567




How to Cite

Tykhonov, I., Baranov, G., Doronin, V., & Nosovskyi, A. (2018). Analysis and algebraic­symbolic determination of conditions forsafe motion of a vessel in a non­stationary environment. Eastern-European Journal of Enterprise Technologies, 1(3 (91), 40–49.



Control processes