Abstract
It is established that when the Hamilton-Ostrogradsky principle is satisfied, the solution to the extremal control problem can be obtained on the basis of the combined maximum principle up to a synthesizing function. This allows to find a lot of controls that, with the use of fuzzy logic, can serve as the basis for the synthesis of multi-mode dynamic systems. The effectiveness of the approach is demonstrated on the basis of mathematical simulation of the solution of the problem of synthesis of control of the mathematical pendulum.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Matyuhin, V.I.: Multimode laws control the motion of a rigid body. Mech. Solids 47, 390–399 (2012)
Taran, V.N., Trofimenko, V.N.: Synthesis of the optimum algorithm of angular stabilization using the method of prediction model. Autom. Control Comput. Sci. 5, 82–85 (1997)
Utkin, V.I.: A conditionally stable system with variable structure in a work of A.M. Letov. Autom. Remote Control 72, 2348–2350 (2011)
Zmeu, K.V., D’yachenko, P.A., Notkin, B.S.: Neural network control relay is substantially uncertain object in the task maximum performance. Intellektual’nye sistemy. 2, 93–105 (2009)
Kostoglotov, A.A., Lazarenko, S.V.: Synthesis of adaptive tracking systems based on the hypothesis of stationarity of the Hamiltonian on the switching hypersurface. J. Commun. Technol. Electron. 62, 123–127 (2017)
Derabkin, I., Kostoglotov, A., Lazarenko, S., Lyashchenko, Z.: Intellectualization of industrial systems based on the synthesis of a robotic manipulator control using a combined-maximum principle method. Advances in Intelligent Systems and Computing, vol. 451, pp. 375–384 (2016)
Kostoglotov, A.A., Lazarenko, S.V., Kuznetcov, A.A., Lyashchenko, Z.V.: Method of quasi-optimal synthesis using invariants. MATEC Web of Conferences, vol. 77, p. 1503 (2016)
Kostoglotov, A.A., Kostoglotov, A.I., Lazarenko, S.V.: Joint maximum principle in the problem of synthesizing an optimal control of nonlinear systems. Autom. Control Comput. Sci. 41, 274–281 (2007)
Kostoglotov, A.A., Kostoglotov, A.I., Lazarenko, S.V.: The combined-maximum principle in problems of estimating the motion parameters of a maneuvering aircraft. J. Commun. Technol. Electron. 54, 431–438 (2009)
Lur’e, A.I.: Analiticheskaya Mekhanika (Analytical mechanics). Gos. Izd. Fiz.-Matem. Liter., Moscow (1961) (in Russian)
Konovalov, A.S., Shumilov, P.E.: The application of fuzzy logic in aircraft systems antiutopii automation. Obrabotka informacii i upravlenie. 5, 12–17 (2003)
Burakov, M.V.: A mechanism of adaptation for a fuzzy controller. J. Comput. Syst. Sci. Int. 1, 80–83 (1998)
Muzychenko, N.Y.U.: Synthesis of an optimum linear meter for observations in the presence of correlated interferences on the basis of fuzzy-logic algorithms. J. Commun. Technol. Electron. 55, 755–758 (2010)
Orlovskij, S.A.: The Problem of Decision Making with Fuzzy Initial Information. Nauka, Moscow (1981)
Acknowledgements
This work is supported by RFBR grants Nos. 15-08-03798, 16-38-00665, 16-37-60034.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Kostoglotov, A., Lazarenko, S., Deryabkin, I., Kuzin, A., Pugachev, I., Manaenkova, O. (2018). Fuzzy Control Laws in the Basis of Solutions of Synthesis Problems of the Combined Maximum Principle. In: Abraham, A., Kovalev, S., Tarassov, V., Snasel, V., Vasileva, M., Sukhanov, A. (eds) Proceedings of the Second International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’17). IITI 2017. Advances in Intelligent Systems and Computing, vol 679. Springer, Cham. https://doi.org/10.1007/978-3-319-68321-8_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-68321-8_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68320-1
Online ISBN: 978-3-319-68321-8
eBook Packages: EngineeringEngineering (R0)