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Ivan Kazachkov



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Ivan Kazachkov


WSEAS Transactions on Circuits and Systems


Print ISSN: 1109-2734
E-ISSN: 2224-266X

Volume 18, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 18, 2019



About Application of the Principle of Maximum in the Problems of Imitative Control

AUTHORS: Ivan Kazachkov

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ABSTRACT: The problem of applying the maximum principle for finding an optimal control for the parameters in simulation for a variety of engineering and industrial systems and processes is considered. The focus is on such systems where the control of a system is difficult or practically impossible due to unknown model of system or some other uncertainties in each particular case. The procedure is constructed that converges and allows obtaining the approximation and optimal control of the system in a finite number of steps with a given accuracy. The theorem about the procedure is proved and illustrative examples are given. Some features of the application of the proposed algorithm to the real problems of simulation control are discussed like the optimal number of points dividing the temporal interval and the tasks for future investigation

KEYWORDS: Principle of Maximum, Optimal Control, Approximation, Model, Imitative

REFERENCES:

[1] Vasil'ev V.I., Kazachkov I.V. Maximum principle in simulation control// Kibernetika i Vychislitel'naya Tekhnika.- 1983.- P. 23-28.

[2] Vasil'ev V.I., Koval' P.N., Konovalenko V.V., Lazarenko I.Yu. Principles of imitative control// Soviet automatic control.- 1982, №1, P. 60-69; №2, P. 58-65.

[3] Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mizhenko E.F. Mathematical theory of optimal processes. John Wiley & sons, New-York, 1962.

[4] Pesch H.J. and Plail M. The Maximum Principle of optimal control: A history of ingenious ideas and missed opportunities// Control and Cybernetics, vol. 38 (2009), No. 4A, P. 973-995.

[5] Kim A.V., Ivanov A.V. Systems with Delays: Analysis, Control, and Computations.- Wiley, Scriver Publ., 2015, 167 pp.

[6] Feldbaum A. A. Optimal systems. Disciplines and Techniques of System Control, Chap. VII, J. Peschon, ed. Random House (Blaisdell), New York, 1965.

[7] Cross K., Torrisi S., Losin E.AR., Iacoboni M. Controlling automatic imitative tendencies: Interactions between mirror neuron and cognitive control systems// NeuroImage.- June 2013, 83.

[8] Klapper A., Ramsey R., Wigboldus D., Cross E.S. The Control of Automatic Imitation Based on Bottom-Up and Top-Down Cues to Animacy: Insights from Brain and Behavior// Journal of Cognitive Neuroscience.- April 2014, P.1-11.

[9] Li X.-Q., Zeng S.-S. Model-establishing and experimental imitation for leaning electric stove's flow and automatic control system.- June 2006 Zhongnan Daxue Xuebao (Ziran Kexue Ban)// Journal of Central South University (Science and Technology) 37(3): 547-552.

[10] Boccia A., Vinter R.B. The Maximum Principle for Optimal Control Problems with Time Delays// SIAM Journal on Control and Optimization.- January 2017.- 55(5): 2905- 2935.

[11] Kazachkov I.V. Determination and Calculation the Critical Levels in Development of Complex Systems of Different Nature with Shifted Arguments for their Investigation and Optimal Control// WSEAS transactions on systems and control.- Volume 12, 2017, P. 21-30.

[12] Zhirmunsky, A.V. and Kuzmin, V.I., Critical Levels in the Development of Natural Systems, Berlin: Springer, 1988

WSEAS Transactions on Circuits and Systems, ISSN / E-ISSN: 1109-2734 / 2224-266X, Volume 18, 2019, Art. #5, pp. 26-31


Copyright © 2019 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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