On the Structural Properties of the Set of Controllability for Differential Inclusion Under Condition Mobility of Terminal Set
Keywords:
dynamic system, differential inclusion, control problem, terminal set, controllability, structural properties
Abstract
In the paper we consider a mathematical model of a dynamic control system in the form of a differential inclusion. The property of controllability of this system under conditions mobility of terminal set M is researched. For this model of dynamical system the structural properties of the set of M-controllability are studied.
References
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2. Clark F. Optimization and non-smooth analysis. John Wiley & Sons. New York, Toronto, Singapore (1983).
3. Borisovich Yu. G., Gelman B. D., Myshkis A.D., Obukhovsky V. V. Introduction to the theory of multivalued maps and differential inclusions. Moscow: KomKniga. 2005.
4. Polovinkin E. S. Multi-valued analysis and differential inclusions. Moscow: Fizmatlit, 2015.
5. Aseev S. M., An optimal control problem for a differential inclusion with a phase constraint. Smooth approximations and necessary optimality conditions, J. Math. Sci. (New York), vol. 103, № 6,2001. pp. 670–685 .
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7. Otakulov S. Problems of controlling an ensemble of trajectories of differential inclusions. LAP Lambert Academic Publishing, 2019.
8. Otakulov S., Kholiyarova F.Kh. Time optimal control problem of ensemble trajectories of differential inclusion with delays. Journal of Advanced Research in dynamic and Control Systems, vol. 12, issue 6, 2020. pp. 1043-1050.
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10. Otakulov S., Rahimov B. Sh. About the property of controllability an ensamble of trajectories of differential inclusion. International Enjineering Journal for Research & Development. Vol.5, issue 4, 2020. pp.366-374.
11. Otakulov S., Rahimov B. Sh. On the structural properties of the reachability set of a differential inclusion. Proceedings of the International Conference "Research Innovations in Interdisciplinary Sciences", March 2021. Received From New York, USA, 2021. pp. 150–153.
12. Otakulov S., Rahimov B. Sh., Haydarov T.T. The nonsmoth optimal control problem for ensamble of trajectories of dynamic system under conditions of indeterminacy. Middle European Scientific Bulletin, vol. 5, 2020. pp. 38-42.
13. Varga J. Optimal control of differential and functional equations. Academic Press, New York and London, 1975.
14. Lee E. B., Markus L. Fundamentals of the theory of optimal control. John Willey & Sons, inc., New York, London,Sidney, 1971.
2. Clark F. Optimization and non-smooth analysis. John Wiley & Sons. New York, Toronto, Singapore (1983).
3. Borisovich Yu. G., Gelman B. D., Myshkis A.D., Obukhovsky V. V. Introduction to the theory of multivalued maps and differential inclusions. Moscow: KomKniga. 2005.
4. Polovinkin E. S. Multi-valued analysis and differential inclusions. Moscow: Fizmatlit, 2015.
5. Aseev S. M., An optimal control problem for a differential inclusion with a phase constraint. Smooth approximations and necessary optimality conditions, J. Math. Sci. (New York), vol. 103, № 6,2001. pp. 670–685 .
6. Plotnikov A.V., Komleva T.A. Piecewise constant controlled linear fuzzy differential inclusions. Universal Journal of Applied Mathematics. vol.1, No 2, 2013. pp. 39-43.
7. Otakulov S. Problems of controlling an ensemble of trajectories of differential inclusions. LAP Lambert Academic Publishing, 2019.
8. Otakulov S., Kholiyarova F.Kh. Time optimal control problem of ensemble trajectories of differential inclusion with delays. Journal of Advanced Research in dynamic and Control Systems, vol. 12, issue 6, 2020. pp. 1043-1050.
9. Otakulov S., Kholiyarova F.Kh. About conditions of controllability of ensamble trajectories of differential inclusion with delay. International Journal of Statistics and Applied Mathematics. vol.5(3), 2020. pp.59–65.
10. Otakulov S., Rahimov B. Sh. About the property of controllability an ensamble of trajectories of differential inclusion. International Enjineering Journal for Research & Development. Vol.5, issue 4, 2020. pp.366-374.
11. Otakulov S., Rahimov B. Sh. On the structural properties of the reachability set of a differential inclusion. Proceedings of the International Conference "Research Innovations in Interdisciplinary Sciences", March 2021. Received From New York, USA, 2021. pp. 150–153.
12. Otakulov S., Rahimov B. Sh., Haydarov T.T. The nonsmoth optimal control problem for ensamble of trajectories of dynamic system under conditions of indeterminacy. Middle European Scientific Bulletin, vol. 5, 2020. pp. 38-42.
13. Varga J. Optimal control of differential and functional equations. Academic Press, New York and London, 1975.
14. Lee E. B., Markus L. Fundamentals of the theory of optimal control. John Willey & Sons, inc., New York, London,Sidney, 1971.
Published
2022-05-11
How to Cite
Salim , O., & Shermuhamedovich, R. B. (2022). On the Structural Properties of the Set of Controllability for Differential Inclusion Under Condition Mobility of Terminal Set. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 3(5), 1-6. https://doi.org/10.17605/OSF.IO/6NJQ9
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