On optimal periodic solution of differential equations

Authors

  • Methaq Hamza Geem

DOI:

https://doi.org/10.31642/JoKMC/2018/050103

Keywords:

Hamilton's function, periodic differential equations, optimal solution, direct method, differential equations.

Abstract

this paper dedicated to the construction of solution of a three time scale periodic singular perturbed non-linear quadratic optimal control problem by using the direct method. The algorithm of the method is the direct substitution of the postulated asymptotic expansion of the solution of the problem and then by the conditions of the problem we constructed of a series of problem and find terms of the asymptotic. We find the solution by using the Hamilton's function and maximum principle

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References

Kokotovic P. V., Khalil N. K., O'Reilly J., Singular perturbation methods in control, Academic Press. London, 1986.

Panovko Ya. G. ,Fundamentals of the Applied Theory of Elastic Oscillations, M .: Engineering,1967

Pervozvansky AA ,Course of the theory of automatic control, M .: Nauka, 1986.

Plotnikov V.A., Asymptotic methods of optimal control problem, M. .: Nauka of physic-mathematic,Moscow,1980.

Sobolev V. A., Integral manifolds and decomposition of singularly perturbed systems , System of Control Lett. 1984, no. 5. P. 169-279. DOI: https://doi.org/10.1016/S0167-6911(84)80099-7

Sobolev V.A. , Singular perturbations in a linearly quadratic optimal control problem, Moscow: Nauka, 1991. No. 2. P. 53-64.

Strygin VV, Sobolev VA, Separation of motions by the method of integral manifolds, Moscow: Nauka, 1988.

Vasilieva AB, Dmitriev MG ,Singular perturbations in optimal control problems, Moscow: VINITI, 1982. P. 3-78.

Yu. A. Mitropolsky and OB Lykova, Integral manifolds in nonlinear mechanics, Moscow: Nauka, 1973.

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Published

2018-05-23

How to Cite

Geem, M. H. (2018). On optimal periodic solution of differential equations. Journal of Kufa for Mathematics and Computer, 5(1), 21–24. https://doi.org/10.31642/JoKMC/2018/050103

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