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On stationarity conditions in an optimal control problem with a simple contact with the phase boundary

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Abstract

A certain class of optimal control problems with a one-dimensional phase constraint is considered. When a trajectory contacts the phase boundary on an interval, we employ a special procedure (two-stage variation) to obtain optimality conditions in the Gamkrelidze form and then in the Dubovitskii–Milyutin form, including the sign definiteness property measure density and its jumps at junction points.

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References

  1. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1969) [in Russian].

    Google Scholar 

  2. A. Ya. Dubovitskii and A. A. Mulyutin, “Extreme-value constrained problems,” Zh. Vychisl.Mat. Mat. Fiz. 5 (3), 395–453 (1965).

    Google Scholar 

  3. F. H. Hartl, S. P. Sethi, and R. G. Vickson, “A survey of the maximum principles for optimal control problems with state constraints,” SIAM Rev. 37 (2), 181–218 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. V. Arutyunov, D. Y. Karamzin, and F. L. Pereira, “The maximum principle for optimal control problems with state constraints by R.V. Gamkrelidze: revisited,” J. Optim. Theory and Appl. 149 (3), 474–493 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  5. A. V. Dmitruk and N. P. Osmolovskii, “Necessary conditions for a weak minimum in optimal control problems with integral equations on a variable time interval,” Discrete and Continuous Dynamical Systems 35 (9), 4323–4343 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. V. Dmitruk and A. M. Kaganovich, “The hybrid maximum principle is a consequence of Pontryagin maximum principle,” System Control Letters 57 (11), 964–970 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. A. Milyutin and N. P. Osmolovskii, Calculus of Variations and Optimal Control (Providence: American Mathematical Society, 1998).

    MATH  Google Scholar 

  8. A. A. Milyutin, A. V. Dmitruk, and N. P. Osmolovskii, Maximum Principle in Optimal Control (Tsentr Prikl. Issled.,Mosk. Gos. Univ.,Moscow, 2004) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119899, Russia

    A. V. Dmitruk & I. A. Samylovskii

Authors
  1. A. V. Dmitruk
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  2. I. A. Samylovskii
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Correspondence to A. V. Dmitruk.

Additional information

Original Russian Text © A.V. Dmitruk, I.A. Samylovskii, 2016, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2016, No. 2, pp. 6–13.

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Dmitruk, A.V., Samylovskii, I.A. On stationarity conditions in an optimal control problem with a simple contact with the phase boundary. MoscowUniv.Comput.Math.Cybern. 40, 57–64 (2016). https://doi.org/10.3103/S0278641916020047

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  • DOI: https://doi.org/10.3103/S0278641916020047

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