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Saddle-Point Method in Terminal Control with Sections in Phase Constraints

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Optimization and Applications (OPTIMA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12422))

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Abstract

A new approach to solving terminal control problems with phase constraints, based on saddle-point sufficient optimality conditions, is considered. The basis of the approach is Lagrangian formalism and duality theory. We study linear controlled dynamics in the presence of phase constraints. The cross section of phase constraints at certain points in time leads to the appearance of new intermediate finite-dimensional convex programming problems. In fact, the optimal control problem, defined over the entire time interval, is split into a number of independent intermediate subproblems, each of which is defined in its own sub-segment. Combining the solutions of these subproblems together, we can obtain solutions5 to the original problem on the entire time interval. To this end, a gradient flow is launched to solve all intermediate problems at the same time. The convergence of computing technology to the solution of the optimal control problem in all variables is proved.

Supported by the Russian Science Foundation (Research Project 18-01-00312).

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Authors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Vavilov Street 40, 119333, Moscow, Russia

    Anatoly Antipin

  2. CMC Faculty, Lomonosov MSU, Leninskiye Gory, 119991, Moscow, Russia

    Elena Khoroshilova

Authors
  1. Anatoly Antipin
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  2. Elena Khoroshilova
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Corresponding author

Correspondence to Elena Khoroshilova .

Editor information

Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  4. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Antipin, A., Khoroshilova, E. (2020). Saddle-Point Method in Terminal Control with Sections in Phase Constraints. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_2

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