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On Methods of Terminal Control with Boundary-Value Problems: Lagrange Approach

In: Optimization and Its Applications in Control and Data Sciences

Author

Listed:
  • Anatoly Antipin

    (Dorodnicyn Computing Centre)

  • Elena Khoroshilova

    (Lomonosov Moscow State University)

Abstract

A dynamic model of terminal control with boundary value problems in the form of convex programming is considered. The solutions to these finite-dimensional problems define implicitly initial and terminal conditions at the ends of time interval at which the controlled dynamics develops. The model describes a real situation when an object needs to be transferred from one state to another. Based on the Lagrange formalism, the model is considered as a saddle-point controlled dynamical problem formulated in a Hilbert space. Iterative saddle-point method has been proposed for solving it. We prove the convergence of the method to saddle-point solution in all its components: weak convergence—in controls, strong convergence—in phase and conjugate trajectories, and terminal variables.

Suggested Citation

  • Anatoly Antipin & Elena Khoroshilova, 2016. "On Methods of Terminal Control with Boundary-Value Problems: Lagrange Approach," Springer Optimization and Its Applications, in: Boris Goldengorin (ed.), Optimization and Its Applications in Control and Data Sciences, pages 17-49, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-42056-1_2
    DOI: 10.1007/978-3-319-42056-1_2
    as

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