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

Anatoly Antipin () and Elena Khoroshilova ()
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Anatoly Antipin: Dorodnicyn Computing Centre
Elena Khoroshilova: Lomonosov Moscow State University

A chapter in Optimization and Its Applications in Control and Data Sciences, 2016, pp 17-49 from Springer

Abstract: 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.

Keywords: Terminal control; Boundary values problems; Controllability; Lagrange function; Saddle-point method; Convergence (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-42056-1_2

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DOI: 10.1007/978-3-319-42056-1_2

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