University of Hertfordshire

From the same journal

By the same authors

A self-stabilizing Pantoja-like indirect algorithm for optimal control

Research output: Contribution to journalArticlepeer-review

Documents

View graph of relations
Original languageEnglish
Pages (from-to)131-149
JournalOptimization Methods and Software
Volume16
Issue1-4
DOIs
Publication statusPublished - 2001

Abstract

In 1983 Pantoja described a computationally efficient stagewise construction of the Newton direction for the discrete time optimal control problem. Automatic Differentiation can be used to implement Pantoja's algorithm and calculate the Newton direction, without truncation error, and without extensive manual re-writing of targetfunction code to form derivatives. Pantoja's algorithm is direct, in that the independent variables are the control vectors at each timestep. In this paper we formulate an indirect analogue of Pantoja's algorithm, in which the only independent variables are the components of a costate vector corresponding to the initial timestep. This reformulated algorithm gives exactly the Newton step for the initial costate with respect to a terminal transversality condition: at each timestep we solve implicit equations for the current controlsand successor costates. A remarkable feature of the indirect algorithm is that it is straiehtforward to comensate for the effect of non-zero residuals in the implicit costate equations. .The indirect reformulation of Pantoja's algorithm set out in this paper is a suitable basis for verified optimization using interval methods.

Notes

Original article can be found at: http://www.informaworld.com/smpp/title~content=t713645924 Copyright Taylor and Francis / Informa.

ID: 89165