Touch points in optimal ascent trajectories with first-order state inequality constraints

Sang-Young Park, Srinivas R. Vadali

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Two- and three-dimensional optimal ascent trajectories with a dynamic pressure inequality constraint are analyzed for the existence of nontrivial touch points. These studies verify for the first time that such trajectories can have the usual boundary arcs, where the constraint becomes active, as well as touch points, which are isolated points where the trajectory touches the constraint boundary. Some of the costates are discontinuous at the touch point. It is also possible to obtain additional insights into the nature of the Lagrange multipliers without solving the optimal control problem, specifically, for the numerical example treated, some of the costate variables can be shown to be zero at a touch point, if it exists.

Original languageEnglish
Pages (from-to)603-610
Number of pages8
JournalJournal of Guidance, Control, and Dynamics
Volume21
Issue number4
DOIs
Publication statusPublished - 1998 Jan 1

Fingerprint

ascent trajectories
Ascent
touch
State Constraints
Inequality Constraints
trajectory
Trajectories
Trajectory
First-order
Lagrange multipliers
trajectories
dynamic pressure
optimal control
Optimal Control Problem
Arc of a curve
arcs
Verify
Numerical Examples
Three-dimensional
Zero

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Space and Planetary Science
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

@article{6271daa5ebe44ebeb48fda6ef14d7949,
title = "Touch points in optimal ascent trajectories with first-order state inequality constraints",
abstract = "Two- and three-dimensional optimal ascent trajectories with a dynamic pressure inequality constraint are analyzed for the existence of nontrivial touch points. These studies verify for the first time that such trajectories can have the usual boundary arcs, where the constraint becomes active, as well as touch points, which are isolated points where the trajectory touches the constraint boundary. Some of the costates are discontinuous at the touch point. It is also possible to obtain additional insights into the nature of the Lagrange multipliers without solving the optimal control problem, specifically, for the numerical example treated, some of the costate variables can be shown to be zero at a touch point, if it exists.",
author = "Sang-Young Park and Vadali, {Srinivas R.}",
year = "1998",
month = "1",
day = "1",
doi = "10.2514/2.4278",
language = "English",
volume = "21",
pages = "603--610",
journal = "Journal of Guidance, Control, and Dynamics",
issn = "0731-5090",
publisher = "American Institute of Aeronautics and Astronautics Inc. (AIAA)",
number = "4",

}

Touch points in optimal ascent trajectories with first-order state inequality constraints. / Park, Sang-Young; Vadali, Srinivas R.

In: Journal of Guidance, Control, and Dynamics, Vol. 21, No. 4, 01.01.1998, p. 603-610.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Touch points in optimal ascent trajectories with first-order state inequality constraints

AU - Park, Sang-Young

AU - Vadali, Srinivas R.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - Two- and three-dimensional optimal ascent trajectories with a dynamic pressure inequality constraint are analyzed for the existence of nontrivial touch points. These studies verify for the first time that such trajectories can have the usual boundary arcs, where the constraint becomes active, as well as touch points, which are isolated points where the trajectory touches the constraint boundary. Some of the costates are discontinuous at the touch point. It is also possible to obtain additional insights into the nature of the Lagrange multipliers without solving the optimal control problem, specifically, for the numerical example treated, some of the costate variables can be shown to be zero at a touch point, if it exists.

AB - Two- and three-dimensional optimal ascent trajectories with a dynamic pressure inequality constraint are analyzed for the existence of nontrivial touch points. These studies verify for the first time that such trajectories can have the usual boundary arcs, where the constraint becomes active, as well as touch points, which are isolated points where the trajectory touches the constraint boundary. Some of the costates are discontinuous at the touch point. It is also possible to obtain additional insights into the nature of the Lagrange multipliers without solving the optimal control problem, specifically, for the numerical example treated, some of the costate variables can be shown to be zero at a touch point, if it exists.

UR - http://www.scopus.com/inward/record.url?scp=0032122050&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032122050&partnerID=8YFLogxK

U2 - 10.2514/2.4278

DO - 10.2514/2.4278

M3 - Article

VL - 21

SP - 603

EP - 610

JO - Journal of Guidance, Control, and Dynamics

JF - Journal of Guidance, Control, and Dynamics

SN - 0731-5090

IS - 4

ER -