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

Sang Young Park, Srinivas R. Vadali

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number4
Publication statusPublished - 1998

All Science Journal Classification (ASJC) codes

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


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