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