Optimal thrust programming for intermediate vehicle model

Abstract

The problem of maximization of the horizontal coordinate of the intermediate vehicle model is considered. It is assumed, that vehicle is moving in the vertical plane driven by gravity, viscous drag, and thrust. Goal function is a horizontal coordinate of the vehicle. The slope angle and the thrust are considered as a control variables. Principle maximum procedure allows to reduce the optimal control problem to the boundary value problems for a system of two nonlinear differential equations. The extremal thrust is designed in feedback form depending on the slope angle and state variables. The qualitative analysis of the extremal trajectories is performed, and the characteristic features of the optimal solutions are determined. It is established that for the case of linear viscous drag the optimal thrust program does not contain any singular arcs. Besides, it is shown that optimal thrust program consists of either two arcs, maximum thrust at the beginning and zero thrust at the end, or three arcs: zero thrust at the beginning, then maximum thrust and again zero thrust at the end.