MODE SWITCH SEQUENCE ANALYSIS ON ONE-DIMENSIONAL TRAJECTORY OPTIMIZATION OF STRATOSPHERIC AIRSHIPS

摘要

This paper addresses one-dimensional trajectory optimization problem for stratospheric airships by analyzing model switch sequence of optimal working modes. By the Pontryagin's minimum principle, an optimal trajectory is a combination of three optimal working modes, that is, acceleration, deceleration, and singular interval (constant speed). In this paper, we show that there exists an optimal trajectory which has the following properties: (1) its optimal airspeed curve has at most one extremum during the travelling time; (2) it includes at most one singular interval; (3) if a singular interval is included in the optimal trajectory, there is no extremum in the airspeed curve beyond the singular interval. With these properties, the possible mode switch sequences are limited, and the exact mode switch sequence of the optimal trajectory can be determined by boundary conditions. Thus, the trajectory optimization problem can be solved by the exact mode switch sequence and the boundary conditions.