Energy-optimal rectilinear trajectory for stratospheric airships in constant wind field

The rectilinear trajectory optimization problem for stratospheric airship flights is addressed in this paper. To minimize energy consumption under the assumption of constant wind field, the trajectory optimization problem is formulated as a nonlinear optimal singular control problem. Pontryagin Maximum Principle is utilized to determine the optimal control strategies. By repeatedly using the additional necessary conditions of Maximum Principle, the singular optimal control is investigated, and all possible optimal strategy candidates that may achieve energy minimization are discussed. In the end, the optimal strategies under different boundary conditions are established.