## 1 Introduction
Therefore, flight strategy optimizations in these two major areas have made significant contributions to the development for SPA. Currently, researches on flight strategy optimization that combined the altitude and attitude optimizations have began to attract the interest of research scholars. The first most similar completed study on this topic was carried out by [PERSON] et al. [21] in 2016. The author establishes a system for HALE flight that uses the altitude and attitude change to store and account more energy, and the final state of charge of the SPA battery has been maximized. [PERSON] et al. [22] have proposed a simulation to maximize the total remaining energy in the system while the aircraft stay within a 3 km mission radius as well as meeting other system constraints, showing an 8.2% increase in end-of-day battery energy for the most limiting flight condition of the winter solstice. [PERSON] et al. [23] also investigate the three-dimensional flight strategy optimization without the mission area constraint, compared with constant-altitude constant-velocity flight strategy, finding that the optimization flight strategy has more profits when the flight conditions are in lower sunlight intensity at a shorter daytime. However, none of these studies have a higher altitude level flight process in engineering applications, which is generally required for the energy storage battery smooth charging and task execution for the advantage of wind field environment in higher altitude. Besides, the SPA need to cruise in a lower altitude at night based on the gravity energy reserving and lower power consumption. Therefore, two different level flight altitudes including the higher mission altitude at daytime and the lower cruising altitude at night should be designed in the HALE flight strategy for SPA, and this flight strategy is hardly involved in published literatures. This paper was inspired by those considerations and an integrated flight strategy optimization model was proposed to solve the problem of the three-dimensional flight strategy optimization for the HALE SPA, which is based on gravity energy reserving and mission altitude in engineering application. In this study, the integrated model includes: the flight path phase model, the three-dimensional kinematic model, aerodynamic model, solar irradiation model and energy store and loss model. To solve this nonlinear strategy optimization control problem with dynamic constraints and boundary constraints, the Gauss pseudo-spectra method (GPM) is employed to obtain the minimal energy consumed flight strategy with minimum battery in given configuration of SPA. The contributions of this paper can be summarized as follows. 1. A flight path phase model based on gravity energy reserving and mission altitude is proposed for engineering applications and day and night cycle flight. 2. In order to calculate the three-dimensional solar energy collection, an energy collection model which contains geolocation, height, aircraft attitude angle is established. 3. Due to the mission altitude level flight of the high-attitude SPA, this study shows that the mission altitude may be more beneficial to engineering applications for multiple task execution, like circle hover and Regional residency for natural monitoring, field investigations, communications relay and so on. 4. A unique family of solution model of three-dimensional flight strategy optimization for SPA with minimal battery mass is proposed by GPM. 5. Due to the particularity of the solar aircraft energy harvesting system, the study results also indicate that a three-dimensional flight strategy optimization may be more beneficial for gaining more solar energy.