## 1 Introduction  
Aircraft that use solar radiation as propulsive energy are called solar-powered aircraft (SPA). As a new energy aircraft, it has irreplaceable advantages than the conventional aircraft [1; 2]. The SPA can flight higher, with a long time cruise, covering a wide area. In August 2001, Helios achieved the first goal with an unofficial world-record altitude of a 29524 m, 40 min flight above 29261m near Hawaii [3]. In June 2018, the \"Zephyr-S\" flew a record 25 d 23 h 57 min without interrupted [4]. Therefore, high-altitude SPA with annual continuous flight capability in area residency can be widely applied in the natural monitoring, planetary exploration, border patrol, field investigations, communications relay and electronic warfare. As a result, the high-altitude SPA is definitely a research hotspot for world aviation countries in science and technology [5; 6; 7; 8]. Over the past decade, the study of HALE SPA is mainly focused on the overall parameter design methods, the solar cell technology and applications, efficient aerodynamic layout, the design of internal energy storage systems and energy manage system, the structure design for high aspect ratio wing, et al. [8; 9; 10; 11; 12; 13; 14], and these researches have made significant contributions to the development of SPA. Simultaneously, some HALE flight strategy studies for SPA are also been studied relatively as the special nature of energy systems. As shown in these works, the research of flight strategy can be carried out in two major areas, and one of which is the SPA was considered in particle. Then the SPA can use gravitational potential, wind shear and other methods [2] as the flight strategy to reduce the weight of the energy storage battery. [PERSON] et al. [15] first proposed the conception of gravity energy storage to reduce the battery mass and did not give a detailed analytical model or quantitative conclusions. [PERSON] et al. [16] carried out the optimized flight trajectory for SPA so that it could achieve the day and night flight theoretically without battery for the first time, and the SPA need to glide from 20 km to 2 km. [PERSON] and [PERSON] [17] describe the method of dynamic gliding that can improve the flight time of unmanned aerial vehicles and expand application in Science journal. The same authors also design a method for autonomously sensing the gradient wind field intensity in a dynamic process [18], which is of great significance for SPA to use wind shear potential energy by gliding. Besides, [PERSON] et al. [2; 19] who based on the basic problems of HALE flight and dynamics simulations have proposed the method of energy storage by wind shear, and this idea and method have great significance for further research. [PERSON] et al. also explored the equivalence of energy storage battery and gravity energy storage as well as the energy management strategy, showing that energy storage in altitude is most efficient when the initial altitude is below 10 km [2; 12]. On the other hand, the SPA can increase solar radiation in the normal direction of wing for photovoltaic cells by adjusting the attitude. [PERSON] et al. [11], with the objective of maximizing surplus energy, have studied the relationship between the hovering and the max remaining energy for the SPA at fixed altitude. The final result shows that the remaining electric energy obtained by the optimized hovering flight trajectory is much larger than the horizontal straight flight trajectory. [PERSON] et al. [20] have further expanded the flight space and researched the three-dimensional cylindrical space for the relations between the remaining energy and flight trajectory, which has given the optimization method for designing the flight path and some similar qualitative conclusions. [PERSON] et al. [9] also study cylindrical space path planning as the same kinetic equation model as [PERSON] and indicate that the net energy can increase by 70% of the horizontal circular flight in a recent research.