General Periodic Cruise Guidance Optimization for Hypersonic Vehicles

Abstract

Periodic cruise has the potential to improve the fuel efficiency of a hypersonic vehicle. However, the optimization of periodic cruise is very difficult and can only be performed inefficiently through trial-and-error due to the parameterized form. In this paper, we systematically optimized the hypersonic periodic cruise using the pseudo-spectral method (PSM) scheme. We specify the main variables as the given forms of periodic functions and parameterize the periodic guidance. The characteristic parameters can then be considered as augmented states to generate augmented dynamics. Therefore, periodic cruise optimization can be directly obtained by using GPOPS (Gauss Pseudo-spectral OPtimization Software). The numerical results demonstrate the effectiveness of the proposed method. The approach in this case study can be generalized to solve similar trajectory optimization problems that can be parameterized in a unified manner.

A Two-Level Optimization Method for Hypersonic Periodic Cruise Trajectory

“…Owning to that γ is 0 while h and M remain unchanged. The fuel consumption averaged by flight range can be simplified as in (15) and [6]. Thus, all parameters in the trajectory of steady-state cruise can be solved.…”

“…The limits of α and s are determined according to the original data benchmark [15], as shown in Table 1.…”

“…It proved that the value of throttle was only 0 or 1, and the engine only started once in a cycle. Gao et al [15] regarded the highest point of periodic cruise trajectory as the starting point and assumed that the curve which depicted the change of altitude was approximately a cosine curve with the increase of range. The cosine curve was introduced into the optimal control problem as a path constraint, and the parameters which determined the shape of cosine curve were regarded as the augmented state.…”

“…The engine switches on and off according to a periodic law, which makes the powered propulsion and unpowered glide alternate, and the altitude, velocity, and other state variables change periodically. At the end of a cycle, the parameters of flight state are the same as that of the initial state [15].…”

“…While these two variables are nonlinear and discontinuous sometimes, thus, it is not easy to deal with them at the same time in an optimization algorithm unless new constraints are added. So far, there is no effective indirect numerical method and professional software that can deal with the problem of periodic cruise trajectory design in a unified framework [15]. Therefore, it is significant to explore new method to optimize the trajectory of periodic cruise.…”