# Analytic Time Reentry Cooperative Guidance for Multi-Hypersonic Glide Vehicles
## 1 Introduction
The convex optimization method has fast calculation speed and good real-time performance when dealing with the reentry guidance problem of a single aircraft. However, when solving the reentry cooperative guidance problem of multiple hypersonic vehicles, the penalty function term becomes complicated due to too many constraints, and the size of each coefficient is not easy to determine. Furthermore, [PERSON] et al. [18] proposed a time-controlled reentry guidance law based on a reinforcement learning strategy for online planning of roll angle symbols. [PERSON] et al. [19] used neural networks and Gauss-Newton iterative optimization to adjust the width of the course angle corridor and designed a reentry cooperative guidance law that can achieve time control. Similarly, [PERSON] et al. [20] used the reinforcement learning method to optimize the inertial weights of an improved particle swarm optimization algorithm to improve the efficiency of collaborative online planning. [PERSON] et al. [21] proposed a reentry cooperative guidance algorithm based on analytical calculations and a deep Q network algorithm, which designs the online bank angle symbol decision-maker of lateral intelligent maneuver guidance. Such algorithms generally need to have an offline learning process to be able to play a better online role, which is inconvenient for practical applications in engineering. Analytical methods have gradually attracted attention in the field of hypersonic reentry guidance because they can quickly solve the guidance command [22; 23], establish a relationship between the reentry range, energy, and bank angle based on the quasi-equilibrium glide condition (QEGC), and obtain reentry guidance command. Based on the QEGC, [PERSON] et al. [24] proposed a reentry guidance method that can analytically predict the remaining flight time and analyze the relationship between the remaining flight time, the remaining range, and the terminal speed. [PERSON] et al. [25] proposed an analytical multi-aircraft cooperative reentry guidance method, which can quickly solve the predicted flight time, but this method requires the aircraft to have a specific lift-to-drag ratio form, so it has certain limitations. [PERSON] et al. [26] designed the altitude-velocity profile, used a numerical algorithm to correct the profile design parameters, analytically obtained the guidance command, and finally increased the time controllable range to achieve time reentry cooperative guidance. Through reasonable simplification, analytical methods can be used to derive the reentry guidance command analytically with only a small amount of calculation, and they have the potential to be applied to the cooperative guidance problem of multi-hypersonic vehicles. Based on the above review, this paper proposes a time-cooperative reentry guidance method for multi-hypersonic gliders based on a swarm optimization algorithm and an analytical algorithm. First, the reentry flight is divided into the initial reentry phase and the equilibrium glide phase, and the angle of attack (AOA) profile is parameterized. Considering the timing of entering the equilibrium glide phase, bank angle parameters are designed, and the design parameters are optimized by the group optimization algorithm. Then, an analytical calculation method of the remaining time and the remaining range is derived by using the QEGC, and the terminal velocity expectation value is continuously corrected online to realize the reentry guidance satisfying the time constraint. On this basis, the reentry time-cooperative guidance task of multi-hypersonic gliders is completed. Simulation experiments of cooperative flying to fixed targets and low-speed simple moving targets show that the proposed algorithm can accurately meet the time constraints. Monte Carlo simulation experiments showed that the proposed algorithm has better anti-interference performance. The main innovations of this paper are as follows:  
1. A reentry cooperative guidance algorithm that can meet the specified time is proposed.