Wanchun Chen

This paper proposes a trajectory-tracking algorithm for reentry vehicles based on KalmanNet with a time-varying observation matrix. First, a nonlinear state evolution model of the reentry vehicle and a radar measurement model are developed in the radar measurement coordinate system. Then, inspired by the computation process of the Kalman gain (KG) in the extended Kalman filter (EKF), the recurrent neural network (RNN) architecture of KalmanNet is improved. The gated recurrent unit (GRU) originally used to track process noise statistics is removed. Instead, the input features are redesigned to directly estimate the prior state covariance. Furthermore, another GRU is introduced to estimate the time-varying observation matrix, considering the nonlinear characteristics of radar measurements. The calculated observation matrix is fed into both the GRU responsible for estimating the covariance of the difference between the predicted observation and the observed value and the fully connected layer that computes the KG. Finally, the proposed method is compared with six representative algorithms, including EKF, particle filter (PF), unscented Kalman filter (UKF), convolutional neural network (CNN), Long Short-Term Memory (LSTM), and the original KalmanNet. Simulation results demonstrate that the proposed method achieves the highest estimation accuracy, while its computational time remains nearly the same as that of the original KalmanNet. Monte Carlo simulations under three model-mismatch conditions are conducted to validate the robustness of the proposed method.

To address the challenge of precise impact time and angle control during the terminal phase of high-speed vehicle flight, this paper proposes a pseudospectral online planning terminal guidance law incorporating time and angle constraints. This approach effectively accounts for the nonlinear varying velocity characteristics under significant aerodynamic drag. Initially, an analytical expression for the optimal acceleration in angle control is derived based on a biased proportional guidance framework. Subsequently, a time control bias term is designed, building upon the analytical acceleration formula for angle control. To reduce computational complexity in numerical solutions, the time bias term is parameterized, and the deviation propagation equations are linearized. Then, utilizing Lagrange interpolation polynomials with Legendre-Gauss points as nodes, the state and control variables are discretized. Through pseudospectral approximation in the polynomial space, an analytical correction formula for time control is derived. Finally, numerical simulation results demonstrate that, compared to existing methods, the proposed algorithm offers superior control precision and computational efficiency, making it more suitable for the complex terminal flight environment of high-speed vehicles.

Guidance poses a significant issue in aerospace vehicle development. Simultaneous impacts and higher lethality necessitate constraints on impact time and angles, posing a substantial obstacle to effective guidance law design. Similarly, the flexibility and maneuverability of aerospace vehicles, which require a designable acceleration profile, are equally essential issues in guidance law design. Therefore, to overcome the limited selectable constraint ranges and the challenges of shaping acceleration profiles in existing guidance laws, without sacrificing their penetration and cooperation capabilities, a three-stage catenary-based guidance law is proposed that considers constrained impact and robustness to external disturbances. To begin with, the desired launch angle and initial velocity direction of the catenary are enforced during the first stage, which uses a circular arc. Subsequently, the impact time constraint is met in the second catenary-based stage, and the final stage employs an additional circular arc to enforce the desired impact angle. Using the proposed analytical geometric rules, trajectory parameters are determined explicitly. Meanwhile, a robust guidance law is developed, with all constraints met. The proposed guidance law requires no numerical calculations, nonlinear model linearization, or reliance on time-to-go error estimation, making it convenient to implement. Furthermore, the proposed guidance law extends the range of available time constraints from the minimum to infinity and the range of angle constraints from 0 degrees to 360 degrees, thereby addressing the issue of a wide range of spatiotemporal multi-constraints. The adaptability issue arising from an extensive range of impact time constraints and arbitrary angle constraints is addressed by a shapeable acceleration profile, enabling the maximum acceleration value or peak time to be adjusted to meet mission requirements. Various disturbed-engagement scenarios are simulated, and numerous analyses are conducted to evaluate the effectiveness and robustness of the proposed sliding mode control guidance law.

This paper presents an integrated algorithm for dynamic target assignment and entry guidance, which considers the dynamic variations in threat values of multiple targets and the strong nonlinear constraints of energy management during entry flight. This paper establishes an integrated computational framework by designing an energy management algorithm, an intelligent target assignment algorithm, and a guidance algorithm. It enables simultaneous target assignment and guidance command execution. Firstly, a high‐precision reduced‐order glide dynamics model, which more comprehensively accounts for the effects of Earth's rotation, is derived. This model, despite containing only three state variables, is capable of accurately predicting the glide trajectory of high‐speed vehicles. To further reduce the solution scale, control is parameterized as longitudinal lift‐to‐drag ratio and energy at two reversal points. Subsequently, a quasi‐second‐order enhanced linear pseudospectral method is developed. This method initially expands the deviation propagation equation to the second order. To derive the analytical correction formula for control, the method further conducts Gaussian pseudospectral discretization and quasi‐second‐order linearization. Although the correction is more mathematically complex, it encompasses additional second‐order information, which enables it to converge to higher precision within fewer iterations. Based on the energy management of the aircraft, the aforementioned work can be realized. To find a comprehensive optimal solution that meets the energy management requirements and maximizes the target value, the dynamic target assignment during entry is abstracted into a Markov decision process. The proximal policy optimization intelligent algorithm is employed for offline training of the assignment strategy, where the energy management algorithm is invoked to solve the energy management problem for each episode. The aircraft's energy and position, along with the threat values of each target, are utilized as observations, with the selected target number serving as the action. The reward function is designed as a composite function of target threat value, range‐to‐go, and energy management results. Finally, extensive numerical simulations are conducted to evaluate the algorithm. The results indicate that the aircraft can intelligently assign targets based on the remaining energy and the threat values of each target while strictly satisfying all constraints, which proves the algorithm's wide applicability, high precision, and fast computational efficiency. Furthermore, Monte Carlo simulation results indicate that even in highly dispersed environments, this integrated algorithm exhibits strong robustness.