The capture zones of the continuous and pulsed guidance laws in the pursuit-evasion game are analytically discussed in this paper to provide deep insights into the capturability distinction between the continuous guidance law and the pulsed guidance law. Specifically, first, in the pursuit-evasion game, various capture cases are defined regarding the Zero-Effort Miss distance (ZEM) to facilitate the capturability analysis. Then, for both the evader and the pursuer, the Linear-Quadratic Differential Game (LQDG) guidance laws concerning the continuous acceleration and the pulsed acceleration are converted into a unified form. In each capture case, the optimal solution existence conditions are derived, and the corresponding capture zones are formulated. The discussion on the capture zones shows that if the optimal solution exists, the distinction between the pulsed guidance law and the continuous guidance law can be neglected under small guidance effort weight. However, the capture zone of the continuous guidance law is larger than that of the pulsed guidance law with large pursuer guidance effort weight, but smaller with large evader guidance effort weight. Finally, various simulations are conducted to illustrate the distinction of the continuous and pulsed guidance laws, as well as the impact of the acceleration ratio and the time constant ratio on the capturability.

The attitude tracking of an underactuated spacecraft with two independent actuators of the momentum exchange type is considered, and an arbitrary attitude trajectory tracking control law is proposed based on the transverse function. The kinematic equations of the rigid spacecraft attitude are established using the three-dimensional special orthogonal group $\mathrm{S}\mathrm{O}(\mathrm{3})$. Based on the momentum conservation condition, the kinematic equations are unified with the kinematics as a reduced-order system with the output angular momentum of the actuator as the control input. The transverse condition is used to construct the transverse function based on the Lie algebraic rank condition, which is essentially an embedded submanifold that can approach the equilibrium point arbitrarily. The adjoint system of the reduced-order tracking control system is established based on the transverse function and the attitude error. For the accompanying system, a smooth static feedback control law is proposed, and the ultimately bounded stability of the closed-loop system for arbitrary trajectories is proved by using the Morse function. Furthermore, for the feasible trajectory, the parameter adjustment law of the transverse function is designed based on the zero dynamic system, so that the transverse function converges to the equilibrium point of the tracking system at zero dynamic, and the closed-loop system is proved to have exponential stability. Finally, the effectiveness of the proposed controller is verified by numerical simulation.

This paper proposes a neural network-based fault diagnosis scheme to address the problem of fault isolation and estimation for the Single-Gimbal Control Moment Gyroscopes (SGCMGs) of spacecraft in a periodic orbit. To this end, a disturbance observer based on neural network is developed for active anti-disturbance, so as to improve the accuracy of fault diagnosis. The periodic disturbance on orbit can be decoupled with fault by resorting to the fitting and memory ability of neural network. Subsequently, the fault diagnosis scheme is established based on the idea of information fusion. The data of spacecraft attitude and gimbals position are combined to implement fault isolation and estimation based on adaptive estimator and neural network. Then, an adaptive sliding mode controller incorporating the disturbance and fault estimation results is designed to achieve active fault-tolerant control. In addition, the paper gives the proof of the stability of the proposed schemes, and the simulation results show that the proposed scheme achieves better diagnosis and control results than compared algorithm.