Performance of 3D TPN against true-arbitrarily maneuvering target for exoatmospheric interception

True proportional navigation(TPN) guidance law is widely used for exoatmospheric interception, for its robustness and ease of implementation. The performance of TPN against nonmaneuvering target or the maneuvering target with a specific acceleration had been analyzed before. However, the obtained results are not suitable for the realistic exoatmospheric interception scenario,since the target may maneuver along an arbitrary direction with an arbitrary but upper-bounded acceleration in the threedimensional(3 D) space, which is the so-called "true-arbitrarily maneuvering target" in this paper. With the help of the line-ofsight(LOS) rotation coordinate system, the performance of 3 D TPN against the true-arbitrarily maneuvering target is thoroughly analyzed using the Lyapunov-like approach. The upper-bound of the 3 D LOS rate is obtained, and so is that of the commanded acceleration of 3 D TPN. After that, the capture region of 3 D TPN is presented on the initial relative velocity plane. The nonlinear3 D relative kinematics between the interceptor and the target is taken into full account. Finally, the new theoretical findings are demonstrated by numerical simulations.

Optimal terminal guidance for exoatmospheric interception

In this study, two optimal terminal guidance (OTG) laws, one of which takes into account the final velocity vector constraint, are developed for exoatmospheric interception using optimal control theory. In exoatmospheric interception, because the proposed guidance laws give full consideration to the effect of gravity, they consume much less fuel than the traditional guidance laws while requiring a light computational load. In the development of the guidance laws, a unified optimal guidance problem is put forward, where the final velocity vector constraint can be considered or neglected by properly adjusting a parameter in the cost function. To make this problem analytically solvable, a linear model is used to approximate the gravity difference, the difference of the gravitational accelerations of the target and interceptor. Additionally, an example is provided to show that some achievements of this study can be used to significantly improve the fuel efficiency of the pulsed guidance employed by the interceptor whose divert thrust level is fixed. (C) 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license.

Ideal proportional navigation for exoatmospheric interception

Ideal proportional navigation （IPN） is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation （TPN）, no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.

Novel TPN control algorithm for exoatmospheric intercept

A novel control algorithm with fixed pulse thrust, based on true proportional navigation（TPN）, is proposed for exoatmospheric intercept.According to the TPN guidance law and pulse thrust characteristics, the principle of control command is presented, the control stability and precision are analyzed.With the help of the TPN guidance law, the algorithm can automatically modulate the turn-on time and duration of the thrust, which could effectively limit the impact of measure noise of the line-of-sight（LOS） angle and rate on the interception miss-distance.At last, the number-theoretic method（NTM） is introduced to acquire the relation between control algorithm and miss-distance, even as it simulates the intercept process with initial state noise.And the reliability of the algorithm is demonstrated with the simulation result.