Midcourse Guidance Design For Air-based Interceptors Targeting Hypersonic Weapon

In recent years,near-space hypersonic weapon has been maturing constantly,posing a serious threat to homeland security.Compared with those traditional cruise missiles or ballistic missiles,hypersonic weapon can take the advantages of fast flight speed,active maneuverability and wide operational range,which accordingly,puts extremely high requirements on the defense system and interceptor design.Midcourse guidance is responsible for smoothly and effectively sending the interceptor into the mid-to-end handover window.Its performance directly affects the weapon’s combat operation and final intercept probability.Starting from the air-based interception scheme,this paper researches on three major problems in the interceptor’s midcourse guidance,that is,the tracking and predicting of the hypersonic target trajectory,the optimization and guidance for the interceptor’s ascent trajectory,and the optimal midcourse guidance with terminal constraints.Main contents and results are summarized as follows:(1)The design scheme of air-based defense system and modelling of midcourse guidance for interceptor are presented in the first place.Ballistic characteristics of both air-breathing and boost glide hypersonic vehicles are analyzed,which leads to the design ideas of defense system,namely,point air defense,cruise or glide phase strike,close range interception and networked operation.After then,the air-based anti hypersonic system is introduced,specifically,the composition of defense system and operation rules in the battle field are clarified.The requirements of midcourse guidance design are further analyzed,and the handover conditions for hypersonic weapon interception are clarified.Finally,the kinematic models of interceptor and hypersonic target are established in relevant coordinate system.(2)To provide credible target information for interceptor’s midcourse guidance,the problems of hypersonic target tracking and trajectory prediction are researched.On the one hand,a set of filter models is established according to the flight characteristics of hypersonic target,and the interactive multi-model method is applied for target tracking,thus to improve the accuracy and robustness of target’s information.On the other hand,the attack hypothesis of hypersonic weapon is made based on goal oriented approach,and kinematics models of the line-of-sight between hypersonic weapon and protected point are established relating to different attacking routes.Afterwards,the probability of each model is identified to realize trajectory prediction on account of different attack hypotheses.Simulation results demonstrate the effectiveness of the proposed target tracking method and target’s position accuracy and velocity accuracy are increased by 15% and 40% respectively when compared with single model algorithm.In addition,the trajectory prediction method can be used to identify the target’s attack route.By choosing the most likely route,the interception strategy can be formulated and target trajectory can be extrapolated,thus providing reliable target information for midcourse guidance.(3)Considering the optimization and guidance of the interceptor’s ascent trajectory,this paper presented a finite-horizon optimal tracking guidance based on approximate dynamic programming.A cluster of optimized ascent trajectories is generated by means of Gauss pseudospectral method with different final conditions and cost functions.Next,a closed-loop tracking controller is designed to ensure that interceptor flies according to the reference trajectory.In order to simplify the manual design process of the tracking controller,the approximate dynamic programming approach is applied.An actor-critic structure is established to approximate the optimal tracking controller and quadratic cost function.Least squares method and Adam optimization algorithm are adopted to learn the parameters of critic network and actor network respectively.The trained tracking controller can not only resist the random disturbance,but also correct the initial altitude deviation and flight path angle deviation.Simulation results show that the averaged maximum altitude deviation is 0.909 m and flight path angle deviation is 0.081°within additional attack angle,which achieves the goal of following given ascent trajectory.(4)Aiming at the problem of interceptor’s midcourse guidance,on condition that target’s acceleration stays constant,this paper proposed a novel time-to-go weighted trajectory shaping guidance with line-of-sight tube.For the convergence of terminal guidance command,timeto-go weighted quadratic performance is applied,and its boundedness is proved immediately.Thereafter,time-to-go weighted trajectory shaping guidance is derived by Cauchy-Schwartz inequality mathematics in reference to linear engagement model,which may lead to the divergences of line-of-sight states and acceleration command.To solve this problem,line-of-sight tube is introduced.Once the line-of-sight bias enters the tube,this method becomes augmented proportional navigation to ensure the convergence of line-of-sight rate.On the contrary,if lineof-sight bias exits the tube,this method turns to the extended trajectory shaping guidance,so that the terminal line-of-sight constraint can be satisfied.In order to achieve the encounter angle constraint,the transition between terminal encounter angle and terminal line-of-sight angle is further presented under zero angular rate of line-of-sight.Simulation results show that,the LOSB-TWTSG method can effectively meet the final requirements of capture range,encounter angle,zero angular rate of line-of-sight and command convergence.In addition,this proposed method has significant effect in dealing with guidance noise.Applying the LOSB-TWTSG method,the probability of meeting required handover conditions is 99%,and 96.8% cases are at easy level under the given Monte Carlo simulation conditions,which shows obvious advantages over the control midcourse guidance laws.(5)Aiming at the problem of interceptor’s midcourse guidance,on condition that target’s acceleration changes over time,this paper proposed an attack hypothesis analyzed trajectory shaping guidance with model predictive static programming algorithm.Line-of-sight model concerning missile-target-defender relationship is established under the hypersonic attack hypothesis.Midcourse guidance with terminal line-of-sight constraint is derived by means of model predictive static programming algorithm.In the model prediction stage,the extrapolation of target’s trajectory is brought in,thus the quality of guidance can be improved by making corrections according to target’s maneuver in advance.In the static programming stage,the time-to-go weighted performance function is adopted again to converge terminal guidance command.Simulation results show that,the MPSP-TWTSG method can effectively meet the final requirements of capture range,encounter angle,zero angular rate of line-of-sight and command convergence.In particular,this proposed method can intercept targets from different attacking routes,and will respond accordingly once the target changed attacking route,so as to cope with the maneuverability of hypersonic weapon.Applying the MPSP-TWTSG method,the probability of meeting required handover conditions is nearly 100%,and 83% cases are at easy level under the given Monte Carlo simulation conditions,which shows obvious advantages over the control midcourse guidance laws.Focusing on the defense task of hypersonic weapons,this paper completes the analysis of system composition and operation rules for the air-based interception scheme.Most importantly,problems including acquisition and prediction of target information,tracking guidance of ascent trajectory and design of relay guidance are researched within the interceptor’s midcourse phase,therefore provides a useful reference for the development of related scientific research projects in the future.