Optimal Guidance Law For Ballistic Missile Midcourse Anti-Penetration

With the continuous development of missile technology,the penetration capability of ICBM is also increasing.In the face of more and more advanced ballistic missiles,the future battlefield environment has become more and more complicated.The traditional single interceptor has been unable to meet the requirements of intercepting incoming missiles.To enhance the ability of defense against the enemy and improve the success rate of missile interception,using multiple interceptors to intercept the target has gradually attracted the attention of the military field at home and abroad.This dissertation takes interceptors intercepting incoming missiles in the middle of the atmosphere as the research background and studies the cooperative guidance strategy of multiple interceptors.By using the method of predicting hit points,multiple interceptors can hit the incoming missiles in the middle of the atmosphere at the same time,while meeting certain attack angle constraints.This paper mainly carries out the following research work:Firstly,this paper briefly introduces the research background and research status,establishes the coordinate system,and defines the transformation relationship.The kinematics and dynamics model of the mass center of the target and the interceptor,the relative motion model of the missile and the target,and the maneuvering model of the target are established to lay the foundation for the follow-up study of the guidance law.Secondly,the non-maneuvering target is studied in this paper.According to the characteristics of the midcourse trajectory of a non-maneuvering target,a method of non-maneuvering hit point prediction is proposed.The trajectory of the interceptor is simplified as a straight trajectory,and the dichotomy method is used to calculate the predicted life point,which can accurately predict the future position of the non-maneuvering target.Because it takes a long time to make a prediction,the step prediction method is used to meet the real-time requirements.However,the method of non-maneuvering hit point prediction is not effective for maneuvering target prediction.This paper proposes a linear prediction method and maneuvering identification prediction method.A linear prediction has the advantages of fast calculation speed and high accuracy in the case of a small period.The maneuver identification and prediction method collects the motion information of the target through the state observer and then fits these data to identify the maneuvering mode of the target.This method can predict a more accurate life point at an earlier time point.The combination of the three prediction methods predicts the life point faster and more accurately.Then,to achieve the requirements of both time constraint and angle constraint,this paper studies them respectively.Firstly,the structure of "leader-follower" is adopted.The leader uses proportional guidance to attack the target.At the same time,the remaining flight time of the leader is estimated.The follower adjusts its flight trajectory to meet the requirement of hitting the target at the same time as the leader.However,the structure has a high limit on the initial position of the leader and follower.In addition,in the case of attacking the maneuvering target,it is easy to lead to the situation that the trajectory of the follower cannot be adjusted.Therefore,this paper cancels the structure of "leader-follower" and uses the method of preset attack time to constrain the interceptor,so that three interceptors can hit the target at the same time.For the limitation of attack angle,based on the optimal control theory,the control condition is obtained by Pontryagin’s maximum law,which has a good effect on the constraint of attack angle.Finally,the combination of time constraint and angle constraint can control the attack time and attack angle of interceptors at the same time.The simulation program is written to simulate the target under different maneuvering modes with three interceptors.The simulation results show that the time angle cooperative guidance law has a good interception effect for different maneuvering models,and the attack time and attack angle can meet the preset requirements.