Penetration Game Strategy For Hypersonic Vehicles

The development of hypersonic vehicles has enriched the content of attack and defense countermeasure in near space dramatically,and in near future,they will be developed into a sort of tactical weapons but be capable of attacking strategic targets,which further stimulates the revolution of air defense anti-missile systems.Therefore,the hypersonic vehicles will be confronted with rigorous interception threat.Different from the penetration of traditional weapons,that of hypersonic vehicles possesses its distinctive properties,including expansive maneuver scope,weak transient maneuverability and adaptive penetration according to information support.And besides,hypersonic vehicles are constantly encountered with a series of difficulties and problems,such as high detectability and trackability,limited maximum transient maneuverability,coping with air defense anti-missile system and attacking targets simutaneously.Consequently,they should resort to game theory to conduct penetration guidance,which requires the vehicles to analyze attack and defense countermeasure and to predict its final results in real-time and on the basis of its own penetration capacity and defender’s interception capacity(kinetics properties,dynamics properties,maneuverability etc.),and then to conduct penetration maneuver with optimal strategy(minimum efforts and so forth).With regarding to the attack and defense countermeasure and penetration problem a hypersonic vehicle encounters in the whole flight duration,the following research was conducted in this article:(1)In the midcourse flight duration,the hypersonic vehicle makes full use of its expansive maneuver scope to conduct game penetration.In detail,it includes:Firstly,a game strategy is proposed,which makes a feint to somewhere and attack in another place to hide the relation between current flight heading and final targets.Then,combined with Model Predictive Static Programming algorithm,the game penetration trajectory is generated.For the final target with 10000 km distance,the vehicle’s lateral maneuver can lead to 1400 km lateral distance with its turning load factor less than 0.2,with limited maximum load factor 2.0,which exceeds the moving distance of the defense system with its velocity of 300km/h and thus the tactical trick is implemented.Next,against to the moving air defense anti-missile systems with known motion information,a dynamic avoidance algorithm by the combination of slack variables with Sliding Mode Control(SMC)is proposed to carry out safe avoidance.The algorithm allows the vehicle to maintain the course shortcut more than 200 km with load factor less than 2.0,and it can be implemented online and in real-time.Eventually,as for the demerit of dynamic avoidance algorithm that it does not possess optimality,the dynamic avoidance trajectory is further optimized by Differential Dynamic Programming.The energy consumption is decreased significantly under the premise in safe avoidance.The variation of turning load factor is smoothed and the maximum load factor is less than 1.0.(2)When the hypersonic vehicle fly into the threat area of air defense anti-missile system with unknown motion information,in the midcourse interception of the interceptor,to break out the interceptor’s condition of the shifting of duty between midcourse and terminal interception,the hypersonic vehicle conducts game penetration by its velocity advantage and maneuverability.And in the terminal interception of the interceptor,the hypersonic vehicle conducts game penetration to produce the miss distance as large as possible,relying on its initiative maneuver and the interceptor’s dynamics lag.In detail,it includes:In the midcourse interception of the interceptor,a trajectory programming method is utilized to breaking out the near head-on engagement scenario.And an Optimized Model Predictive Static Programming(OMPSP)is proposed to handle with this complicated trajectory programming problems.It facilitates the algorithm’s convergence properties and enhances its robustness by adaptively adjusting the relevant weight matrices.Consequently,the hypersonic vehicle is able to construct the engagement scenario with a heading error more than 20 degree,which succeeds in breaking out the near head-on engagement scenario.In addition,on the basis of proper hypothesis on bilateral capacity,penetration area without maneuver,game penetration area and invalid penetration area of the vehicle are expressed by warning distance and course shortcut.For the vehicle with 80 km warning distance,if the course shortcut is larger than 19 km,the vehicle can penetrate successfully without any maneuver and if the course shortcut lies between 8km and 19 km,the vehicle is capable of penetrating by game maneuver,or it will be pretty difficult for the vehicle to penetrate successfully.When the warning distance is less than 67 km,whether the vehicle can succeed in penetrating mainly depends on the course shortcut and the interceptor’s capacity.In the terminal interception of the interceptor,to produce the miss distance as large as possible with minimum efforts,the Differential Game/One-Sided Optimal Penetration Guidance Strategies are derived according to Differential Game Theory and Optimal Control Theory respectively.On the basis of proper hypothesis and by mathematical simulation,the average miss distance increases with the manverability ratio of the vehicle relative to interceptor and there is an approximate exponential relation.The miss distance decreases significantly when the vehicle’s maximum rate of the velocity deflection angle is less than 45 degree per second.When both of the vehicle and interceptor utilize differential game(DG)strategy,the ratio is required to be larger than 0.39 to implement successful penetration(with miss distance larger than 5m).When the interceptor employs augmented proportional navigation(APN)guidance with N ? as the navigation gain,the ratio is required to be larger than 0.36 for the vehicle with one-sided optimal(OSO)penetration guidance and the switch times for control command is N?-1,while the ratio is required to be larger than 0.63 for the vehicle with DG penetration strategy.With regarding to the same interceptor with APN guidance,the DG penetration strategy is superior than OSO penetration strategy if the ratio is larger than 0.66,or the OSO penetration strategy is more effective.DG penetration strategy relies more on the vehicle’s maneuverability,while OSO penetration strategy pays more attention to the selection of maneuvering time points.In addition,when the variations of the model’s parameters caused by internal disturbance and uncertainties are within 20 percents,the average miss distances of OSO and DG penetration strategy nearly maintain invariant.(3)When the hypersonic vehicle approaches final attacking target,it breaks away from the angle of attack constraint arising from its engine’s normal function and consequently,its maneuverability enhances dramatically to the similar level of the interceptor.Then,the vehicle takes advantage of this capacity and the interceptor’s dynamics lag to conduct game penetration,and a relative high maneuver is executed to lead to the interceptor’s saturation of load factor as early as possible.In horizontal plane,an optimal guidance law is derived,which enables the vehicle to evade the interceptor with specific miss distance.And in vertical plane,a combined guidance technique between tracking programmed trajectory and proportional navigation with terminal angle constraint is put forward to compromise the velocity loss,attacking precision and terminal constraints.On the basis of proper hypothesis and by mathematical simulation in three dimensions,the window of the distance to target for the vehicle to penetrate from interceptor and then to attack the final target precisely is [62.79,68.33](km).The window’s far edge increases with the hypersonic vehicle’s velocity and maximum load factor and its near edge decreases with the interceptor’s velocity and maximum load factor.The optimal time point for descending is when the distance to target is 68.33 km.Under this circumstance,on the basis of precise engagement,the vehicle executes an evasive maneuver with an angle of attack of 13 degree and then a miss distance more than 10 m is obtained.Eventually,at the final attacking time point,the vehicle’s velocity is larger than 2Ma,with an falling angle near-70 degree.Last but not least,when the variations of the model’s parameters caused by internal disturbance and uncertainties are within 20 percents,the penetration and attack performance of the terminal game penetration guidance strategy keeps pretty robust.