Optimal-control-based cooperative evasion and pursuit strategies are derived for an aircraft and its defending missile. The aircraft-defending missile team cooperates in actively protecting the aircraft from a homing missile. The cooperative strategies are derived assuming that the incoming homing missile is using a known linear guidance law. Linearized kinematics, arbitrary-order linear adversaries' dynamics, and perfect information are also assumed. Specific limiting cases are analyzed in which the attacking missile uses proportional navigation, augmented proportional navigation, or optimal guidance. The optimal one-on-one, noncooperative, aircraft evasion strategies from a missile using such guidance laws are also derived. For adversaries with first-order dynamics it is shown that depending on the initial conditions, and in contrast to the optimal one-on-one evasion strategy, the optimal cooperative target maneuver is either constant or arbitrary. These types of maneuvers are also the optimal ones for the defender missile. Simulation results confirm the usefulness and advantages of cooperation. Specifically, it is shown how the target can lure in the attacker, allowing its defender to intercept the attacking missile even in scenarios in which the defender's maneuverability is at a disadvantage compared with the attacking missile.

Optimal Cooperative Pursuit and Evasion Strategies Against a Homing Missile

Cooperative pursuit―evasion strategies are derived for a team composed of two agents. The specific problem of interest is that of protecting a target aircraft from a homing missile. The target aircraft performs evasive maneuvers and launches a defending missile to intercept the homing missile. The problem is analyzed using a linear quadratic differential game formulation for arbitrary-order linear players' dynamics in the continuous and discrete domains. Perfect information is assumed. The analytic continuous and numeric discrete solutions are presented for zero-lag adversaries' dynamics. The solution of the game provides 1) the optimal cooperative evasion strategy for the target aircraft, 2) the optimal cooperative pursuit strategy for the defending missile, and 3) the optimal strategy of the homing missile for pursuing the target aircraft and for evading the defender missile. The obtained guidance laws are dependent on the zero-effort miss distances of two pursuer―evader pairs: homing missile with target aircraft and defender missile with homing missile. Conditions for the existence of a saddle-point solution are derived and the navigation gains are analyzed for various limiting cases. Nonlinear two-dimensional simulation results are used to validate the theoretical analysis. The advantages of cooperation are shown. Compared with a conventional one-on-one guidance law, cooperation significantly reduces the maneuverability requirements from the defending missile.

Cooperative Differential Games Strategies for Active Aircraft Protection from a Homing Missile

A cooperative guidance law, for a defender missile protecting an aerial target from an incoming homing missile, is presented. The filter used is a nonlinear adaptation of a multiple model adaptive estimator, in which each model represents a possible guidance law and guidance parameters of the incoming homing missile. Fusion of measurements from both the defender missile and protected aircraft is performed. A matched defender’s missile guidance law is optimized to the identified homing missile guidance law. It utilizes cooperation between the aerial target and the defender missile. The cooperation stems from the fact that the defender knows the future evasive maneuvers to be performed by the protected target and thus can anticipate the maneuvers it will induce on the incoming homing missile. Moreover, the target performs a maneuver that minimizes the control effort requirements from the defender. The estimator and guidance law are combined in a multiple model adaptive control configuration. Simulation results show that combining the estimations with the proposed optimal guidance law, that utilizes cooperation between the defending missile and protected target, yields hit-to-kill closed loop performance with very low control effort. This facilitates the use of relatively small defending missiles to protect aircrafts from homing missiles.

Cooperative Multiple-Model Adaptive Guidance for an Aircraft Defending Missile

Aircraft protection from a missile employing a known linear guidance strategy is considered The aircraft protects itself by using a cooperating defensive missile Depending on the available cooperation scheme, three different cooperative linear quadratic guidance strategies are derived and investigated for arbitrary-order linear-adversaries dynamics: 1) two-way cooperation, where the target–defender team employs its optimal cooperative strategy, 2) one-way cooperation, realized by the defender employing a classical one-on-one guidance law while the target helps by luring in the missile, and 3) one-way cooperation, realized by the target employing an arbitrary evasive strategy while the defender attempts to reach the predicted interception point The performance of the three different cooperative strategies is compared and analyzed via simulation using the notion of Pareto fronts It is shown that the performance of the target and the defender is highly dependent on the cooperation scheme As expected, th

Linear Quadratic Optimal Cooperative Strategies for Active Aircraft Protection

A novel efe cient algorithm, featuring a highly reduced computational load, is presented for multiple model adaptive estimation in a future real-life ballistic missile defense scenario, where the blind incoming target (having no information on the interceptor’ s state ) performs a bang ‐bang evasive maneuver characterized by a random switching time. The efe ciency of the algorithm derives mainly from its exploitation of the special structure of the hypothesis space in this problem to drastically reduce the number of concurrently active e lters in the bank without incurring any signie cant performance degradation. The proposed algorithm’ s efe ciency allows a substantial increase in the resolution of the discretized hypothesis space, thus enhancing considerably the attainable estimation performance. The effect of the new estimator’ s performance on guidance accuracy is examined. The homing performance of various perfect information guidance laws using this efe cient estimation method is compared, via Monte Carlo simulations, to the use of a Kalman e lter incorporating a shaping e lter representing the random target maneuver. The results demonstrate the superiority and viability of the proposed method.

Efficient Multiple Model Adaptive Estimation in Ballistic Missile Interception Scenarios

The effects of non-linear kinematics on optimal evasive strategies from a pursuer guided by proportional navigation are investigated in a plane. Non-linear analysis is mandatory since, for certain values of system parameters and initial conditions, linearized kinematic models are not valid. The investigation discloses two principles of optimal evasion. For long pursuit time, both principles are satisfied and the relatively large miss distance is almost independent of the initial conditions. Short pursuit time does not allow simultaneous satisfaction of both principles, and the two-dimensional optimal compromise results in a reduced miss distance. The inability to satisfy both principles suggests a three-dimensional manoeuvre perpendicular to the initial collision plane.

I. Forte

Papers

The effects of non‐linear kinematics in optimal evasion