Abstract: In this study, we present an optimal cooperative guidance law for a defending missile in an active defense scenario in which an aerial target launches a defending missile to hit a homing missile. First, we assume that the target employs a Bang-Bang maneuver and the defending missile knows the target's state and maneuver strategy. Next, considering that the homing missile's guidance strategy is unknown and the measurement information has noise, we use the unscented Kalman-based multiple-model adaptive estimator to estimate the homing missile's state. Then, we propose an adaptive optimal cooperative guidance law based on optimal control for the defending missile. Since the switch time of the target's Bang-Bang maneuver has great influence on the control energy of the defending missile, we use a genetic algorithm to optimize the switch time. Simulation results indicate that our adaptive multiple-model estimator can quickly and accurately estimate the homing missile's guidance law, navigation parameters, distance, line-of-sight angle, acceleration, flight-path angle, and speed. Compared with the failure of interception when a defending missile uses the proportional navigation (PN) guidance law, its use of the proposed optimal cooperative guidance law enables it to hit the homing missile accurately with 7 g maximum acceleration load. After optimizing the switch time of the target's Bang-Bang maneuver, the proposed guidance law can ensure the successful attack of the homing missile with a 3 g maximum acceleration load.