Optimal midcourse trajectory cluster generation and trajectory modification for hypersonic interceptions

The hypersonic interception in near space is a great challenge because of the target's unpredictable trajectory, which demands the interceptors of trajectory cluster coverage of the predicted area and optimal trajectory modification capability aiming at the consistently updating predicted impact point (PIP) in the mid-course phase. A novel midcourse optimal trajectory cluster generation and trajectory modification algorithm is proposed based on the neighboring optimal control theory. Firstly, the midcourse trajectory optimization problem is introduced; the necessary conditions for the optimal control and the transversality constraints are given. Secondly, with the description of the neighboring optimal trajectory existence theory (NOTET), the neighboring optimal control (NOC) algorithm is derived by taking the second order partial derivations with the necessary conditions and transversality conditions. The revised terminal constraints are reversely integrated to the initial time and the perturbations of the co-states are further expressed with the states deviations and terminal constraints modifications. Thirdly, the simulations of two different scenarios are carried out and the results prove the effectiveness and optimality of the proposed method.