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 midcourse 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.

Neighboring optimal guidance using higher-order dynamics approximation with application to orbital injection problem

Neighboring optimal guidance,a method to obtain a suboptimal guidance law by approximately solving the first-order necessary conditions based on a nominal trajectory,is widely used in the aerospace field due to its high computational efficiency and low resource usage.For more advanced scenarios,the existing methods still have a problem that the guidance accuracy and optimality will seriously degrade when the actual state largely deviates from the nominal trajectory.This is mainly caused by the approximate description of the first-order conditions in terms of total flight time and nonlinear constraints.To address this problem,a higher-order neighboring optimal guidance method is proposed.First,a novel total flight time updating strategy,together with a normalized time scale,is presented that transforms the optimal problem with free total flight time into a more tractable optimal problem with fixed total flight time.Then,using the vector partial derivative method,a higher-order approximation is adopted,instead of the first-order approximation,to accurately describe the nonlinear dynamical and terminal constraints,thus obtaining a polynomially constrained quadratic optimal problem.Finally,to numerically solve the polynomially constrained quadratic optimal problem,a Newton-type iterative algorithm based on the orthogonal decomposition is designed.Through the iterative solution within each guidance period,the corrections to control quantities and total flight time are generated.The proposed method is applied to a launch vehicle orbital injection problem,and simulation results show that it achieves high accuracy of orbital injection and optimality of performance index.