Online optimal midcourse trajectory modification algorithm for hypersonic vehicle interceptions

This paper presents an online optimal midcourse trajectory modification algorithm for the hypersonic interceptions based on the neighboring optimal control theory, which takes the current states deviations and the revised terminal constraints as inputs and generates the optimal control modifications. Firstly, the midcourse guidance for hypersonic interception is introduced as an optimal control problem, which is solved with the well-developed Gauss Pseudospectral Method (GPM) to generate a nominal trajectory that satisfies the first order optimality conditions. Secondly, the Neighboring Optimal Trajectory Existence Theory (NOTET) is given and the first order optimality equations are further differentiated to second order to acquire the control modifications. The perturbations of the terminal co-states are expressed with the current states perturbations and the revised terminal constraints by solving the second order equations and inversely integrating the perturbation dynamic equations. The optimality of the proposed algorithm is proved. Finally, five different interception scenarios are simulated and comparisons are made with particle swarm optimization (PSO) method and GPM. Simulation results reveal that the proposed method has the merits of high precision equivalent with GPM and better computing efficiency than PSO and GPM, which testifies the effectiveness and online application feasibility.