Design of Tracking Guidance Law Based on Neighboring Optimal Control

To improve the midcourse guidance process of the interception against hypersonic targets in near space, a novel trajectory tracking guidance law based on neighboring optimal control (NOC) was designed. Firstly, the nominal trajectory satisfying terminal and path constraints were generated by Gauss pseudospectral method. Secondly, in order to track nominal trajectory accurately, the first order necessary conditions were further differentiated to second order to obtain the second-order optimal updating trajectory in the neighborhood of nominal trajectory. Finally, based on indirect Gauss pseudospectral method, the transformed two-point boundary value problem was discretized to algebraic equation for matrix inverse operation at Legendre-Gauss (LG) point and then feedback control law was obtained using nominal trajectory. Simulation results show that this method can eliminate tracking error effectively and satisfy the requirements of on-line implementation.