Reduced-Order Desensitized Optimal Control for Mars Entry Trajectory Optimization

The entry terminal point control (ETPC) algorithm generates the guidance command based on the reference trajectory while it may lead to control saturation because large control corrections are needed to offset the large state error caused by uncertainties. To address this issue, a reduced-order desensitized optimal control (DOC) method is proposed to reduce the sensitivity of the reference trajectory to uncertainties and, thus, improve the accuracy of the ETPC algorithm. First, the existing sensitivity theories are analyzed to demonstrate that the adjoint system in the ETPC is a reduced form of the sensitivity matrix in the DOC, which can capture sensitivity information of the longitudinal range. Next, the adjoint system is used to replace the sensitivity matrix, and the reduced-order DOC method is proposed. Finally, the adaptive pseudospectral method is employed to solve the reduced-order DOC problem, and the resulting desensitized optimal trajectory is used for Mars entry guidance. The numerical simulations demonstrate that the algorithm with a reduced order has higher computational efficiency compared to classical DOC and is superior to the linear quadratic regulator tracking guidance law in terms of guidance accuracy.