Non-oscillatory Hermite-Simpson convex method for solving nonsmooth optimal control problems

This paper presents a non-oscillatory Hermite-Simpson convex framework for solving nonsmooth convex optimal control problems. A separated Hermite-Simpson transcription is formulated to provide a fourth-order discretization for convex optimal control, resulting in a sparse formulation well suited for second-order cone programming. To preserve the accuracy and polynomial consistency of the Hermite-Simpson scheme, piecewise quadratic control reconstruction is employed, and a specially designed midpoint-control constraint is incorporated to suppress interpolation-induced oscillations. The proposed method is evaluated on two representative trajectory optimization problems: Mars powered descent and landing and fuel-optimal low-thrust transfer. Numerical simulations demonstrate that the proposed method effectively suppresses interpolation-induced control oscillations, ensures consistency between discrete and propagated trajectories, and achieves high computational efficiency. Comparative studies show superior propagation accuracy, competitive computational efficiency, and robust numerical performance. The low-thrust transfer example additionally confirms the method’s applicability to challenging long-duration trajectory optimization problems with nonsmooth control profiles.