Uncertain parameters analysis of powered-descent guidance based on Chebyshev interval method

This paper focuses on the powered-descent guidance (PDG) problem involving uncertain-but-bounded parameters. An efficient numerical algorithm based on the high approximation accuracy of the Chebyshev series expansion is presented to solve the nonlinear optimal control problem with interval uncertain parameters. First, an infinite number of uncertain optimal control problems is translated into a series of deterministic optimal control problems by exploiting the Chebyshev interval inclusion. Subsequently, the deterministic optimal control problem is solved by a convex optimization method based on the lossless convexification of the PDG problem. Afterwards, these techniques are used to generate the enclosure of the PDG trajectory with uncertainty and the upper and lower bounds of the minimum fuel consumption during the pinpoint landing mission. Finally, the effectiveness and superiority of the proposed approach are validated by illustrative numerical simulations.