MODEL PREDICTIVE STATIC PROGRAMMING FOR BANG-OFF-BANG LOW-THRUST NEIGHBORING CONTROL LAW DESIGN

摘要

Model Predictive Static Programming (MPSP) was used under the assumption of continuous control, which impedes it for applications with bang-off-bang control. In this paper, MPSP is employed for the first time as a guidance scheme for low-thrust transfers with bang-off-bang control where the fuel-optimal reference trajectory is used as initial guess solution. In our method, dynamical equations in Cartesian coordinates are augmented by the mass costate equation, while the unconstrained velocity costate vector is used as control variable, and is expressed as a combination of Fourier basis functionss with corresponding weights. A two-loop MPSP algorithm is designed where the weights are updated in the inner loop and continuation is conducted on the outer loop in case of large perturbations. The sensitivity matrix (SM) is recursively calculated using analytical derivatives and SM at switching points is compensated. An sample interplanetary CubeSat mission to an asteroid is used as study case to illustrate the effectiveness of the method developed.