Pareto-optimal control of relative motion in the orbital maneuvering problem of spacecraft with finite thrust

To solve the time-free rendezvous problem of two spacecraft, the multi-criteria optimization of the relative motion trajectory of the linear motion model in an orbiting cylindrical reference frame is studied. The equations for describing the secular and periodic parameters of the relative motion are obtained. The structure of the nominal control program for the longitudinal motion control variant with finite transversal thrust is investigated in some detail, and its analytical solutions are obtained. An algorithm for solving the Pareto-optimal control program for arbitrary boundary conditions and thrust control acceleration values in the standard time including maneuver time and total time is developed. The algorithm uses the Pareto optimal method to achieve two kinds of multi-objective optimization (total time optimization and fuel optimization). The numerical calculation results on the geostationary planar orbit parameter correction variants are given.