Mathematical problems in the analysis and control of spatial non-keplerian orbits

Currently, the research on analysis and optimal control of spatial non-Keplerian orbits becomes a very active topic. Through such research, we can analyze and realize free transitions of satellites among non-Keplerian orbits, arriving at expectation goals such as detective, anti-detective, interception, connection and so on. Since behaviors exhibited by spatial non-Keplerian orbits, in the viewpoint of Mathematics, have dynamical properties, based on our previous research results, we, therefore, in this paper provided a general mathematical model (that is, a dynamical-like system with parameters and constraints, i.e., a hybrid system) for studying them. Based on this mathematical model, we further disclosed that detective, anti-detective, parametric adjustment and delay control actually correspond to four key mathematical problems in the research area on hybrid systems: stability analysis, safety verification, bifurcation and robust control, respectively. Based on this finding, we also proposed some primitive ideas for studying these problems.