Structural Controllability-Based Control-Oriented Modeling of Relative Orbits Considering Continuous Controllability

In space systems, controlled dynamics are often modeled using linear time-varying (LTV) models due to the periodic orbital motion of spacecraft. When designing such models, it is advantageous to construct computationally feasible representations that exhibit clear controllability properties. Network modeling approaches are particularly effective in this context. This paper addresses the need for efficient rendezvous techniques in emerging orbital services, such as active debris removal and cargo delivery. To improve sustainability and extend satellite lifespans, a continuous-time feedback control framework is proposed for autonomous rendezvous operations, utilizing low-thrust propulsion based on relative orbit elements. Controllability is enhanced by deriving a periodic LTV model that incorporates J2 perturbations. Additionally, structural controllability is employed as a key design principle in the development of a control-oriented surrogate model that ensures persistent controllability throughout an entire orbital revolution while simultaneously minimizing modeling error. The proposed framework constructs a surrogate model that preserves the essential orbital dynamics while enforcing continuous controllability. The effectiveness of the framework is validated through numerical examples.