I. Introduction
The Low-Earth-Orbit (LEO) mega-constellation networks, with more than 10 times the number of satellites in orbit today, have been widely studied in recent years [1]. Compared with traditional constellations such as the Iridium system, the LEO mega-constellation networks are believed to be indispensable infrastructures for the six-generation (6G) and satellite based Internet of Things architecture in the foreseeable future [2], [3]. However, the limited number of complete discharge and charge battery cycles of the on-orbit satellites challenges the mega-constellation design, for example, it will be a massive device update cost for Starlink with eventually more than 40,000 nodes. Besides, complex link switches and fluctuating loads further complicate the topology control. Hence, realizing energy-efficient topology control with good adaptation to the varying load is a critical but difficult problem [4], [5].