Leader-Follower Formation Control of a Large-Scale Swarm of Satellite System using the State-Dependent Riccati Equation: Orbit-to-Orbit and in-Same-Orbit Regulation

The state-dependent Riccati equation (SDRE) is a nonlinear optimal controller with a flexible structure which is one of the main advantages of this method. Here in this work, this flexibility is used to present a novel design for handling a soft constraint for state variables (trajectories). The concept is applied to a large-scale swarm control system, with more than 1000 agents. The control of the swarm satellite system is devoted to two modes of orbit-to-orbit and in-same-orbit cases. Keeping the satellites in one orbit in regulation (point-to-point motion) requires additional constraints while they are moving in Cartesian coordinates. For a small number of agents trajectory design could be done for each satellite individually, though, for a swarm with many agents, that is not practical. The constraint has been incorporated into the cost function of optimal control and resulted in a modified SDRE control law. The proposed method successfully controlled a swarm case of 1024 agents in leader-follower mode for orbit-to-orbit and in-same-orbit simulations. The soft constraint presented a percentage of 0.05 in the error of the satellites with respect to travel distance, in in-same-orbit regulation. The presented approach is systematic and could be performed for larger swarm systems with different agents and dynamics.