Robust Macroscopic Density Control of Microsatellite Swarm Via Local Measurement

The macrohigh-level control problem of microsatellite swarm subject to safety constraints is studied in this article. The macroscopic motion dynamics of this swarm is described by the probability transition of the Markov chain with its state described by probability density distribution. Based on this model, a macroequilibrium density controller is first presented. Unlike the conventional global measurement-based control methods, this controller is implemented by using local measurement, which is provided by a decentralized counting method. The computation and the communication burden can be decreased significantly. Then, a fast temporary transition control effort is designed and added to the macroequilibrium density controller to synthesize a robust and fast macrodensity controller. It is proved that the swarm's state can asymptotically and fast converge to the desired density distribution. The key features of this robust controller are that it cannot only balance the swarm transition cost and the transition rate despite multiple constraints, but also has great robustness to initial states. The swarm control can be achieved with fast convergence rate even for the case that the microsatellites are extensively crowded at the initial. The effectiveness of this control scheme is finally verified by numerical simulation.