H-infinity Controller Design for Spacecraft Terminal Rendezvous on Elliptic Orbits using Differential Game Theory

The paper presents a H-infinity guidance law for spacecraft low-thrust terminal rendezvous on elliptic orbits. The dynamics of the rendezvous on elliptic orbits are governed by a set of linear time-varying equations, in literature known as linear equations of relative motion. Standard H-infinity controller design technique for linear systems cannot be adopted, since the system is time-varying. Therefore, the problem is formulated as a zero-sum two-person differential game following the minimax H-infinity design technique developed by Başar and Bernhard. The main result is a closed-form solution of the terminal rendezvous on elliptic orbits H-infinity control problem. In addition, we prove that the H-infinity norm of the closed-loop system is bounded.