Rendezvous and Proximity Operations with Ellipsoidal and Zonotopic Set-Membership Filtering in MPC

This paper introduces a model predictive control (MPC) strategy incorporating state estimates derived from set-membership filtering, tailored for time-varying discrete systems experiencing bounded process and measurement disturbances. We employ an ellipsoidal set description, founded on a dual-phase prediction and measurement update mechanism. At each time step, we construct ellipsoids through the resolution of a semi-definite program to encapsulate the system's true state. In a related development, we develop a zonotope set-membership filter for these time-varying systems, where the zonotope's dimensions are minimized via segment minimizations. These estimated sets are then utilized in an MPC scheme, where the control input sequence is optimized by minimizing a defined cost function. The efficacy of our approach is validated through a rendezvous and proximity operation simulation, where a chaser spacecraft is guided toward a target. Comparative analysis with the traditional Kalman filter is presented, demonstrating the advantages and effectiveness of our proposed method.