Robust Variable-Horizon MPC with Adaptive Terminal Constraints

TL;DR

This paper introduces a robust variable-horizon MPC with an adaptive terminal constraint mechanism, ensuring finite-time convergence and reduced conservatism in target interception tasks for linear systems with disturbances.

Contribution

It proposes a novel adaptive terminal constraint selection method within a tube-based MPC framework, enhancing feasibility and performance over fixed-set approaches.

Findings

Finite-time convergence proven.

Significant reduction in conservatism demonstrated.

Effective in satellite orbital rendezvous simulation.

Abstract

This paper presents a novel robust variable-horizon model predictive control scheme designed to intercept a target moving along a known trajectory, in finite time. Linear discrete-time systems affected by bounded process disturbances are considered and a tube-based MPC approach is adopted. The main contribution is an adaptive mechanism for choosing the terminal constraint set sequence in the MPC optimization problem. This mechanism is designed to ensure recursive feasibility while promoting minimization of the final distance to the target. Finite-time convergence of the proposed control scheme is proven. In order to evaluate its effectiveness, the designed control law is tested through numerical simulations, including a case study involving orbital rendezvous of a satellite with a tumbling object. The results indicate a significant reduction in conservatism compared to existing state-of-the-art methods using a fixed terminal set sequence.