Time-Optimal Model Predictive Control for Linear Systems with Multiplicative Uncertainties
This work addresses control challenges for systems with uncertainties, such as in aerospace applications, but it is incremental as it builds on existing MPC and zonotope methods.
The paper tackles the problem of time-optimal control for linear systems with multiplicative uncertainties by developing a Model Predictive Control scheme that uses matrix-zonotope approximations to handle uncertainty propagation, and it demonstrates effectiveness in a satellite orbital rendezvous case study.
This paper presents a time-optimal Model Predictive Control (MPC) scheme for linear discrete-time systems subject to multiplicative uncertainties represented by interval matrices. To render the uncertainty propagation computationally tractable, the set-valued error system dynamics are approximated using a matrix-zonotope-based bounding operator. Recursive feasibility and finite-time convergence are ensured through an adaptive terminal constraint mechanism. A key advantage of the proposed approach is that all the necessary bounding sets can be computed offline, substantially reducing the online computational burden. The effectiveness of the method is illustrated via a numerical case study on an orbital rendezvous maneuver between two satellites.