Robust model predictive control using tubes

Tube-based distributed control of linear constrained systems

“…Our method hinges on the availability of a decentralized stabilizing regulator for the unconstrained system and provides a two-layer controller for each subsystem. Upper controllers receive planned state trajectories from neighboring subsystems and exploit the notion of tubes [12] for achieving robustness of stability with respect to coupling. Lower controllers generate planned trajectories using Model Predictive Control (MPC) independently of the other subsystems.…”

“…We first propose a standard procedure for turning a state-feedback stabilizing decentralized controller (that can be computed using the procedures reviewed in [13] and [23]) into a stabilizing distributed controller. Our method is based on the notion of tubes proposed in [12] for developing computationally affordable, robust MPC schemes and used in [21,7,6] for designing DMPC regulators. Here we extend the approach of [7,6] in order to propose local controllers that have a hierarchical structure.…”

A Simple Tube Controller for Efficient Robust Model Predictive Control of Constrained Linear Discrete Time Systems Subject to Bounded Disturbances

“…A set of necessary ingredients ensuring robust exponential stability has been identified. The proposed scheme is computationally simpler than the schemes proposed in (Löfberg, 2003;van Hessem and Bosgra, 2003;Kerrigan and Alamo, 2004;Langson et al, 2004) and it has an advantage over schemes proposed in (Kouvaritakis et al, 2000;Chisci et al, 2001;Mayne and Langson, 2001;Smith, 2004;Mayne et al, 2005) because the feedback component of control policy, which is piecewise affine, results in a smaller tube cross-section.…”

“…Tubes have been extensively studied, see for instance (Quincampoix and Veliov, 2002;Calafiore and El Ghaoui, 2004;Kurzhanski, 2004) and references therein. Application of tubes to robust model predictive control has been reported in (Langson et al, 2004;Mayne et al, 2005;Raković and Mayne, 2004).…”

Stock management in hospital pharmacy using chance-constrained model predictive control

“…Furthermore, since CC-MPC takes into account the expected performance of the closed loop with probabilistic constraints instead of directly trying to assure robust constraint satisfaction, it avoids the conservatism present in other robust MPC techniques, e.g. : [21,22].…”