Nested distributed MPC

Abstract

Abstract:We propose a distributed model predictive control approach for linear time-invariant systems coupled via dynamics. The proposed approach uses the tube MPC concept for robustness to handle the disturbances induced by mutual interactions between subsystems; however, the main novelty here is to replace the conventional linear disturbance rejection controller with a second MPC controller, as is done in tube-based nonlinear MPC. In the distributed setting, this has the advantages that the disturbance rejection controller is able to consider the plans of neighbours, and the reliance on explicit robust invariant sets is removed.

Coalitional predictive control: Consensus-based coalition forming with robust regulation

“…As explained in the Introduction, however, the features of the coalitional control problem render these approaches impractical. To address this challenge, we adopt therefore the "nested" robust approach initially developed in (Baldivieso Monasterios et al, 2017). This approach replaces the ancillary robust control law-which usually requires knowledge of R c -with a secondary MPC controller.…”

“…• In Section 3, we present a distributed scheme for timeinvariant coalitions of subsystems with guarantees of robust recursive feasibility and stability, despite the apriori unknown disturbances arising from interactions, yet minimal reliance on invariant sets. The proposed scheme, first developed in (Baldivieso Monasterios et al, 2017), employs two MPC controllers for each subsystem. Crucially, the design and formulation of the MPC problems, and the invariance-inducing control law, does not require the explicit characterization of a robust invariant set, but relies only implicitly on the existence of one.…”

Coalitional predictive control: consensus-based coalition forming with robust regulation

“…As explained in the Introduction, however, the features of the coalitional control problem render these approaches impractical. To address this challenge, we adopt therefore the "nested" robust approach initially developed in (Baldivieso Monasterios et al, 2017). This approach replaces the ancillary robust control law-which usually requires knowledge of R c -with a secondary MPC controller.…”

“…Recursive feasibility and stability of the algorithm were established in Baldivieso Monasterios et al (2017), and are here tailored to the coalitional setting. The procedure for the design of the final term in the control law and the constraint scaling parameters, given in Appendix A, is assumed to terminate having met the following assumptions.…”

“…• In Section 3, we present a distributed scheme for time-invariant coalitions of subsystems with guarantees of robust recursive feasibility and stability, despite the a-priori unknown disturbances arising from interactions, yet minimal reliance on invariant sets. The proposed scheme, first developed in (Baldivieso Monasterios et al, 2017), employs two MPC controllers for each subsystem. Crucially, the design and formulation of the MPC problems, and the invariance-inducing control law, does not require the explicit characterization of a robust invariant set, but relies only implicitly on the existence of one.…”