From non-cooperative to cooperative distributed MPC: A simplicial approximation perspective

The paper deals with the coordination of dynamical systems by distributed model predictive control.We consider a set-up in which the subsystems dynamics are decoupled, while the subsystems outputs are coupled by some constraint. Starting from a well established non-iterative and non-cooperative architecture, we provide a novel interpretation for this non-cooperative scheme as a simplicial approximation of a convex program. Thanks to this novel interpretation, we are able to show why the existing algorithm, while guaranteeing feasibility, fails to compute an optimal solution to the centralized problem. Furthermore, by exploiting the simplicial approximation structure, we are able to propose a novel algorithm. The proposed algorithm inherits all the properties of the existing one, namely little communication, and feasibility. Furthermore, increasing the communication among the subsystems between two control updates improves the performance of the algorithm, regaining in the limit optimality in a cooperative sense.