Parallelized Robust Distributed Model Predictive Control in the Presence of Coupled State Constraints

In this paper, we present a robust distributed model predictive control (DMPC) scheme for dynamically decoupled nonlinear systems which are subject to state constraints, coupled state constraints and input constraints. In the proposed control scheme, all subsystems solve their local optimization problem in parallel and neighbor-to-neighbor communication suffices. The approach relies on consistency constraints which define a neighborhood around each subsystem's reference trajectory where the state of the respective subsystem is guaranteed to stay in. Reference trajectories and consistency constraints are known to neighboring subsystems. Contrary to other relevant approaches, the reference trajectories are improved iteratively. The presented approach allows the formulation of convex optimization problems even in the presence of non-convex state constraints. Moreover, we employ tubes in order to ensure the controller's robustness against bounded uncertainties. In the end, we show that with some minor modifications, the proposed scheme can be also applied to dynamically coupled systems when the dynamic couplings are bounded. The algorithm's effectiveness is demonstrated with a simulation