Cooperative distributed stochastic MPC for systems with state estimation and coupled probabilistic constraints

A cooperative distributed stochastic model predictive control (CDSMPC) algorithm is given for multiple dynamically decoupled subsystems with additive stochastic disturbances and coupled probabilistic constraints, for which states are not measurable. Cooperation between subsystems is promoted by a scheme in which a local subsystem designs hypothetical plans for others in some cooperating set, and considers the weighted costs of these subsystems in its objective. To achieve satisfaction of coupled probabilistic constraints in a distributed way, only one subsystem is permitted to optimize at each time step. In addition, by using a lifting technique and the probabilistic information on additive disturbances, measurement noise and the state estimation error, a set of deterministic constraints is constructed for the predictions of nominal models. Recursive feasibility with respect to both local and coupled probabilistic constraints is guaranteed and stability for any choice of update sequence and any structure of cooperation is ensured. Numerical examples illustrate the efficacy of the proposed algorithm.