Distributed stochastic MPC of linear systems with parameter uncertainty and disturbances

In this paper, we propose a distributed stochastic model predictive control (DSMPC) algorithm for a team of linear subsystems sharing coupled probabilistic constraints. Each subsystem is subject to both parameter uncertainty and stochastic disturbances. To handle the probabilistic constraints, we first decompose the state trajectory into a nominal part and an uncertain part. The latter one is further divided into two parts: one is bounded by probabilistic tubes that are calculated offline by making full use of the probabilistic information on disturbances, whereas the other is bounded by polytopic tubes whose scaling is optimized online and whose facets' orientations are chosen offline. Under the update strategy that only one subsystem is permitted to optimize at each time step, probabilistic constraints are transformed into linear constraints, and the original optimization problem is then formulated as a convex problem. In addition, this new algorithm does not rely on instantaneous inter-subsystem exchanges of data during a time step, and therefore may have a relatively low susceptibility to communication delay. By constructing a decoupled terminal set for each subsystem, the proposed algorithm guarantees recursive feasibility with respect to both local and coupled probabilistic constraints and ensures stability in closed-loop operation. Finally, numerical simulations illustrate the efficacy of the theoretical results.