  In this paper, we propose a chance constrained stochastic model predictive
control scheme for reference tracking of distributed linear time-invariant
systems with additive stochastic uncertainty. The chance constraints are
reformulated analytically based on mean-variance information, where we design
suitable Probabilistic Reachable Sets for constraint tightening. Furthermore,
the chance constraints are proven to be satisfied in closed-loop operation. The
design of an invariant set for tracking complements the controller and ensures
convergence to arbitrary admissible reference points, while a conditional
initialization scheme provides the fundamental property of recursive
feasibility. The paper closes with a numerical example, highlighting the
convergence to changing output references and empirical constraint
satisfaction.
