Distributed model predictive control for linear systems under communication noise: Algorithm, theory and implementation

We study the distributed model predictive control (DMPC) problem for a network of linear discrete-time subsystems in the presence of stochastic noise among communication channels, where the system dynamics are decoupled and the system constraints are coupled. The DMPC is cast as a stochastic distributed consensus optimization problem by modeling the exchanged variables as stochastic ones and a novel noisy alternating direction multiplier method (NADMM) is proposed to solve it in a fully distributed way. We prove that the sequences of the primal and dual variables converge to their optimal values almost surely (a.s.) with communication noise. Furthermore, a new stopping criterion and a DMPC scheme termed as current–previous DMPC (cpDMPC) are proposed, which guarantees deterministic termination even when the NADMM algorithm may not converge in a practical realization. Next, the strict analysis on the feasibility of the cpDMPC strategy and the closed-loop stability is carried out, and it is shown that the cpDMPC strategy is feasible at each time step and the closed-loop system is asymptotically stable. Finally, the effectiveness of the proposed NADMM algorithm is verified via an example.