Suboptimal distributed MPC based on a block-coordinate descent method with feasibility and stability guarantees

In this paper we propose a distributed optimization algorithm to solving discrete linear model predictive control (MPC) problems for general networked systems. The new optimization algorithm is based on block coordinate descent updates in parallel with very simple iteration complexity and using only local information. We show that for smooth objective functions it has sublinear rate of convergence, while for strongly convex objective functions it converges linearly. An MPC controller based on this distributed optimization method is derived, for which every subsystem in the network can compute feasible and stabilizing control inputs using distributed computations. For ensuring stability of the MPC scheme, we use a terminal cost formulation and we eliminate the need for a zero terminal state, which proves to be less conservative than some terminal cost - terminal set approaches. We provide a distributed synthesis for a terminal cost, which satisfy distributed invariance conditions for the whole system and guarantees stability of the closed-loop interconnected system.