Stability analysis of a system of systems controlled via MPC and consensus ADMM for a generic consensus horizon

This paper deals with the distributed control of a System of Systems (SoS) via an unconstrained Model Predictive Control (MPC) approach integrated with the Consensus Alternating Direction Method of Multipliers (C-ADMM). In this work, it is shown how the stability of the resulting controlled system can be affected and determined a priori on the basis of different parameters of the control problem. One of these parameters is the consensus horizon, which represents a relaxation of the consensus constraints to a reduced number of time instants with respect to the standard C-ADMM formulation. So, a way to analytically check the closed-loop behavior is provided by calculating the closed-form solution of the control algorithm and then computing the closed-loop poles of the controlled system. Finally, to demonstrate the functionality of the obtained results, multiple numerical experiments are performed on a simulated version of an interconnected quadruple tank plant and on a second larger illustrative SoS.