A Decentralized Consensus Algorithm via LMI-Based Model Predictive Control and Primal Decomposition

This paper proposes a decentralized model predictive control method for solving an optimal consensus problem, where a system consists of networked multiple subsystems and the states of all the subsystems converge to a common point. The problem is formulated as a convex optimization problem involving linear matrix inequalities, and then is solved by using an incremental subgradient method based on primal decomposition. In the proposed scheme, the state feedback matrix for each subsystem is computed at each time in a decentralized way. It is shown that the states of all the subsystems asymptotically converge by the proposed method if the optimization problem is feasible at the initial time. A numerical example is given to show the effectiveness of the proposed method.