Stability analysis of decentralized RHC for decoupled systems

A detailed study on the stability and design of decentralized Receding Horizon Control (RHC) schemes for decoupled systems is presented. An optimal control problem is formulated for a set of decoupled dynamical systems where cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a connected graph where each system is a node and, cost and constraints of the optimization problem associated to each node are only function of its state and the states of its neighbors. The complexity of the problem is addressed by breaking a centralized RHC controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated to a different node and computes the local contol inputs based only on the states of the node and of its neighbors. Stability of the decentralized scheme is analyzed and its properties are compared with alternative decentralized RHC approaches being proposed in the literature.