Distributed Linear Quadratic Regulator for the Synthesis of a Separable Terminal Cost for Distributed Model Predictive Control

摘要

In distributed model predictive control the global optimization problem is split into simpler problems through the use of decomposition methods. To enable such a decomposition, the problem is required to be separable, a property which is in general fulfilled when dealing with networks of dynamically coupled systems. The standard linear quadratic regulator used to provide stability through a terminal cost function, however, destroys the problem's inherent structure and can therefore not be directly employed. In this paper an alternative suboptimal design providing both a stabilizing terminal cost function which preserves the network structure and a nominal distributed control law for the unconstrained system is presented. The proposed iterative algorithm is based on the standard Riccati iteration and on semidefinite programming. The global synthesis problem is itself amenable to distributed optimization and can hence be executed online. The controllers can therefore easily adapt to general network changes enabling full Plug&Play capabilities. The implemented method is tested numerically on a chain of inverted penduli network.