LQG control of large networks: A clustering-based approach

In this paper we present a Linear Quadratic Gaussian (LQG) control design for large-dimensional network dynamic systems using the idea of network clustering. When networks have tens of thousands of nodes spread over a wide geographical span, the design of conventional output feedback controllers becomes numerically challenging, and their implementation requires a large number of communication links. Our proposed algorithm bypasses these difficulties by clustering the network nodes using structural properties of its closed-loop transfer matrix. The cluster assignment is applied for constructing a structured projection matrix P, which is used to pose a significantly lower-dimensional controller design. The problem is, therefore, posed in terms of finding the optimal set of clusters or P that minimizes the ℋ₂-norm of the error between the transfer matrices of the full-order network with a conventional LQG controller and that with the projected LQG controller. We derive an upper bound on this error as a function of P, and design a P that minimizes this bound.