Optimal Control of Large-Scale Networks using Clustering Based Projections
This work provides a scalable control design for large-scale network systems, reducing computational and communication overhead, which is crucial for applications like power grids or traffic networks.
The paper addresses the computational and communication challenges of designing LQR controllers for large-scale networks with tens of thousands of states by proposing a clustering-based projection method. The method reduces the controller dimension, achieving a tractable design with far fewer communication links while minimizing the H2-norm error between full-order and reduced-order controllers.
In this paper we present a set of projection-based designs for constructing simplified linear quadratic regulator (LQR) controllers for large-scale network systems. When such systems have tens of thousands of states, the design of conventional LQR controllers becomes numerically challenging, and their implementation requires a large number of communication links. Our proposed algorithms bypass these difficulties by clustering the system states using structural properties of its closed-loop transfer matrix. The assignment of clusters is defined through a structured projection matrix P, which leads to a significantly lower-dimensional LQR design. The reduced-order controller is finally projected back to the original coordinates via an inverse projection. The problem is, therefore, posed as a model matching problem of finding the optimal set of clusters or P that minimizes the H2-norm of the error between the transfer matrix of the full-order network with the full-order LQR and that with the projected LQR. We derive a tractable relaxation for this model matching problem, and design a P that solves the relaxation. The design is shown to be implementable by a convenient, hierarchical two-layer control architecture, requiring far less number of communication links than full-order LQR.