Sensitivity-based link addition for robust dynamical networks

Abstract

This study considers a link addition problem for a directed network in order to improve the stability margin of the network. Optimal identification of links such that the stability margin is maximized by their addition, requires solving a complex combinatorial problem. Here two efficient methods are proposed for suboptimal link addition by exploiting the sensitivity being embedded in the derivative of singular value and Lagrange multiplier. First, suboptimal link identification is done by utilizing the direct derivative of the minimum singular-value representing the network's SM. Second, the optimal link identification problem for maximizing the SM of a dynamical network is formulated into that for minimizing the sensitivity function associated with the dynamical network. Then, the suboptimal link identification is done by minimizing an augmented Lagrangian subject to LMIs (Linear Matrix Inequalities), yielding the Lagrange multiplier which explicitly indicates the sensitivity of SM with respect to link addition. Numerical tests are presented to demonstrate the efficacy of the proposed methods.