Determining r- and (r, s)-robustness of digraphs using mixed integer linear programming. (January 2020)

• Record Type: Journal Article
• Authors: Usevitch, James; Panagou, Dimitra
• Is Part Of: Automatica. Volume 111(2020)
• Publication Date: 2020-01
• Subjects: Networks -- Robustness -- Graph theory -- Optimization problems -- Integer programming; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.108586
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: There has been an increase in the use of resilient control algorithms based on the graph theoretic properties of r - and ( r, s ) -robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number of arbitrarily misbehaving agents if the values of the integers r and s are sufficiently large. However, determining an arbitrary graph's robustness is a highly nontrivial problem. This paper introduces a novel method for determining the r - and ( r, s ) -robustness of digraphs using mixed integer linear programming; to the best of the authors' knowledge it is the first time that mixed integer programming methods have been applied to the robustness determination problem. The approach only requires knowledge of the graph Laplacian matrix, and can be formulated with binary integer variables. Mixed integer programming algorithms such as branch-and-bound are used to iteratively tighten the lower and upper bounds on r and s . Simulations are presented which compare the performance of this approach to prior robustness determination algorithms.