Maximizing Algebraic Connectivity of Constrained Graphs in Adversarial Environments

This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design problem of adding edges to an initial graph, which introduces a nonconvex binary decision variable, in addition to subjugation to general convex constraints on the feasible edge set. Unlike previous methods, our method is justifiably not greedy and capable of accommodating these additional constraints. We also study a scenario in which a coordinator must selectively protect edges of the network from a chance of failure due to a physical disturbance or adversarial attack. The coordinator needs to strategically respond to the adversary's action without presupposed knowledge of the adversary's feasible attack actions. We propose three heuristic algorithms for the coordinator to accomplish the objective and identify worst-case preventive solutions. Each algorithm is shown to be effective in simulation and we provide some discussion on their compared performance.Comment: 8 pages, submitted to European Control Conference 201

Consensus on Nonlinear Spaces

peer reviewedConsensus problems have attracted significant attention in the control community over the last decade. They act as a rich source of new mathematical problems pertaining to the growing field of cooperative and distributed control. This paper is an introduction to consensus problems whose underlying state-space is not a linear space, but instead a highly symmetric nonlinear space such as the circle and other relevant generalizations. A geometric approach is shown to highlight the connection between several fundamental models of consensus, synchronization, and coordination, to raise significant global convergence issues not present in linear models, and to be relevant for a number of engineering applications, including the design of planar or spatial coordinated motions