Airlie Chapman

Controllability and Observability of Network-of-Networks via Cartesian Products

The paper presents a system theoretic analysis framework for a network-of-networks, formed from smaller factor networks via graph Cartesian products. We provide a compositional framework for extending the controllability and observability of the factor networks to that of the composite network-of-networks. We then delve into the effectiveness of designing control and estimation algorithms for the composite network via its symmetry and gramian structure. An example demonstrating the usefulness of our results in the context of social networks with a Cartesian product structure is then presented.

Transverse characterization of high air-fill fraction tapered photonic crystal fiber

We demonstrate tapering of a high air-fill fraction photonic crystal fiber by using the flame-brushing technique. Transverse probing along the taper allows us to ascertain how the microstructure is preserved during tapering. Experimental results are compared with numerical simulations performed with the finite-difference time-domain and plane-wave expansion methods. Through this investigation we find that the fiber geometry is well preserved throughout the tapering process and we resolve the apparent discrepancies between simulation and experiment that arise through the finite extent of the fiber microstructure.

On strong structural controllability of networked systems: A constrained matching approach

This paper examines strong structural controllability of linear-time-invariant networked systems. We provide necessary and sufficient conditions for strong structural controllability involving constrained matchings over the bipartite graph representation of the network. An O(n2) algorithm to validate if a set of inputs leads to a strongly structurally controllable network and to find such an input set is proposed. The problem of finding such a set with minimal cardinality is shown to be NP-complete. Minimal cardinality results for strong and weak structural controllability are compared.

Online distributed optimization via dual averaging

This paper presents a regret analysis on a distributed online optimization problem computed over a network of agents. The goal is to distributively optimize a global objective function which can be decomposed into the summation of convex cost functions associated with each agent. Since the agents face uncertainties in the environment, their cost functions change at each time step. We extend a distributed algorithm based on dual subgradient averaging to the online setting. The proposed algorithm yields an upper bound on regret as a function of the underlying network topology, specifically its connectivity. The regret of an algorithm is the difference between the cost of the sequence of decisions generated by the algorithm and the performance of the best fixed decision in hindsight. A model for distributed sensor estimation is proposed and the corresponding simulation results are presented.

Advection on graphs

This paper examines the dynamics of a networked, multi-agent system operating with an advection-based coordination algorithm. Flow advection is a close relative of diffusion whose discretized version forms the basis of the popular consensus dynamics. We endeavor to demonstrate in this paper that discretizing the continuous advection equation also forms an attractive set of system dynamics for coordinated control. The key advantage of advection-based algorithms over directed consensus is that the sum of the states is always conserved. This paper includes a formulation of the advection dynamics on directed graphs and a presentation of some of its characteristics, which are compared to the consensus dynamics. We also provide examples of the versatility of the advection dynamics: a formation control and sensor coverage example.

Bearing-compass formation control: A human-swarm interaction perspective

The paper considers the distributed formation control problem given bearing-only sensing of nearby agents with respect to a global vector frame, provided by a compass. We propose a bearing-compass control law and prove its convergence to a formation that is unique up to translation and scaling. We present results that describe the formations evolution in terms useful to a human operator, focusing on scale, translation and rotation of the formation. The results are supported with a number of illustrative examples.

On symmetry and controllability of multi-agent systems

This paper delves into the link between symmetry and controllability of networked systems. We examine symmetry results pertaining to the determining sets of a graph and eigenvalue multiplicity. These provide methods to reason how symmetry structure of the network informs the control input design. We generalize graph automorphisms, which represent graph symmetries, to signed fractional graph automorphisms via a semi-definite programming relaxation. Consequently, we extend existing results on the relationship between graph automorphisms and uncontrollability to signed fractional graph automorphisms, showing necessary and sufficient conditions for controllability.

System Theoretic Aspects of Influenced Consensus: Single Input Case

This technical note examines the dynamics of networked multi-agent systems operating with a consensus-type algorithm, under the influence of an attached node or external agent. Depending on the specific scenario, the attached node can be viewed as a network intruder or an administrator. We introduce an influence scheme, naive of the network topology, involving predictable excitation of the network with the objective of manipulating, disrupting, or steering its evolution. The spectrum of the corresponding Dirichlet matrix provides bounds on the system-theoretic properties of the resulting influenced network, quantifying its security-or viewed differently-its manageability. Finally, the controllability gramian for influenced consensus is examined, providing insights into its H2-norm and controllability properties.

Online Distributed Convex Optimization on Dynamic Networks

This note presents a distributed optimization scheme over a network of agents in the presence of cost uncertainties and over switching communication topologies. Inspired by recent advances in distributed convex optimization, we propose a distributed algorithm based on dual sub-gradient averaging. A convergence rate analysis for the offline optimization, and a regret analysis for the online case, as a function of the underlying dynamic network topology are then presented for both classes of uncertainties. Application of the proposed setup is then discussed for uncertain sensor networks.

Strong Structural Controllability of Networked Dynamics

This chapter examines strong structural controllability of linear-time-invariant networked systems. We provide necessary and sufficient conditions for strong structural controllability involving constrained matchings over the bipartite graph representation of the network. An \(\mathcal{O}(n^{2})\) algorithm to validate if a set of inputs leads to a strongly structurally controllable network and to find such an input set is proposed. The problem of finding such a set with minimal cardinality is shown to be NP-complete. Minimal cardinality results for strong and weak structural controllability are compared.