Name
Abstract | ||
|---|---|---|
We investigate robustness of networks with linear time-invariant dynamics under external stochastic disturbances. We propose a partial ordering on this class of dynamical networks and exploit their structural properties to characterize their robustness properties and fundamental limits. Then, we show that several existing and widely used scalar robustness measures are indeed Schur-convex functions on the spectrum of the Laplacian of the networks. We show that certain robustness features of the first-order consensus networks can be formulated as Schur-convex functions of their Laplacian eigenvalues. Specifically, we define the uncertainty volume and entropy based on the minimum-volume covering ellipsoid of the steady-state output points of the excited network. It is shown that the uncertainty volume is directly related to the number of spanning trees of the underlying graph of the network. Furthermore, we show that for networks with regular lattice interconnection topologies this measure scales asymptotically with network size. Finally, we propose an optimization-based method to improve robustness in linear dynamical networks. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/ACC.2014.6859345 | American Control Conference |
Keywords | Field | DocType |
eigenvalues and eigenfunctions,graph theory,network theory (graphs),optimisation,Laplacian eigenvalues,Schur-convex robustness measures,external stochastic disturbance,first-order consensus networks,linear dynamical networks,linear time-invariant dynamics,minimum-volume covering ellipsoid,network graph,network size,optimization-based method,partial ordering,regular lattice interconnection topologies,robustness properties,Optimization,Robust control,Stochastic systems | Ellipsoid,Lattice (order),Computer science,Control theory,Scalar (physics),Regular polygon,Robustness (computer science),Spanning tree,Partially ordered set,Laplace operator | Conference |
ISSN | Citations | PageRank |
0743-1619 | 4 | 0.43 |
References | Authors | |
7 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Milad Siami | 1 | 122 | 15.65 |
| Nader Motee | 2 | 181 | 28.18 |