Dr. Victor Preciado of University of Pennsylvania

We propose a theoretical framework to study the eigenvalue spectra of the controllability Gramian of systems with random state transition matrices, such as networked systems with a random graph structure. Using random matrix theory, we provide expressions for the moments of the eigenvalue distribution of the controllability Gramian. These moments can then be used to derive useful properties of the eigenvalue distribution of the Gramian (in some cases, even closed-form expressions for the distribution). We illustrate this framework by considering system matrices derived from common random graph and matrix ensembles, such as the Wigner ensemble, the Gaussian Orthogonal Ensemble (GOE), and random regular graphs. Subsequently, we illustrate how the eigenvalue distribution of the Gramian can be used to draw conclusions about the energy required to control random system.

Biography:

Victor M. Preciado is the Raj and Neera Singh Assistant Professor of Electrical and Systems Engineering at the University of Pennsylvania, where he is affiliated with the Networked & Social Systems Engineering program and the Warren Center for Network & Data Sciences. He received his Ph.D. degree in Electrical Engineering and Computer Science from MIT. He has also been a visiting scientist at UC Berkeley and Santa Fe Institute. His main research interests lie in the modeling, analysis, control, and optimization of large-scale complex dynamic networks, with applications in social networks, technological infrastructure, and biological systems.

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Dr. Victor Preciado of University of Pennsylvania

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