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Center for Nonlinear Studies |
In recent years, analyzing stability and robustness of complex networks with various practical applications has been a topic of interest. It stems from an open problem in system realization theory, where given a set of non-linear systems with bounded inputs, interconnecting them to obtain a desired output is of primary interest. We consider a simplified version of this problem, focusing on maximizing the robustness of networks for the following applications: a) Linear mechanical systems, b) Motion control problems related to vehicle localization with noisy measurements, and c) Rigid formation of UAV adhoc infrastructure networks with data congestion. We pose this network synthesis problem (NP-hard) as a Mixed Integer Semi-Definite Program and equivalently as a Fiedler vector based Mixed Integer Linear Program (MILP) to obtain optimal solutions and upper bounds for moderate sized problems. We also discuss some neighborhood search heuristics based on reduced search space methods to quickly obtain good feasible solutions for large scale problems.
Host: Jeffrey D. Hyman