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This article proposes methods for identification of large-scale networked systems with guarantees that the resulting model will be contracting—a strong form of nonlinear stability—and/or monotone, i.e., order relations between states are preserved. The main challenges that we address are simultaneously searching for model parameters and a certificate of model stability, and scalability to networks with hundreds or thousands of nodes. We propose a model set that admits convex constraints for stability and monotonicity, and both model and stability certificates have a separable structure that allows distributed identification via the alternating directions method of multipliers. The performance and scalability of the approach is illustrated on a variety of linear and nonlinear case studies, including a nonlinear traffic network with a 200-D state space. [ABSTRACT FROM AUTHOR]

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and nonconvexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP); however, the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper, we develop a path-following interior-point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the dataset. The new algorithm enables empirical comparisons to established methods including nonlinear autoregressive models with exogenous inputs, and we demonstrate superior generalization to new data. We also explore the “regularizing” effect of stability constraints as an alternative to regressor subset selection. [ABSTRACT FROM AUTHOR]