Distributed Identification of Contracting and/or Monotone Network Dynamics

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.