Distributed Identification of Contracting and/or Monotone Network Dynamics

Abstract

This paper 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 (ADMM). 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-dimensional state space.

Kernel-Based Models for System Analysis

“…Note that we focus on the operator-theoretic notion of monotonicity. Other concepts of monotonicity arise in the context of state-space systems, which has recently received attention in data-based studies as well[42],[43] 3. In Section IX, we will also briefly discuss the case of (nonincremental) dissipativity, i.e., items 4 and 5 of Definition 1.Authorized licensed use limited to: University of Groningen.…”