Distributed Identification of Contracting and/or Monotone Network Dynamics
This work addresses the challenge of scalable and stable model identification for networked systems, which is incremental as it builds on existing methods like ADMM to handle large-scale problems with specific stability guarantees.
The paper tackles the problem of identifying large-scale networked systems with guarantees of stability (contracting) and monotonicity, proposing a method that simultaneously searches for model parameters and stability certificates while scaling to networks with hundreds or thousands of nodes. It demonstrates performance on case studies, including a nonlinear traffic network with a 200-dimensional state space.
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 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 has 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 non-linear case studies, including a nonlinear traffic network with a 200-dimensional state space.