Inverse Inference on Cooperative Control of Networked Dynamical Systems

2025-04-18

AI Summary

This study addresses the critical component inference problem for networked dynamical systems (NDSs) under continuous-time state-feedback cooperative control, using discrete-time observational data. We propose a two-layer inference framework: first estimating the discrete-time closed-loop system matrix, then recovering the continuous-time model via a sampling-period-constrained matrix logarithm method to decouple node dynamics from topology. Our contributions include: (i) establishing, for the first time, a rigorous mapping from discrete observations to the continuous-time closed-loop model; (ii) developing a theoretically guaranteed matrix logarithm recovery algorithm; and (iii) resolving component identifiability under scalar ambiguity and reconstructing the inverse-optimal control cost function. We prove asymptotic unbiasedness of the estimator, derive explicit recovery error bounds, and specify sufficient sampling conditions. Extensive simulations demonstrate high accuracy and strong robustness in both component decoupling and cost function reconstruction.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Recent years have witnessed the rapid advancement of understanding the control mechanism of networked dynamical systems (NDSs), which are governed by components such as nodal dynamics and topology. This paper reveals that the critical components in continuous-time state feedback cooperative control of NDSs can be inferred merely from discrete observations. In particular, we advocate a bi-level inference framework to estimate the global closed-loop system and extract the components, respectively. The novelty lies in bridging the gap from discrete observations to the continuous-time model and effectively decoupling the concerned components. Specifically, in the first level, we design a causality-based estimator for the discrete-time closed-loop system matrix, which can achieve asymptotically unbiased performance when the NDS is stable. In the second level, we introduce a matrix logarithm based method to recover the continuous-time counterpart matrix, providing new sampling period guarantees and establishing the recovery error bound. By utilizing graph properties of the NDS, we develop least square based procedures to decouple the concerned components with up to a scalar ambiguity. Furthermore, we employ inverse optimal control techniques to reconstruct the objective function driving the control process, deriving necessary conditions for the solutions. Numerical simulations demonstrate the effectiveness of the proposed method.

Problem

• Infer continuous-time NDS control from discrete observations
• Decouple nodal dynamics and topology components
• Reconstruct objective function of cooperative control

Innovation

• Bi-level framework infers NDS control from discrete data
• Matrix logarithm recovers continuous-time system matrix
• Least squares decouples nodal dynamics and topology