Inverse Inference on Cooperative Control of Networked Dynamical Systems
Yushan Li, Jianping He, Dimos V. Dimarogonas
TL;DR
The paper addresses the problem of inferring the underlying cooperative control mechanism of a networked dynamical system from discrete, noisy observations. It proposes a bi-level framework that first estimates the discretized closed-loop matrix $A_d$ through a causality-based estimator, then recovers the continuous-time matrix $A_c$ via a matrix logarithm under a guaranteed sampling period. It further decouples and recovers the nodal dynamics $(A,B)$, topology $L$, and feedback $K$ using least-squares approaches that leverage graph structure, and reconstructs the LQ cost function via inverse optimal control techniques, with guarantees on identifiability up to scalar ambiguities and asymptotic accuracy under sufficient data. Numerical simulations validate the method, showing asymptotic unbiasedness for $A_d$ when stable, sampling-period dependent accuracy for $A_c$, and successful recovery of $L$, $BK$, and the cost matrices. The work provides a principled path to reveal hidden control mechanisms in NDSs from limited data, with potential extensions to heterogeneous networks and broader cooperative settings.
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.