Inverse Inference on Cooperative Control of Networked Dynamical Systems

Dimarogonas 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. I NTRODUCTION In the last decades, networked dynamical systems (NDSs) have played a crucial role in many engineering and biological fields, e.g., multi-robot formation [1], power grids [2], human brain [3], and immune cell network [4]. An NDS, comprising multiple interconnected nodes, is characterized by not only the self-dynamics of a single node (nodal dynamics) but also the interaction structure (topology) between nodes, and can achieve various cooperative behaviors such as synchronization. However, the prior information about the nodal dynamics and topology is not always accessible in practice, and needs to be inferred from observations. This inference enhances our ability to understand, predict, and intervene with the NDS [5]. A. Motivations This paper focuses on the continuous-time linear state-feedback cooperative control of NDSs, where only discrete and noisy observations on a single round of the system's trajectory are available. In particular, we aim to provide a: Y ushan Li and Dimos V . Dimarogonas are with the Division of Decision and Control Systems, KTH Royal Institute of Technology, Stockholm, Sweden. The motivation for addressing this problem stems from two main aspects.