Shared hidden state and network representations of interconnected dynamical systems

Abstract

This paper demonstrates that the signal structure of an interconnected dynamical system, such as that represented by various dynamical graphical models, can be very different from the interconnection structure of its subsystems. These differences are revealed by considering the network semantics of each representation, characterized by the set of realizations consistent with each network structure. The reason these system networks can be so different is that subsystems never share hidden state, and thus subsystem structures partition the entire system state, while signal structures remain agnostic towards the presence of shared hidden state. Remaining agnostic towards the presence of shared hidden state make signal structures a weaker description of the underlying system structure, but it also gives signal structures a lower information cost for identification. Identifying a system's subsystem structure demands the identification of the correct partition of system states, which can be very expensive.

Dynamic Network Reconstruction from Heterogeneous Datasets

“…To study network identifiability, the work in [15] proposed dynamical structure functions (DSFs) for linear time-invariant (LTI) systems as a general network representation. Similar network models appeared in [16,17], and their differences are discussed in [18]. Theoretical results on network identifiability were firstly presented in [15].…”

Optimal Distributed Control for Platooning via Sparse Coprime Factorizations

“…It is precisely this particular type of constraints on the coprime factors of the controller that induces the distributed DRAFT implementation of resulted controllers as a network of linear time-invariant subsystems, such that the sub-controller on board each vehicle uses only information from its predecessor in the string. This approach to distributed controllers as linear dynamical networks hinges on the concept of dynamical structure functions, originally introduced in [47], [35] and further developed in [36], [37], [38], [39], [40], [41], [43], [44], [45].…”

Optimal distributed control for platooning via sparse coprime factorizations

“…We solve the last H 2 model-matching problem for Q * o (see for example [51]) and it follows that the minimum in (44) can be attained via the diagonal Youla parameter…”

“…It is precisely this particular type of constraints on the coprime factors of the controller that induces the distributed DRAFT implementation of resulted controllers as a network of linear time-invariant subsystems, such that the sub-controller on board each vehicle uses only information from its predecessor in the string. This approach to distributed controllers as linear dynamical networks hinges on the concept of dynamical structure functions, originally introduced in [47], [35] and further developed in [36], [37], [38], [39], [40], [41], [43], [44], [45].…”