Dynamical structure function identifiability conditions enabling signal structure reconstruction

Abstract

Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function. Although this notion of structure is among the weakest available, previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs. This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. This extension is important because it significantly broadens the applicability of the identifiability conditions, enabling the design of network reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the engineer or scientist. The work is motivated by the proteomics problem of reconstructing the Per-Arnt-Sim Kinase pathway used in the metabolism of sugars.

Shared hidden state and network representations of interconnected dynamical systems

“…Even when a system is composed as the interconnection of subsystems, it nevertheless exhibits other notions of network structure associated with alternative system representations-network structures that can be quite distinct from the interconnection pattern of subsystems [4]. One of these notions, the system's signal structure, has appeared in a variety of recent works (albeit not always explicitly identified as such) and drives a number of current results for network informativity conditions [5], [6], [7], network identification [8], [9], [10], [11], [12], [13], [14], and distributed controller synthesis [15], [16].…”

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].…”

A Minimal Realization Technique for the Dynamical Structure Function of a Class of LTI Systems

“…Likewise, a state-space realization is consistent with (Q, P ) if that state-space realization gives (Q, P ) from (5) and (6).…”

“…Definition 3: A dynamical structure function, (Q, P ), is defined to be consistent with a particular transfer function, G, if there exists a state-space realization of G, of some order, and of the form (1), such that (Q, P ) are specified by (5) and (6). Likewise, a state-space realization is consistent with (Q, P ) if that state-space realization gives (Q, P ) from (5) and (6).…”

“…The Dynamical Structure Function (DSF), introduced by Goncalves and Warnick in [1] and [11], is a representation of linear time invariant (LTI) systems that encodes more detail about a system's structure than its transfer function (TF), but less than its state-space realization [3]. As a result, the DSF is a useful modeling tool for complex networks where some information about the network's global structure is desired without engaging the full complexity of a complete state-space realization [2], [5], [6], [12]- [14]. Examples of applications that have effectively leveraged the DSF as a modeling technology include system biology, in the reconstruction of biochemical reaction networks [4], [10], [17], [18]; computer science, in the vulnerability analysis and design of secure architectures for cyber-physical systems [26], [27]; and distributed systems, in the design of distributed and decentralized control systems [28]- [30] and structure-preserving model-reduction [15].…”