Dynamical structure function identifiability conditions enabling signal structure reconstruction

in The proceedings of the 51st IEEE Conference on Decision and Control (CDC) (2012, December)

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 ... [more ▼]

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. [less ▲]

Constructive Synchronization of Networked Feedback Systems

in The proceedings of the 49th IEEE Conference on Decision and Control (CDC) (2010)

This paper is concerned with global asymptotic output synchronization in networks of identical feedback systems. Using an operator theoretic approach based on an incremental small gain theorem, the method ... [more ▼]

This paper is concerned with global asymptotic output synchronization in networks of identical feedback systems. Using an operator theoretic approach based on an incremental small gain theorem, the method reformulates the synchronization problem as one of achieving incremental stability using a coupling operator that plays the role of an incrementally stabilizing feedback. In this way, conditions on static or dynamic coupling operators that achieve output synchronization of nodes of arbitrary structure are derived. These conditions lead to a methodology for the construction of coupling architectures that ensure output synchronization of a wide range of systems. The result is illustrated for a network of biochemical oscillators. [less ▲]

Robust dynamical network reconstruction

in The proceedings of the 49th IEEE Conference on Decision and Control (CDC) (2010)

Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise ... [more ▼]

Motivated by biological applications, this paper addresses the problem of network reconstruction from data. Previous work has shown necessary and sufficient conditions for network reconstruction of noise-free LTI systems. This paper assumes that the conditions for network reconstruction have been met but here we additionally take into account noise and unmodelled dynamics (including nonlinearities). Algorithms are therefore proposed to reconstruct dynamical (Boolean) network structure from time-series (steady-state) data respectively in presence of noise and nonlinearities. In order to identify the network structure that generated the data, we compute the smallest distances between the measured data and the data that would have been generated by particular Boolean structures. Information criteria and optimisation technique balancing such distance and model complexity are introduced to search for the true structure. We conclude with biologically-inspired network reconstruction examples which include noise and nonlinearities. [less ▲]