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Journal of Undergraduate Research

Keywords

dynamical structure function, DSF, identifiability conditions, signal structure reconstruction

College

Physical and Mathematical Sciences

Department

Computer Science

Abstract

Networks of controlled dynamical systems exhibit a variety of interconnection patterns that can be interpreted as the structure of a 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 (DSF). 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, i.e., for systems to be reconstructed, each observed state must be independently controlled by an input for the structure of the system to be reconstructible. The work done extended these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. Given the previous set of results, reconstruction of the DSF of a system was limited to systems where independent state perturbation is possible. This extension is important because it 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 scientist.

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