2013/07/31 by Andrew J. Whalen, Sean Brennan, Sean N. Brennan +3 · 4 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Computer science #Control (management) #Control theory (sociology) #Controllability #Gene Regulatory Network Analysis #Geometry #Homogeneous space #Linear subspace #Mathematics #Network controllability #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Observability #Physics #Pure mathematics #Quantum mechanics #Symmetry (geometry) #Topology (electrical circuits) #nlin.CD #q-bio.NC #q-bio.QM
paper · pdf · doi:10.1103/physrevx.5.011005
19 pages, 9 figures
arxiv created 2014/10/06 · openalex publication_date 2015/01/23 · arxiv updated 2018/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. For example, noncontrollable mathematical models of real systems have subspaces that influence model behavior, but cannot be controlled by an input. Such subspaces can be difficult to determine in complex nonlinear networks. Since almost all of the present theory was developed for linear networks without symmetries, here we present a numerical and group representational framework, to quantify the observability and controllability of nonlinear networks with explicit symmetries that shows the connection between symmetries and nonlinear measures of observability and controllability. We numerically observe and theoretically predict that not all symmetries have the same effect on network observation and control. Our analysis shows that the presence of symmetry in a network may decrease observability and controllability, although networks containing only rotational symmetries remain controllable and observable. These results alter our view of the nature of observability and controllability in complex networks, change our understanding of structural controllability, and affect the design of mathematical models to observe and control such networks.