Observability of complex systems

Yang Yu Liu, Jean Jacques Slotine, Albert Laśzló Barab́asi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

A quantitative description of a complex system is inherently limited by our ability to estimate the system's internal state fromexperimentally accessible outputs. Although the simultaneous measurement of all internal variables, like allmetabolite concentrations in a cell, offers a complete description of a system's state, in practice experimental access is limited to only a subset of variables, or sensors. A system is called observable if we can reconstruct the system's complete internal state from its outputs. Here, we adopt a graphical approach derived fromthe dynamical laws that govern a systemto determine the sensors that are necessary to reconstruct the full internal state of a complex system. We apply this approach to biochemical reaction systems, finding that the identified sensors are not only necessary but also sufficient for observability. The developed approach can also identify the optimal sensors for target or partial observability, helping us reconstruct selected state variables from appropriately chosen outputs, a prerequisite for optimal biomarker design. Given the fundamental role observability plays in complex systems, these results offer avenues to systematically explore the dynamics of a wide range of natural, technological and socioeconomic systems.

Original languageEnglish
Pages (from-to)2460-2465
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume110
Issue number7
DOIs
StatePublished - 12 Feb 2013
Externally publishedYes

Keywords

  • Algebraic observability
  • Biochemical reactions
  • Control theory

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