Journal
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS
Volume 8, Issue 4, Pages 1649-1658Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCNS.2021.3077987
Keywords
Computational biology; engineering in medicine and biology; mathematics; reliability; systems engineering and theory
Funding
- Deutsche Forschungsgemeinschaft (DFG) [354645666]
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Understanding the dynamics of complex systems is crucial in various fields, but unexpected behavior and system failures can be challenging to comprehend. Localizing error sources in the system and reconstructing their dynamics require informative measured outputs. Criteria and methods have been proposed to achieve this goal.
Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behavior of dynamic systems or even system failure is sometimes difficult to comprehend. Such a data-mismatch can be caused by endogenous model errors, including misspecified interactions and inaccurate parameter values. These are often difficult to distinguish from unmodeled process influencing the real system like unknown inputs or faults. Localizing the root cause of these errors or faults and reconstructing their dynamics is only possible if the measured outputs of the system are sufficiently informative. Here, we present criteria for the measurements required to localize the position of error sources in large dynamic networks. We assume that faults or errors occur at a limited number of positions in the network. This invariable sparsity differs from previous sparsity definitions for inputs to dynamic systems. We provide an exact criterion for the recovery of invariable sparse inputs to nonlinear systems and formulate an optimization criterion for invariable sparse input reconstruction. For linear systems, we can provide exact error bounds for this reconstruction method.
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