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Abstract A two‐time‐scale system involves both fast and slow dynamics. This article studies observer design for general nonlinear two‐time‐scale systems and presents two alternative nonlinear observer design approaches, one full‐order and one reduced‐order. The full‐order observer is designed by following a scheme to systematically select design parameters, so that the fast and slow observer dynamics are assigned to estimate the corresponding system modes. The reduced‐order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow‐motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that the reduced‐order observer is capable of providing accurate estimation of the states for the detailed system with an exponentially decaying estimation error. In the last part of the article, the two proposed observers are designed for an anaerobic digestion process, as an illustrative example to evaluate their performance and convergence properties.
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Robustness guarantees for structured model reduction of dynamical systems with applications to biomolecular models
Abstract Model reduction methods usually focus on the error performance analysis; however, in presence of uncertainties, it is important to analyze the robustness properties of the error in model reduction as well. This problem is particularly relevant for engineered biological systems that need to function in a largely unknown and uncertain environment. We give robustness guarantees for structured model reduction of linear and nonlinear dynamical systems under parametric uncertainties. We consider a model reduction problem where the states in the reduced model are a strict subset of the states of the full model, and the dynamics for all of the other states are collapsed to zero (similar to quasi‐steady‐state approximation). We show two approaches to compute a robustness guarantee metric for any such model reduction—a direct linear analysis method for linear dynamics and a sensitivity analysis based approach that also works for nonlinear dynamics. Using the robustness guarantees with an error metric and an input‐output mapping metric, we propose an automated model reduction method to determine the best possible reduced model for a given detailed system model. We apply our method for the (1) design space exploration of a gene expression system that leads to a new mathematical model that accounts for the limited resources in the system and (2) model reduction of a population control circuit in bacterial cells.
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- Award ID(s):
- 1903477
- PAR ID:
- 10419805
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal of Robust and Nonlinear Control
- Volume:
- 33
- Issue:
- 9
- ISSN:
- 1049-8923
- Page Range / eLocation ID:
- p. 5058-5086
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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