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Open AccessArticle

Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation

1
BioProcess Engineering Group, IIM-CSIC, 36208 Vigo, Galicia, Spain
2
Department of Applied Mathematics II, University of Vigo, 36310 Vigo, Galicia, Spain
3
Department of Applied Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Galicia, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 1876; https://doi.org/10.3390/math8111876
Received: 30 September 2020 / Revised: 14 October 2020 / Accepted: 22 October 2020 / Published: 29 October 2020
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
The observability of a dynamical system is affected by the presence of external inputs, either known (such as control actions) or unknown (disturbances). Inputs of unknown magnitude are especially detrimental for observability, and they also complicate its analysis. Hence, the availability of computational tools capable of analysing the observability of nonlinear systems with unknown inputs has been limited until lately. Two symbolic algorithms based on differential geometry, ORC-DF and FISPO, have been recently proposed for this task, but their critical analysis and comparison is still lacking. Here we perform an analytical comparison of both algorithms and evaluate their performance on a set of problems, while discussing their strengths and limitations. Additionally, we use these analyses to provide insights about certain aspects of the relationship between inputs and observability. We found that, while ORC-DF and FISPO follow a similar approach, they differ in key aspects that can have a substantial influence on their applicability and computational cost. The FISPO algorithm is more generally applicable, since it can analyse any nonlinear ODE model. The ORC-DF algorithm analyses models that are affine in the inputs, and if those models have known inputs it is sometimes more efficient. Thus, the optimal choice of a method depends on the characteristics of the problem under consideration. To facilitate the use of both algorithms, we implemented the ORC-DF condition in a new version of STRIKE-GOLDD, a MATLAB toolbox for structural identifiability and observability analysis. Since this software tool already had an implementation of the FISPO algorithm, the new release allows modellers and model users the convenience of choosing between different algorithms in a single tool, without changing the coding of their model. View Full-Text
Keywords: observability; identifiability; nonlinear systems; control theory; differential geometry; software observability; identifiability; nonlinear systems; control theory; differential geometry; software
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MDPI and ACS Style

Martínez, N.; Villaverde, A.F. Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation. Mathematics 2020, 8, 1876. https://doi.org/10.3390/math8111876

AMA Style

Martínez N, Villaverde AF. Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation. Mathematics. 2020; 8(11):1876. https://doi.org/10.3390/math8111876

Chicago/Turabian Style

Martínez, Nerea; Villaverde, Alejandro F. 2020. "Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation" Mathematics 8, no. 11: 1876. https://doi.org/10.3390/math8111876

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