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Published January 17, 2019 | Version v1
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Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models

  • 1. Bioprocess Engineering Group, Spanish National Research Council, IIM-CSIC, C/Eduardo Cabello 6, 36208 Vigo (Spain)


This is a supplementary code repository for the article:
N. Tsiantis, A. F. Villaverde, and J. R. Banga.  Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models. Submitted, 2019.

In this article, we investigate the simultaneous inference of states, time-invariant parameters and time-dependent inputs in biological modelling. In other words we consider both the theoretical observability problem (FISPO) and the practical full system reconstruction problem (optimal tracking). 

Here we provide the scripts to run the optimal tracking problem for the case studies presented in the aforementioned article. The implementation is based on the methodology presented in [1] (see references), using the AMIGO2 toolbox.


The users will need:

- a Matlab R2015b (or later) installation, under Windows, Linux or Mac operating systems

- the AMIGO2 toolbox with the IOC add-on, available at:

Users need to make sure that the above AMIGO2 toolbox is fully functional before attempting to run the inverse optimal control case studies. Please refer to the AMIGO2 documentation. More detailed examples of IOC case studies can be also found in [2] (see references)

For any questions please contact us at:, ,


Contact:, , This research was supported by the European Union's Horizon 2020 research and innovation pro-gram under grant agreement No 675585 (MSCA ITN 'SyMBioSys'). This research was alsofunded by the Spanish Ministry of Science, Innovation and Universities, project SYNBIOCON-TROL (ref. DPI2017-82896-C2-2-R).


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Additional details


SyMBioSys – Systematic Models for Biological Systems Engineering Training Network 675585
European Commission


  • N. Tsiantis, E. Balsa-Canto, and J. R. Banga. Optimality and identification of dynamic models in systems biology: an inverse optimal control framework.Bioinformatics, 34(14):2433–2440, 2018.
  • Nikolaos Tsiantis, Eva Balsa-Canto, & Julio R. Banga. (2017, October 12). Inverse optimal control framework in systems biology: case studies. Zenodo.