Complete and Functional Observability of Nonlinear Systems

Codes for analysis of the complete and functional observability of nonlinear systems, based on symbolic computation of Lie derivatives.

• Complete observability establishes a sufficient condition for the reconstruction of the full-state vector x(t) of a nonlinear system f(x) from a measurement function h(x).
• Functional observability, a generalization of complete observability, establishes a sufficient condition for the reconstruction of a nonlinear functional g(x) of a nonlinear system f(x) from a measurement function h(x).

See the references below for more details.

License

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

The full text of the GNU General Public License can be found in the file "LICENSE.txt".

Usage

• nonlinearobsvmatrix.m : Computes the observability matrix of a nonlinear system f(x) with a measurement function h(x) based on symbolic computations of the Lie derivatives of f(x) with respect to h(x).

• example_chaoticsys.m : Complete and functional observability analysis of several chaotic systems (Lorenz, Cord, Hindmarsh-Rose neuron, and Rossler; ODEs available in the folder systems).

• seizure : This folder contains example codes for the functional observability analysis of the Epileptor model and the use of the time-series-based index SVDO for early-warning alert of seizure-like events in synthetic data (generated by the Epileptor model, see example_epileptor.m) and empirical data (human EEG data, see example_eegdata.m).

References

1. A. N. Montanari, L. Freitas, D. Proverbio, J. Gonçalves. Functional observability and subspace reconstruction in nonlinear systems. Physical Review Research, 4:043195 (2022). https://doi.org/10.1103/PhysRevResearch.4.043195.
2. A. N. Montanari, L. A. Aguirre. Observability of Network Systems: A Critical Review of Recent Results. Journal of Control, Automation and Electrical Systems, 31(6):1348–1374 (2020). https://doi.org/10.1007/s40313-020-00633-5.