Structural identifiability and decentralized identification for systems coupled by their outputs

Structural identifiability and decentralized identification for systems coupled by their outputs

Safa Jedidi Romain Bourdais Jean Buisson Marie-Anne Lefebvre 

Equipe AUT (Automatique) CentraleSupelec - IETR UMR 6164, Avenue de la Boulaie CS 47601, F-35576 Cesson-Sévigné Cedex, France

Corresponding Author Email: 
romain.bourdais@centralesupelec.fr
Page: 
137-155
|
DOI: 
https://doi.org/10.3166/JESA.50.137-155
| | | | Citation

OPEN ACCESS

Abstract: 

This paper deals with the identification of large-scale systems that can be decomposed into a collection of subsystems that are coupled by their outputs. It is first shown that if the global system is structurally identifiable, then all the subsystems are also structurally identifiable considering the coupling outputs as new inputs. This property is then used to propose a decentralized identification procedure. The efficiency of the proposed approach is emphasized on an academical example.

Keywords: 

identifiability, decentralized identification, large scale systems

1. Introduction
2. Définitions
3. Formalisation du problème étudié
4. Condition suffisante pour l’identifiabilité structurelle des systèmes locaux
5. Procédure de l’identification décentralisée
6. Conclusion
  References

Bellman R., Astrom K. (1970). On structural identifiability. Mathematical Biosciences, vol. 7, no 34, p. 329 - 339.

Bernussou J., Titli A. (1982). Interconnected dynamical systems: Stability, decomposition and decentralization. North-Holland, New York, vol. 5.

Chappell M., Godfrey K., Vajda S. (1990). Global identifiability of the parameters of nonlinear systems with specified inputs: A comparison of methods. Mathematical Biosciences, vol. 102, no 1, p. 41 - 73.

D’Andrea R., Dullerud G. (2003). Distributed control design for spatially interconnected systems. IEEE Transactions On Automatic Control, vol. 48, p. 1478-1495.

Dion J.-M., Commault C., Van Der Woude J. (2003). Generic properties and control of linear structured systems: a survey. Automatica, vol. 39, no 7, p. 1125 - 1144.

Gerdin M., Glad T., Ljung L. (2007). Global identifiability of complex models, constructed from simple submodels. Rapport technique. Automatic Control at Linkopings universitet(Sweden).

Guinzy N., Sage A. (1973). System identification in large scale systems with hierarchical structures. Computers and Electrical Engineering, vol. 1, no 1, p. 23 - 42.

Jedidi S. (2016). Preuve de l’identifiabilité structurelle d’un grand système de taille M. Rapport technique. CentraleSupélec. Consulté sur www.rennes.supelec.fr/ren/perso/rbourdai/Safa/RapportInterneJedidi.pdf

Ljung L., Glad T. (1994). On global identifiability for arbitrary model parametrizations. Automatica, vol. 30, no 2, p. 265 - 276.

Massioni P., Verhaegen M. (2008). Subspace identification of circulant systems. Automatica, vol. 44, no 11, p. 2825 - 2833.

Mesarovic M., Macko D., Takahara Y. (1970). Theory of hierarchical multi-level systems. Academic Press.

Morosan P., Bourdais R., Dumur D., Buisson J. (2010). Building temperature regulation using a distributed model predictive control. Energy and Buildings, vol. 42, no 9, p. 1445 - 1452.

Norton J. (1982). An investigation of the sources of nonuniqueness in deterministic identifiability. Math Biosciences, vol. 60, p. 89-108.

Perasso A. (2009). Identifiabilité de paramètres pour des systèmes décrits par des équations aux dérivées partielles : Application à la dynamique des populations. Thèse de doctorat non publiée, Université Paris-Sud XI.

Profos G., Delgado M. (1995). Identifiability of linear systems represented by Bond Graphs. In Proceedings of bond Graph modeling and simulation.

Siljak D. (1991). Decentralized control of complex system (vol. 184; G. I. o. T.William F. Ames, Ed.). Georgia Institute of Technology.

Van Den Hof P.M., Dankers A., Heuberger P. S., Bombois X. (2013). Identification of dynamic models in complex networks with prediction error methods. Automatica, vol. 49, no 10, p. 2994 - 3006.

Van Den Hof J. M. (1998). Structural identifiability of linear compartmental systems. IEEE Transactions on Automatic Control, vol. 43, no 6, p. 800-818.

Walter E. (1982). Identification of state space models. Springer Verlag.

Walter E. (1987). Identifiability of state space models. Springer Verlag.

Willems J. L. (1986). Structural controllability and observability. System and Control Letters, vol. 8, no 1, p. 5-12.