The author considers an inverse problem, i.e., the identification of the position-dependent leading coefficient appearing in elliptic ordinary differential equations (a scalar) and partial differential equations (a diagonal matrix). He examines the identification algorithm based on the substitution or comparison model method. As suggested by the method of stationarization, he models the algorithm by a nonlinear dynamical system, the state of which is the unknown coefficient. With reference to some inverse problems in one and two spatial dimensions in the continuum case, the state equations are obtained. The author determines the system's energy function, its decay rate, and the influence constraints have on it. He then considers the admissible equilibrium states. If an admissible coefficient, i.e., a solution to the inverse problem, exists, it is generally not unique: the (admissible) equilibrium state depends on the initial state and on a control term, some preliminary properties of which the author specifies in some special cases

Crosta, G. (1990). Energy Decay-Rates and Equilibrium State Properties for a Distributed-Parameter Identification Algorithm. In C.J. Herget, R.A. De Carlo, P.J. Antsaklis, Y. [...] Yamamoto, K.D. Young, S. Yurkovich, et al. (a cura di), Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) (pp. 1174-1177). I E E E [10.1109/CDC.1990.203788].

Energy Decay-Rates and Equilibrium State Properties for a Distributed-Parameter Identification Algorithm

CROSTA, GIOVANNI FRANCO FILIPPO
Primo
1990

Abstract

The author considers an inverse problem, i.e., the identification of the position-dependent leading coefficient appearing in elliptic ordinary differential equations (a scalar) and partial differential equations (a diagonal matrix). He examines the identification algorithm based on the substitution or comparison model method. As suggested by the method of stationarization, he models the algorithm by a nonlinear dynamical system, the state of which is the unknown coefficient. With reference to some inverse problems in one and two spatial dimensions in the continuum case, the state equations are obtained. The author determines the system's energy function, its decay rate, and the influence constraints have on it. He then considers the admissible equilibrium states. If an admissible coefficient, i.e., a solution to the inverse problem, exists, it is generally not unique: the (admissible) equilibrium state depends on the initial state and on a control term, some preliminary properties of which the author specifies in some special cases
Capitolo o saggio
inverse problems; leading coefficient; elliptic equation; minimisation; stationarisation; gradient flow;
English
Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6)
Herget, CJ; De Carlo, RA; Antsaklis, PJ; [...] Yamamoto, Y; Young, KD; Yurkovich, S; Zheng, YP
1990
3
I E E E
1174
1177
Crosta, G. (1990). Energy Decay-Rates and Equilibrium State Properties for a Distributed-Parameter Identification Algorithm. In C.J. Herget, R.A. De Carlo, P.J. Antsaklis, Y. [...] Yamamoto, K.D. Young, S. Yurkovich, et al. (a cura di), Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) (pp. 1174-1177). I E E E [10.1109/CDC.1990.203788].
none
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/93665
Citazioni
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
Social impact