Extended Global Total Least Square Approach to Multiple-Model Identification

Vinsonneau, B.; Goodall, D.P.; Burnham, Keith J.

doi:10.3182/20050703-6-cz-1902.00144

Cited by 6 publications

(11 citation statements)

References 6 publications

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“…In the sequel, this multiple model is called the heterogeneous multiple model. The previously quoted works have illustrated successful implementations of this structure for modelling (Venkat et al, 2003;Vinsonneau et al, 2005;Orjuela et al, 2006), control (Gawthrop, 1995;Gatzke and Doyle III, 1999;Gregorčič and Lightbody, 2000) or state estimation and diagnostic (Kanev and Verhaegen, 2006;Uppal et al, 2006;Orjuela et al 2008;2009) and have shown its relevance. Hence, this kind of multiple model can be used as an interesting alternative to the homogeneous multiple model.…”

Section: R Orjuela Et Almentioning

confidence: 99%

“…This kind of multiple model, initially proposed by Filev (1991), is reported in the literature under several designations, such as the local-state local model network (Gawthrop, 1995), the multiple local models (Gatzke and Doyle III, 1999;Venkat et al, 2003;Vinsonneau et al, 2005), local model networks by blending the outputs (Gregorčič and Lightbody, 2000;, multiple model for models with a non-common state (Kanev and Verhaegen, 2006), the neuro-fuzzy decoupling multiple model scheme (Uppal et al, 2006) and the recently decoupled multiple model (Orjuela et al, 2006;2009). Despite their different names, these approaches share a similar multiple model structure.…”

Section: R Orjuela Et Almentioning

confidence: 99%

“…This feature also offers the possibility to apply model order reduction techniques to the submodels to reduce the global model complexity. It can be noticed that other multiple model structures can be obtained by blending the inputs of the submodels instead of the outputs (Vinsonneau et al, 2005) or by blending both of them.…”

Section: Heterogeneous Multiple Model Structurementioning

confidence: 99%

“…However, a large number of experiments are necessary to obtain independent data sequences for submodel identification. Vinsonneau et al (2005) perform the identification of heterogeneous multiple model with blended inputs with a global total least square technique. In this section, multiple model identification mainly deals with submodel parameter estimation θ i in (1).…”

Section: Parametric Identification Problemmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear system identification using heterogeneous multiple models

Orjuela¹,

Marx²,

Ragot³

et al. 2013

International Journal of Applied Mathematics and Computer Science

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Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, with the heterogeneous multiple model being of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not the same and consequently they can be of various dimensions. Thanks to this feature, the complexity of the submodels can be well adapted to that of the nonlinear system introducing flexibility and generality in the modelling stage. This paper deals with off-line identification of nonlinear systems based on heterogeneous multiple models. Three optimisation criteria (global, local and combined) are investigated to obtain the submodel parameters according to the expected modelling performances. Particular attention is paid to the potential problems encountered in the identification procedure with a special focus on an undesirable phenomenon called the no output tracking effect. The origin of this difficulty is explained and an effective solution is suggested to overcome this problem in the identification task. The abilities of the model are finally illustrated via relevant identification examples showing the effectiveness of the proposed methods.

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Section: R Orjuela Et Almentioning

confidence: 99%

Section: R Orjuela Et Almentioning

confidence: 99%

Section: Heterogeneous Multiple Model Structurementioning

confidence: 99%

Section: Parametric Identification Problemmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear system identification using heterogeneous multiple models

Orjuela¹,

Marx²,

Ragot³

et al. 2013

International Journal of Applied Mathematics and Computer Science

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show abstract

“…The used model, known as decoupled multiple model, has been suggested in [4] and results of the association of submodels only in the output equation of the multiple model. Note also that this multiple model has been successfully employed in modelling [10], [11], control [12]- [14] and state estimation [15], [16] of nonlinear systems. The main feature of the decoupled multiple model is that submodels of different dimensions (e.g.…”

Section: Introductionmentioning

confidence: 99%

Proportional-Integral observer design for nonlinear uncertain systems modelled by a multiple model approach

Orjuela

Marx

Ragot

et al. 2008

2008 47th IEEE Conference on Decision and Control

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In this paper, a decoupled multiple model approach is used in order to cope with the state estimation of uncertain nonlinear systems. The proposed decoupled multiple model provides flexibility in the modelling stage because the dimension of the submodels can be different and this constitutes the main difference with respect to the classically used multiple model scheme. The state estimation is performed using a Proportional Integral Observer (PIO) which is well known for its robustness properties with respect to uncertainties and perturbations. The Lyapunov second method is employed in order to provide sufficient existence conditions of the observer, in LMI terms, and to compute the optimal gains of the PIO. The effectiveness of the proposed methodology is illustrated by a simulation example.

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On the simultaneous state and unknown input estimation of complex systems via a multiple model strategy

Orjuela

Marx

Ragot

et al. 2009

IET Control Theory Appl.

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This paper addresses the analysis and design of unknown input observer in order to provide both state and unknown input estimation of complex systems modelled with the help of a particular class of multiple model. The proposed observer uses the multi-integral strategy successfully employed in the classic linear control theory and known for its robustness properties. The observer design is based on the representation of the system via a multiple model, known as decoupled multiple model. This structure of multiple model allows to use submodels with different number of states and this fact constitutes the main advantage of the proposed observer with respect to the classic multiple model structure where the submodels have the same dimension. It is shown how the gains of the suggested observer can be obtained by solving a LMI optimal problem. An academic example is also proposed in order to illustrate the proposed methodology.

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Extended Global Total Least Square Approach to Multiple-Model Identification

Cited by 6 publications

References 6 publications

Nonlinear system identification using heterogeneous multiple models

Nonlinear system identification using heterogeneous multiple models

Proportional-Integral observer design for nonlinear uncertain systems modelled by a multiple model approach

On the simultaneous state and unknown input estimation of complex systems via a multiple model strategy

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