Identification of multi-input systems: variance analysis and input design issues

Gevers, Michel; Mišković, Ljubiša; Bonvin, Dominique; Karimi, Alireza

doi:10.1016/j.automatica.2005.12.017

Cited by 48 publications

(27 citation statements)

References 11 publications

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“…Question 4 has been addressed in [8] where it is shown that, when identification cannot be performed using noise excitation only, this does not imply that all reference inputs must be excited. The effect on the covariance of the estimated parameters of applying excitation at one or more entry points has been examined in [5] for open loop identification and in [9] for closed-loop identification.…”

Section: Introductionmentioning

confidence: 99%

“…It was driven by the recent surge of interest in the question of experiment design, itself triggered by the new concept of least costly identification experiment for robust control [2], [3], [4], [5]. Briefly speaking, least costly experiment design for robust control refers to achieving a prescribed accuracy of the estimated model at the lowest possible price, which is typically measured in terms of the duration of the identification experiment, the perturbation induced by the excitation signal, or any combination of these.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Identification and the Information Matrix: How to Get Just Sufficiently Rich?

Gevers

Bazanella

Bombois

et al. 2009

IEEE Trans. Automat. Contr.

133

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Abstract-In prediction error identification, the information matrix plays a central role. Specifically, when the system is in the model set, the covariance matrix of the parameter estimates converges asymptotically, up to a scaling factor, to the inverse of the information matrix. The existence of a finite covariance matrix thus depends on the positive definiteness of the information matrix, and the rate of convergence of the parameter estimate depends on its "size". The information matrix is also the key tool in the solution of optimal experiment design procedures, which have become a focus of recent attention. Introducing a geometric framework, we provide a complete analysis, for arbitrary model structures, of the minimum degree of richness required to guarantee the nonsingularity of the information matrix. We then particularize these results to all commonly used model structures, both in open loop and in closed loop. In a closed-loop setup, our results provide an unexpected and precisely quantifiable trade-off between controller degree and required degree of external excitation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Identification and the Information Matrix: How to Get Just Sufficiently Rich?

Gevers

Bazanella

Bombois

et al. 2009

IEEE Trans. Automat. Contr.

133

View full text Add to dashboard Cite

show abstract

“…For identification the choice of excitation signals and patterns for MIMO identification is known to be critical (Gevers et al, 2006). Figure 7 presents the applied identification input signals as well as the measured system outputs.…”

Section: Implementation Of Multi-linear Mpcmentioning

confidence: 99%

A Design Framework for Predictive Engine Control

Wang

Waschl

Alberer

et al. 2011

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Résumé -Un cadre de conception pour la commande prédictive de moteurs -La commande prédictive par modèle (Model Predictive Control ; MPC) a été proposée plusieurs fois dans l'automatique pour l'automobile, avec des résultats prometteurs, principalement à partir d'une approche MPC linéaire. Toutefois, comme la plupart des systèmes automobiles sont non linéaires, la commande prédictive non linéaire (Nonlinear MPC ; NMPC) pourrait représenter une option intéressante. Malheureusement, la conception d'une commande optimale à partir d'un modèle non linéaire générique conduit généralement à un problème non convexe complexe. Dans ce contexte, cet article présente deux schémas différents pour prendre en compte la non linéarité du système en vue de la conception de la commande. En premier lieu, une méthode MPC multilinéaire est présentée sur la base d'une segmentation du système et, en second lieu, une conception de système de commande basée sur une identification de système non linéaire utilisant une structure quasi linéaire à paramètres variants (Linear Parameter Varying ; LPV) est proposée ; celle-ci est alors utilisée dans un cadre de conception de NMPC. Cet article présente ces approches et leur application à un système bien connu, le module d'air (air path) d'un moteur Diesel. Abstract -A Design Framework for Predictive Engine Control -Model Predictive Control (MPC) has been proposed several times for automotive control, with promising results, mostly based on a linearMPC approach. However, as most automotive systems are nonlinear, Nonlinear MPC (NMPC) would be an interesting option. Unfortunately, an optimal control design with a generic nonlinear model usually leads to a complex, non convex problem. Against this background, this paper presents two different schemes to take into account the system nonlinearity in the control design. First, a multi-linear MPC method is shown based on the segmentation of the system and then a control system design based on a nonlinear system identification using a quasi Linear Parameter Varying (LPV) structure is proposed, which is then used in a NMPC design framework. This paper presents the approaches and the application to a well studied system, the air path of a Diesel engine.

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“…A priori information also affects the choice of sensors and the design of input signal excitation. The paper Gevers et al (2006) gives a thorough variance analysis for identification of multi-input systems, together with its implications for input design, while Dayal and MacGregor (1997) consider multi-output process identification. The paper Wahlberg et al (2009a) analyzes variance properties of cascade systems with three subsystems.…”

Section: Introductionmentioning

confidence: 99%

On Identification of Parallel Cascade Serial Systems

Hägg

Wahlberg

2011

IFAC Proceedings Volumes

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We consider identification of systems with a parallel serial (cascade) structure with multiple-input and multiple-output signals. The statistical properties of estimated models are studied with respect to input signals and possible sensor locations. The quality of the estimates are analyzed by means of the asymptotic covariance matrix of the estimated parameters. This is an extension of previous work on identification of cascaded linear systems. The key result concerns systems where the sub-systems have common dynamics. An interesting observation is that for this case the variance for the parameters belonging to the unmeasured subsystem always is larger than for the other sub-systems. This is not true for general parameters. The variance results can be used for optimal input and sensor location design. The results are illustrated by some simple FIR examples and numerical evaluations.

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Identification of multi-input systems: variance analysis and input design issues

Cited by 48 publications

References 11 publications

Identification and the Information Matrix: How to Get Just Sufficiently Rich?

Identification and the Information Matrix: How to Get Just Sufficiently Rich?

A Design Framework for Predictive Engine Control

On Identification of Parallel Cascade Serial Systems

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