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MIMO-systems identification by minimum error bounds
120
Abstracts
models have distinct advantages. The data investigated corresponds to aircraft fright flutter, which is a state when an aircraft component starts to oscillate.
010 On the i a t i o n
of DiscRete Parameters in Linear
Linear models are by far the most commonly used approach for describing physical signals and systems. However, in many applications a linear model is adequate only if some information of a discrete nature is available. This paper presents a general problem formulation and some optimal eatimatom for discrete parameters in linear systems. A survey is # y e n of proposed algodthn~ in a number of applications. The objective of the present work is to discuss the problem of discrete parameters in a general framework, relating the proposed statistical methods and their .a~pmximations at a higher level of abstraction, to reveal the ioeag.
011
H. ~ ,
pp51-54
Preproccssing performed in some "optimal" fashion on data received by a uniform linear sensor array is shown to improve the pedotmmace of Eigen-based techniques for parameter estimation and detection. For the sake of generality, it is assumed that a coherency class exists in the observed process. The optimal filters for both detection and parameter estimation are derived and applied to the received d~tA=
012 N4SID: N
~
Aigeritiuas for /
Slmee Suhslmee
s y m m ldeatinentlan P. Van Overschee,B. De Moor, pp 55-58 This paper presents a new dynamic system-identification algorithm. In this new framework, the concept of a "state" is emphasised.
016 Identification and A ~ l m e n t of Rda~ve Degrees and Zero D!mmics Uatae Bend Graphs S.-T. Wa, K. Yoncef-Temai, pp 71-74 In the design of output tracking controllers, the relative degree and the stability of the zero dynamics of the control plant are usually assumed to be known in advance. This paper shows how relative degrees and zero dynamics me related to the physical structures, with the help of bond graphs. A set of roles is proposed to determine the relative degree and the sta~lity of the zero dynamics for a class of systems, independent of the system dynamic equations. The roles establish a connection between these system properties and the physical structures, and are useful for the purIx~e of control design. 017 On the Use of Regulartzation in System Identification J. SJ(Iberg,T. MeKelvey, L. I4'ung, pp 75-80 Regularlzafion is a standard statistical technique to deal with illconditioned p a r a m e t e r - i o n problems. It reduces the variance error of a model, but at the same time it introduces a bias. The familiar trade-off between bias and variance error for the choice of model order/structure can therdore he discussed in terms of the regularization l~xameter. The well-known problem of parametedzing multivarinble systems can he dealt with using overparameterization plus regnlurization. A characteristic feature of this method is that it is an easy and "automatic" way of finding the important parameters and good parameterization. No statistical penalty is paid, but there is a higher computational burden. 018 A Principle for System Identification in the Behavioeenl Ft.amewerk E. Weyer, R.C. Wflthanson, I.M.Y. Mareels, pp 81-84 This paper proposes and investigates a principle for system identification in the behavioural framework. In the bchavionral framework a system is defined as a set of trajectories, using risk minimisation methods. Subsequently, the identified trajectories are used in an exact modelling procedure due to Antoulas and Willems (1992). The modelling procedure Oves all the linear, time-invariant, continuous-time systems that could have generated the identified trajectories. 019 MIMO-Systems Idemiflcation by Minimum Error Bounds T J j . Van Den Boom, pp 85-88
Several techniques for estimating frequency are discussed. The fixed block length algorithms treat frequency as being fixed over short lengths of time, while two algorithms are descnhed which are able to update the estimate of frequency with each new time measurement. The concepts of accuracy and resolution are discussed in some detail.
In this paper a system identification procedure for MIMO-systems is presented, that yidds a model with bounded e~ror. Various model error structures (additive, multiplicadve or coprime factor) are considered. The input and output noise are assumed to be bounded in the frequency domain. An upper bound for the model error is derived, using measured data and knowledge about the noise. The model error bound can be minimized in an Hv-norm sense by tuning the model parameters. The choice of a linear parametriz~'on will lead to a convex optimization problem, and the algorithms will be robustly convergent.
014 Performance of Subqmce Based State-Space System Idmtiflcatlon M e t h o d s M. Vlberg, B. O t t e r , . n , B. Wahlberg, L. l ~ m ~ pp 63-65
020 Quantification of Uncertainty in Transfer Function Entimati~: A Mixed Determ~istic-Probabil~c Apprmch D.K. De Vrles, P.M.J. Van Den HOf, pp 89.92
Traditional prediction-error techniques for multivafiable system identification require canonical descriptions using a l~ge number of tmameters. This problem can be avoided using suhsgmce-based methods, since these estimate a state-space model directly from the data. The main computations consist of a QR-decomposition and a singular-value decomposition. Here, a suhspace-based technique for identifying general fiuite-dimensional linear systems is presented and analyzed. The technique is applicable to general noise covariance structures. Explicit formulas for the asymptotic pole-estimation error variances are given. The proposed method is found to perform comparably to a prediction error method in a simple example.
A procedure is presented to obtain an estimate of the transfer function of a linear system together with a confidence interval, using only limited a priori information. By applying Bartlett's procedure of periodogram averaging to the non-parametric empirical transfer function estimate, and by employing a periodic input signal, the statistics of the resulting estimate can be asymptotically obtained from the data. The model error consists of two parts: a probabilistic part, due to the stochastic noise disturbance on the data, and a deterministic part, due to the bias in the estimate. For this analysis only minor assumptions are made on the distribution of the noise.
013 F ~ u e n c y i ~ o n ~. H ~
D. H u n g , ~ G . ~ n n ;
~ 59-62
0Lq Determining Model Uncertainty of Identified Models for
Rebtm Central D e a n
021 Worst-Case Systan Identification in H~: Error Bounds
i
oti=a Mi
IlG. Hakveort, pp 93-96
IlL. Kemt, pp 6%70 The problem of identifying a model set for use in robust control design is formulated, and some promising new techniques are reviewed.
An identification procedure is developed which yields an upper bound for the Hoo-norm of the model error for a Oven nominal model, using measurement data and a priori information consisting of a time-domain bound on the noise, and information about the
Abstracts
models have distinct advantages. The data investigated corresponds to aircraft fright flutter, which is a state when an aircraft component starts to oscillate.
010 On the i a t i o n
of DiscRete Parameters in Linear
Linear models are by far the most commonly used approach for describing physical signals and systems. However, in many applications a linear model is adequate only if some information of a discrete nature is available. This paper presents a general problem formulation and some optimal eatimatom for discrete parameters in linear systems. A survey is # y e n of proposed algodthn~ in a number of applications. The objective of the present work is to discuss the problem of discrete parameters in a general framework, relating the proposed statistical methods and their .a~pmximations at a higher level of abstraction, to reveal the ioeag.
011
H. ~ ,
pp51-54
Preproccssing performed in some "optimal" fashion on data received by a uniform linear sensor array is shown to improve the pedotmmace of Eigen-based techniques for parameter estimation and detection. For the sake of generality, it is assumed that a coherency class exists in the observed process. The optimal filters for both detection and parameter estimation are derived and applied to the received d~tA=
012 N4SID: N
~
Aigeritiuas for /
Slmee Suhslmee
s y m m ldeatinentlan P. Van Overschee,B. De Moor, pp 55-58 This paper presents a new dynamic system-identification algorithm. In this new framework, the concept of a "state" is emphasised.
016 Identification and A ~ l m e n t of Rda~ve Degrees and Zero D!mmics Uatae Bend Graphs S.-T. Wa, K. Yoncef-Temai, pp 71-74 In the design of output tracking controllers, the relative degree and the stability of the zero dynamics of the control plant are usually assumed to be known in advance. This paper shows how relative degrees and zero dynamics me related to the physical structures, with the help of bond graphs. A set of roles is proposed to determine the relative degree and the sta~lity of the zero dynamics for a class of systems, independent of the system dynamic equations. The roles establish a connection between these system properties and the physical structures, and are useful for the purIx~e of control design. 017 On the Use of Regulartzation in System Identification J. SJ(Iberg,T. MeKelvey, L. I4'ung, pp 75-80 Regularlzafion is a standard statistical technique to deal with illconditioned p a r a m e t e r - i o n problems. It reduces the variance error of a model, but at the same time it introduces a bias. The familiar trade-off between bias and variance error for the choice of model order/structure can therdore he discussed in terms of the regularization l~xameter. The well-known problem of parametedzing multivarinble systems can he dealt with using overparameterization plus regnlurization. A characteristic feature of this method is that it is an easy and "automatic" way of finding the important parameters and good parameterization. No statistical penalty is paid, but there is a higher computational burden. 018 A Principle for System Identification in the Behavioeenl Ft.amewerk E. Weyer, R.C. Wflthanson, I.M.Y. Mareels, pp 81-84 This paper proposes and investigates a principle for system identification in the behavioural framework. In the bchavionral framework a system is defined as a set of trajectories, using risk minimisation methods. Subsequently, the identified trajectories are used in an exact modelling procedure due to Antoulas and Willems (1992). The modelling procedure Oves all the linear, time-invariant, continuous-time systems that could have generated the identified trajectories. 019 MIMO-Systems Idemiflcation by Minimum Error Bounds T J j . Van Den Boom, pp 85-88
Several techniques for estimating frequency are discussed. The fixed block length algorithms treat frequency as being fixed over short lengths of time, while two algorithms are descnhed which are able to update the estimate of frequency with each new time measurement. The concepts of accuracy and resolution are discussed in some detail.
In this paper a system identification procedure for MIMO-systems is presented, that yidds a model with bounded e~ror. Various model error structures (additive, multiplicadve or coprime factor) are considered. The input and output noise are assumed to be bounded in the frequency domain. An upper bound for the model error is derived, using measured data and knowledge about the noise. The model error bound can be minimized in an Hv-norm sense by tuning the model parameters. The choice of a linear parametriz~'on will lead to a convex optimization problem, and the algorithms will be robustly convergent.
014 Performance of Subqmce Based State-Space System Idmtiflcatlon M e t h o d s M. Vlberg, B. O t t e r , . n , B. Wahlberg, L. l ~ m ~ pp 63-65
020 Quantification of Uncertainty in Transfer Function Entimati~: A Mixed Determ~istic-Probabil~c Apprmch D.K. De Vrles, P.M.J. Van Den HOf, pp 89.92
Traditional prediction-error techniques for multivafiable system identification require canonical descriptions using a l~ge number of tmameters. This problem can be avoided using suhsgmce-based methods, since these estimate a state-space model directly from the data. The main computations consist of a QR-decomposition and a singular-value decomposition. Here, a suhspace-based technique for identifying general fiuite-dimensional linear systems is presented and analyzed. The technique is applicable to general noise covariance structures. Explicit formulas for the asymptotic pole-estimation error variances are given. The proposed method is found to perform comparably to a prediction error method in a simple example.
A procedure is presented to obtain an estimate of the transfer function of a linear system together with a confidence interval, using only limited a priori information. By applying Bartlett's procedure of periodogram averaging to the non-parametric empirical transfer function estimate, and by employing a periodic input signal, the statistics of the resulting estimate can be asymptotically obtained from the data. The model error consists of two parts: a probabilistic part, due to the stochastic noise disturbance on the data, and a deterministic part, due to the bias in the estimate. For this analysis only minor assumptions are made on the distribution of the noise.
013 F ~ u e n c y i ~ o n ~. H ~
D. H u n g , ~ G . ~ n n ;
~ 59-62
0Lq Determining Model Uncertainty of Identified Models for
Rebtm Central D e a n
021 Worst-Case Systan Identification in H~: Error Bounds
i
oti=a Mi
IlG. Hakveort, pp 93-96
IlL. Kemt, pp 6%70 The problem of identifying a model set for use in robust control design is formulated, and some promising new techniques are reviewed.
An identification procedure is developed which yields an upper bound for the Hoo-norm of the model error for a Oven nominal model, using measurement data and a priori information consisting of a time-domain bound on the noise, and information about the