ISSN:0890-6327    

DOI:10.1002/acs.4480080101

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractWhen the error between the data and the corresponding model output is affine in the parameters to be estimated, the set § of all values of the parameter vector that are feasible (in the sense that the error between the model and the data falls within known prior bounds) is a convex polyhedron, or even a convex polytope if the regressors span the parameter space. Although most of the literature on parameter bounding has been concerned with finding simple‐shaped sets (ellipsoids or boxes) guaranteed to contain §, methods have also been developed that make it possible to characterize this polytope exactly and recursively as the convex combination of its vertices. the basic principles of this approach are explained and the results obtained are illustrated. For time‐varying systems a new simple policy is suggested to expand the previous polytope before intersecting it with the feasible region corresponding to the new datum. This policy allows algorithms developed for time‐invariant systems to be used without any modification. When no reliable bounds are available for the error, an extension of the exact description approach is suggested. This makes it possible to obtain the minimax estimate of the parameters exactly and recursively. As a byproduct, the polyhedral cone obtained contains all values of § that would be obtained if a bound larger than the minimax bound were assumed for the absolute value of t

ISSN:0890-6327    

DOI:10.1002/acs.4480080102

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractIn bounded‐error estimation one is interested in characterizing the set § of all values of the parameters of a model which are consistent with the data in the sense that the corresponding errors fall between known prior bounds. the problem treated here is the computation of aminimal volume ellipsoidguaranteed to contain §. Although this ellipsoidal approach to parameter bounding was initially applied to models linear in their parameters, where the only error to be accounted for was an output error, it can be extended to deal with errors‐in‐variables problems. This makes it possible to consider models nonlinear in their parameters or dynamical models where both inputs and outputs are subject to bounded errors.Recursivealgorithms are considered first. the basic algorithm of Fogel and Huang (1982), developed from the seminal work of Schweppe (1973) and modified as suggested by Belforte and co‐workers (1985, 1990), is derived in detail, which makes it possible to clarify the nature of the tests needed. This algorithm is proved to be mathematically equivalent to arecursively optimalalgorithm independently developed by Todd (1980) and König and Pallaschke (1981) in the context of linear programming after the celebrated work of Khachiyan (1979). A recursive approach, also developed in this context, is suggested for errors‐in‐variables problems. Recursively optimal ellipsoids, however, are not globally optimal because of the approximations committed at each step. Using a methodology borrowed from experiment design, we obtain optimality conditions which can be used to derive a number of algorithms guaranteed to converge to the

ISSN:0890-6327    

DOI:10.1002/acs.4480080103

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractThe use of a dead zone and a bounding ellipsoid for parameter estimation when measurement errors are bounded is discussed. the size of the dead zone is set to be exactly equal to the assumed noise bound. The algorithm retains the properties of computing parameter point estimates and allows a bounding ellipsoid to be computed at each iterative step.

ISSN:0890-6327    

DOI:10.1002/acs.4480080104

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractA general class of optimal bounding elipsoid (OBE) algorithms, including all methods published to date, is unified into a single framework called theunified OBE (UOBE)algorithm. UOBE is based on generalized weighted recursive least squares in which very broad classes of ‘forgetting factors’ and data weights may be employed. Different instances of UOBE are distinguished by their weighting policies and the criteria for determining optimal weight values.A study of existing OBE algorithms, with a particular interest in the trade‐off between algorithm performance interpretability and convergence properties, is presented. Results suggest that an interpretable, converging UOBE algorithm will be found. In this context a new UOBE technique, theset membership stochastic approximation (SM‐SA)algorithm, is introduced. SM‐SA possesses interpretable optimization measures and known conditions under which its pointestimator

ISSN:0890-6327    

DOI:10.1002/acs.4480080105

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractA bank of recursive least‐squares (RLS) estimators is proposed for the estimation of the uncertainty intervals of the parameters of an equation error model (or RLS model) where the equation error is assumed to lie between known upper and lower bounds. It is shown that the off‐line least‐squares method gives the maximum and minimum parameter values that could have produced the recorded input‐output sequence. By modifying the RLS estimator in two ways, it is possible to recursively compute inner and outer bounds of the uncertainty intergals. It is shown that the inner bound is asymptoticall

ISSN:0890-6327    

DOI:10.1002/acs.4480080106

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper shows how bounded‐error on‐line estimation algorithms can be applied in the context of parameter identification of mechanical structures. the modified exponentially weighted recursive least‐squares (MEW‐RLS) estimation algorithm proposed by Canudas de Wit and Carrillo is used in connection with models of mechanical systems with state‐dependent disturbances. These disturbances are provoked on one hand by simplified friction models and on the other hand by the particular model formulation of the multivariable Lagrange mechanical systems.A prioriknowledge on the physics of these systems is used to derive upper bounds on the model disturbances, which are needed for the application of the

ISSN:0890-6327    

DOI:10.1002/acs.4480080107

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper gives a concise description of effective solutions to the guaranteed state estimation problems for dynamic systems with uncertain items being unknown but bounded. It indicates a rather unconventional, rigorous theory for these problems based on the notion of evolution equations of the ‘funnel’ type which could be further transformed ‐ throughexactellipsoidal representations ‐ into algorithmic procedures that allow effective simulation, particularly with computer graphics. the estimation problem is also interpreted as a problem of tracking a partially known system under incomplete measurements.Mathematically, the technique described in this paper is based on a theory of set‐valued evolution equations with the approximation of solutions formulated in terms of set‐valued calculus by ellipsoidal‐val

ISSN:0890-6327    

DOI:10.1002/acs.4480080108

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractA class of linear and time‐invariant large‐scale systems under unknown input signals and measurement errors is considered. No assumptions about statistical properties of the unknown quantities are made. the uncertainty is modelled through bounds that define ellipsoids in which lie unknown initial conditions and unknown ellipsoidal tubes containing signal trajectories. the state estimation problem consists of determining on‐line the smallest sets in the state space in which the unknown system state lies. Two hierarchical estimation algorithms are proposed and compared, namely the ‘completely decentralized with interaction measurements’ (CDIM) algorithm and the two‐level hierarchical with interaction measurements (THIM) algorithm. the THIM algorithm leads to smaller estimating sets owing to additional co‐ordinator‐le

ISSN:0890-6327    

DOI:10.1002/acs.4480080109

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY