Analytical Synthesis of Guaranteed Estimation Algorithms of Dynamic Process States

Bakan, Gennadiy M.

doi:10.1615/jautomatinfscien.v35.i5.30

Cited by 3 publications

(5 citation statements)

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“…In the sequel we assume that there is uncertainty in ( * ) if distributions of random elements or some deterministic parameters of the system are partially unknown. An up to date description of the state of the art in the theory of uncertain estimation problems with special ℓ, L, H, B, D in special spaces is to be found at [1,2,3,4,5,6]. Classical theory of uncertain estimation problems [1,3,4] works well when the linear mapping L in ( * ) has bounded inverse mapping.…”

Section: Introductionmentioning

confidence: 99%

State estimation for a dynamical system described by a linear equation with unknown parameters

Zhuk

2009

Ukr Math J

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519.962.22 We investigate the state estimation problem for a dynamical system described by a linear operator equation with unknown parameters in a Hilbert space. In the case of quadratic restrictions on the unknown parameters, we propose formulas for a priori mean-square minimax estimators and a posteriori linear minimax estimators. A criterion for the finiteness of the minimax error is formulated. As an example, the main results are applied to a system of linear algebraic-differential equations with constant coefficients.

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Section: Introductionmentioning

confidence: 99%

State estimation for a dynamical system described by a linear equation with unknown parameters

Zhuk

2009

Ukr Math J

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“…According to this the linear uncertain estimation problem is said to be minimax if the class of estimations ℓ(ϕ) is restricted to all linear functions (u, y) + c of y and the criteria is set to be the minimum of the worst-case error. A description of the state of the art in the theory of linear uncertain minimax estimation problems with special ℓ, L, H, B, D in special spaces is to be found at [26,27,28,29,30,31,32,33,34].…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

Set-membership state estimation framework for uncertain linear differential-algebraic equations

Zhuk

2008

Preprint

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We investigate a state estimation problem for the dynamical system described by uncertain linear operator equation in Hilbert space. The uncertainty is supposed to admit a set-membership description. We present explicit expressions for linear minimax estimation and error provided that any pair of uncertain parameters belongs to the quadratic bounding set. We introduce a new notion of minimax directional observability and index of noncausality for linear noncausal DAEs. Application of these notions to the state estimation problem for linear uncertain noncausal DAEs allows to derive new minimax recursive estimator for both continuous and discrete time. We illustrate the benefits of non-causality of the plant applying our approach to scalar nonlinear set-membership state estimation problem. Numerical example is presented.

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“…In particular, the load on a node of a Grid system can be described by the model of a linear control object with unknown perturbations, and uncertainties can be represented using the set-theoretic approach [3][4][5]. To represent boundary values of unknowns, the estimation is based on fuzzy ellipsoidal sets [6].…”

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confidence: 99%

“…According to (2) and (3), FEs of a Grid node are characterized by parameter vectors. According to (3), the parameter vector for processors x proc has the form x proc…”

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confidence: 99%

“…Since the Grid system is characterized by the parameter vector according to (5) and (6), to describe its operation, it is expedient to use a more adequate model of the control object in a vector state space with unknown perturbations, which remains in the class of linear models. To estimate the state of a such model under nonstatistical uncertainty, it is expedient to use the set-theoretic approach [5] such as ellipsoidal estimation [3,4]. In the absence of reliable a priori information on the values being estimated, it is proposed to construct fuzzy set estimates of unknown vectors [12].…”

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Model identification and state estimation in grid systems

Lavrenyuk

Shelestov

2009

Cybern Syst Anal

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Depending on the problem statement and av ailable information on the system structure and order, three classes of models are discussed: a linear model of state variables with unknown disturbance, a model in input-output variables, and a neural network model that describes nonlinear objects. To estimate the state and to identify the models, intelligent computations are applied: non-static uncertainty is described using fuzzy sets, and genetic algorithms are used for the structural-parametric identification of input-output models. Keywords: Grid system, model identification, generalized vector of system parameters, structural-functional analysis, fuzzy ellipsoidal sets, neural network model.Introduction. An optimization problem for a Grid system treated as a control object under uncertainty subject to identification and estimation methods and feedback-based control is formulated as job scheduling; to this end, current state of a distributed system and loading of resources should be estimated. Note that control theory has not been used till now to develop and analyze Grid systems since such systems are complex and hierarchical, which hampers their strict analytic description. Among the literary, only several studies that deal with the application of control theory to model the load and to schedule computations in a Grid medium are available. For example, one of them apply Kalman's filter to estimate states of a linear model of a Grid system [1].We will propose models of such systems based on the results of structural-functional analysis (SFA) obtained in [2] to describe functioning of different Grid resources. In particular, the load on a node of a Grid system can be described by the model of a linear control object with unknown perturbations, and uncertainties can be represented using the set-theoretic approach [3][4][5]. To represent boundary values of unknowns, the estimation is based on fuzzy ellipsoidal sets [6]. To describe the operation of a Grid system or its segment and to make a more complete allowance for performance parameters, a cybernetic approach to modeling is proposed, where the system is considered as a "black box" and is described by a neural network model in view of the nonlinearity. For the adaptivity and robustness of the identification of matrices of weight coefficients, the method of the recurrent estimation of parameters of this model is used [7]. Problems of Estimating the States and Parameters of Components of the Structural Model of a GridSystem. The studies [2,8] have considered a Grid-system SFA problem for Earth observation (EOGrid) and have obtained a formal description of such a system. Note that structural decomposition without constraint of generality can be applied to Grid systems. It is in such a context that the present paper should be considered. Figure 1 shows the result of the structural decomposition of the system. The number of parameters of functional elements (FEs) of all the hierarchy levels of the system (system in the large, segments, nodes, and components) is defined by

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Analytical Synthesis of Guaranteed Estimation Algorithms of Dynamic Process States

Cited by 3 publications

References 0 publications

State estimation for a dynamical system described by a linear equation with unknown parameters

State estimation for a dynamical system described by a linear equation with unknown parameters

Set-membership state estimation framework for uncertain linear differential-algebraic equations

Model identification and state estimation in grid systems

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