Model identification and state estimation in grid systems

Abstract

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