Classification of methods of identification

All variety of existing methods of identification can be classified to signs in which basis the basic elements of a problem of identification listed in the previous paragraph are put. Such signs, the kind of mathematical model and character of identified system, a way of reception of the experimental information on properties of system, a kind of criterion of affinity of system and model, volume of the aprioristic information on system are

On character of identified system distinguish identification ­ of linear and nonlinear systems, static and dynamic systems with the constant variable and distributed parametres,­ one-dimensional and multidimensional, continuous and discrete systems.

On a way of reception of experimental data distinguish active and passive methods of identification. At active ­ identification on a system input in advance chosen influence (pulse, step, harmonious, pseudo-casual etc. moves.). At passive, identifications are used the data received in the course of normal functioning of system.

According to the primary goal of identification - procedure of construction optimum in a sense mathematical model of system on realisations of its entrance and target signals - criteria of affinity of system and model should be set. The choice of this criterion is substantially defined ­ by the identification purpose,­ the requirements shown to estimations and volume of the aprioristic information on system and hindrances, present at ­ information transfer channels.

In most general statement such criterion is formed as some function (or функционал) a target error (are nonviscous), representing a difference between an exit - of system at (t) and an exit of model mind (t).

Thus the model exit is formed on the basis of data on in what class of functions to search for model. It means, that is necessary to have the analytical description of model to within final number of parametres. The identification problem параметри­зуется also does by such measure ­ possible use of various methods ­ of an estimation and the decision-making, developed in the mathematical statistics­. In particular, the widest application estimations by criteria of the least squares, the least weighed ­ squares, the maximum credibility and the minimum risk (байе­совские have found ­­ estimations). All listed estimations are ordered on ­ increase of volume of the initial information on object. Application of this or that criterion leads to acceptance of a method of identification by this criterion.

As an example we will consider criterion of the least squares

For the purpose of simplification of calculations we will put, that the system is static and its model looks like

yм (t) = Fм (uм (t), qм, 0),

Where qм - a vector of parametres of model; uм - entrance influence; yм (t) a-scalar exit of model. Besides, we will put, that system and model exits are observed during the discrete moments of time t1, t2... tN. Values of an exit of system and model during these moments of time we will designate at (1), at (2)... At (N) and mind (1), mind (2)... Mind (N) accordingly. Values of a vector of entrance influence and the resulted ­ error during the same discrete moments of time we will designate u (1), u (2)... u (N) and h (1), h (2)... h (N), accordingly.

TO = h^Т h =

In case a model exit - a vector it is necessary to make MM identification on all its components.

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