Identification problem

for multidimensional, multiconnected objects of control

V.N.Tibabishev, S.V.Tibabishev

N.E.Bauman MSTU

Solving identification problem for dynamic responses by the data of passive experiment one should take into account that stochastic processes can describe motions only with restricted velocity and only with restricted acceleration. If stochastic processes are supposed to belong to Hilbert space L₂(-¥, +¥), then imposition of these restrictions results in a subspace of stochastic processes for which active part of spectrum is concentrated in the field of low frequencies, and this complicates solution of identification problem.

Input signals observed during normal operation of multidimensional and multiply connected object of control are usually mutually correlated. Mathematical model of such signals can be presented, for example, in the form of a sum of absolutely independent and completely dependent stochastic processes.

If the number of inputs exceeds the number of outputs then it is impossible to obtain a consistent system of integral equations of the first kind for solution of identification problem of dynamic responses for all channels of multidimensional and multiply connected objects of control in the class of linear steady models even at precise input data.

If the number of inputs is equal to the number of outputs, then identification problem is formally reduced to solution of a system of Wiener-Hopf integral operator defined in Hilbert space L₂(-¥, +¥), is an unbounded operator.

Identification problem for dynamic responses of any allocated channel of multidimensional and multiply connected object of control in the class of linear steady models is simplified and reduced to solution of one integral equation of the first kind, if the signals at outputs of filters of independent components of all input signals are used. Such filtration of all input signals is implemented in identification method which we denote as ASVT51. Submitted identification method is restricted in application to cases, when: for observed stochastic processes the noises induced by substitution of frequencies are completely blocked; implementations of observed signals are synchronously recorded in observation interval, when the system's own motion in control channels can be neglected; normalized mutual correlation coefficients between all input signals by absolute value are less than unit. Information on the method see at http://asvt51.narod.ru/.