COST CONTROL ESTIMATION FOR HARMONIC EXOGENOUS ACTIONS: GRAMIAN APPROACH

D. . Biryukov, A. V. Ushakov


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Abstract

The problem of cost control estimation for the harmonic exogenous actions (HEA) is solved based on gramian approach. This approach was formed within the limits of modern control theory and gives the opportunity to calculate the steady output of the system by means of initial state vector and conformity matrix. This approach analytically determines direct connection between steady output of technical object (TO) motion as a part of produced system with source initial state vector, and this connection is realized by similarity matrix which is the solution of Silvester equation at that. The problem gets transparent solution on the initial states sphere of harmonic exogenous action source, as minor and major values of control costs, a function of mode distribution that is delivered to the system formed by TO and regulator during system synthesis.


Keywords: source of harmonic exogenous action, initial state vector, control object, steady output, cost control gramian, minor and major values
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