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In article specification (in comparison with known) conditions of residual identification error in a closed path of the adaptive control system containing the algorithm of the current parametrical identification (the recurrent method of least squares with a forgetting factor) delivering estimates of unknown parameters of an object of management, and the appointed implicit reference model and also based on the "simplified" adaptability conditions is offered. For this control system the property of adaptability is directly bound to property of a residual identification error. On the example of consideration of a simple problem of creation of an adaptive control of the linear determined stationary object with the description in the state space with completely measured by state vector and its derivative showed conditions of convergence of own high-frequency driving of a residual identification error. They are based on particular requirements to estimates of parameters, the bound with the control. These conditions allow essential inaccuracies of the specified estimates. Generalizations of the received results on more difficult problems are obvious and based on the main advantage of the "simplified" adaptability conditions − to build management on the basis of the approximating model of an object delivered by an identification algorithm. The model example confirming the received theoretical results is presented.

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