**:** ..
**:**
**:** 72
**:**
**:** 2018
**:** .. // . 72. .: , 2018. .52-107. URL: https://doi.org/10.25728/ubs.2018.72.4

** :** , -, , ,

** (.):** adaptive control, PI-controller, neural network learning rate, Lyapunovs second method, sustainability

**:** , , -/- . . , . , , , . , .

** (.):** The problem of a neural network learning rate calculation for online training process is considered. The network is a part of a neural tuner used to adjust linear P-/PI-controllers parameters in real time. Its outputs are the controller parameters values. The problem under consideration is closely related to a control system sustainability estimation, as too high learning rates might make the system unstable. So we propose an approach based on the second Lyapunovs method to calculate learning rate upper acceptance limit for different situations without knowing the plant model. Modeling and laboratory experiments have been conducted using typical plants of heating furnaces and DC drives classes to prove the method reliability. Having analyzed obtained results, the conclusion can be made that for both plant classes learning rate estimations allow to keep the control system stable. At the same time, constant usage of maximum allowed value of the learning rate during the online training process may result in the plant energy efficiency decrease.

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