## Chaos synchronization and parameters identification of single time scale brushless DC motors.(English)Zbl 1071.34048

The purpose of the paper is to study the system of ordinary differential equations, which describes the dynamics of a brushless dc motor. The rescaled system has the form \begin{aligned} x_1' &= v_q -x_1 -x_2 x_3 + \rho x_3,\\ x_2' &= v_d -\delta x_2 +x_1 x_3,\tag{1}\\ x_3' &= \sigma(x_1 - x_3) +\eta x_1 x_2-T_L,\end{aligned} where $$v_q, v_d,T_L,\sigma,$$ and $$\eta$$ are parameters.
The authors identify regions of chaotic behavior of system (1) by computing numerically the Lyapunov exponents. Also, they study synchronization of coupled identical systems of the form (1) using different control schemes. Finally, two methods are applied to achieve parameter identification: the adaptive control and the random optimization method.

### MSC:

 34D05 Asymptotic properties of solutions to ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 34C28 Complex behavior and chaotic systems of ordinary differential equations 34D08 Characteristic and Lyapunov exponents of ordinary differential equations 34A55 Inverse problems involving ordinary differential equations 34H05 Control problems involving ordinary differential equations
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### References:

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