## Adaptive control and synchronization of Lorenz systems.(English)Zbl 1051.93514

Summary: This study addresses the adaptive control and synchronization problems of Lorenz systems with unknown system parameters. Based on the Lyapunov stability theory, an adaptive control law with single-state variable feedback is derived such that the trajectory of the Lorenz system is globally stabilized to an equilibrium point of the uncontrolled system. In addition, the adaptive control law is also applied to achieve the state synchronization of two identical Lorenz systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

### MSC:

 93C40 Adaptive control/observation systems 37N35 Dynamical systems in control 34C99 Qualitative theory for ordinary differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
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### References:

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