Adaptive synchronization of two Lorenz systems. (English) Zbl 1047.37502
Summary: This paper treats the synchronization problem of two Lorenz systems in the presence of unknown system parameters. Based on the Lyapunov stability theory, an adaptive control law is derived such that the two Lorenz systems are to be synchronized. A robust adaptive control law is also presented to guarantee the robustness of the synchronization against a bounded disturbance. Simulation results are given to demonstrate the effectiveness and robustness of the proposed control schemes.
MSC:
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 93D21 | Adaptive or robust stabilization |
Keywords:
Chaos theory; Adaptive control systems; Synchronization; Lyapunov methods; System stability; Robustness; Control system analysis; Computer simulation; Adaptive synchronization; Lorentz system; Synchronization chaos; Lyapunov stability theoryReferences:
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