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Fuzzy model based adaptive synchronization of uncertain chaotic systems: robust tracking control approach. (English) Zbl 1229.34080

Summary: This letter presents fuzzy model-based robust tracking control for the adaptive synchronization of uncertain chaotic systems. Fuzzy model and adaptive algorithm are employed to present the unknown chaotic systems. \(H^{\infty }\) and sliding mode control are combined to construct a robust tracking controller. The incorporated \(H^{\infty }\) controller can attenuate the external disturbance and approximation error to any prescribed level. The proposed scheme guarantees that all the variables are bounded and the tracking error is compensated.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
34A07 Fuzzy ordinary differential equations
93D21 Adaptive or robust stabilization
62F35 Robustness and adaptive procedures (parametric inference)
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