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A Luenberger-like observer for multistable Kapitaniak chaotic system. (English) Zbl 1444.93005

Summary: The objective of this paper is to estimate the unmeasurable variables of a multistable chaotic system using a Luenberger-like observer. First, the observability of the chaotic system is analyzed. Next, a Lipschitz constant is determined on the attractor of this system. Then, the methodology proposed by Raghavan and the result proposed by Thau are used to try to find an observer. Both attempts are unsuccessful. In spite of this, a Luenberger-like observer can still be used based on a proposed gain. The performance of this observer is tested by numerical simulation showing the convergence to zero of the estimation error. Finally, the chaotic system and its observer are implemented using 32-bit microcontrollers. The experimental results confirm good agreement between the responses of the implemented and simulated observers.

MSC:

93B07 Observability
93B53 Observers
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C15 Control/observation systems governed by ordinary differential equations
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