Journal
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
Volume 31, Issue 5, Pages 1689-1703Publisher
WILEY
DOI: 10.1002/rnc.5380
Keywords
adaptive uncertainty estimation; Bernstein polynomial; chaos synchronization; Szá sz– Mirakyan operator; universal approximation theorem
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This article introduces a robust adaptive controller for chaos synchronization utilizing the Szasz-Mirakyan operator as a universal approximator. By employing the Szasz-Mirakyan operator to approximate uncertainties, stability can be ensured, as demonstrated through numerical simulations on the Duffing-Holmes oscillator.
This article presents a robust adaptive controller for chaos synchronization using the Szasz-Mirakyan operator as a universal approximator. In accordance with the universal approximation theorem, the Szasz-Mirakyan operator, an extended version of the Bernstein polynomial, can approximate uncertainties, including unmodeled dynamics and external disturbances. This fact is completely discussed in this article. It is shown that using the Szasz-Mirakyan operator as basis functions and tuning the polynomial coefficients by the adaptive laws calculated in the stability analysis, uniformly ultimately bounded stability can be assured. Performance evaluation has also been carried out to confirm the satisfactory performance of transient response of the controller. Numerical simulations on the Duffing-Holmes oscillator are provided in order to demonstrate the effectiveness of this approach.
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