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Tracking control based on adaptive Bernstein polynomial approximation for a class of unknown nonlinear dynamic systems

Journal of the Franklin Institute, ISSN: 0016-0032, Vol: 360, Issue: 7, Page: 5082-5091
2023
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Article Description

In this article, an adaptive tracking control approach using Bernstein polynomial approximation is firstly proposed for an unknown nonlinear dynamic system. Bernstein polynomial approximation aims to compensate the unknown nonlinear dynamic function. However, if Bernstein theorem is directly used, the Bernstein polynomial's coefficients need to be derived from the system dynamic function. Nevertheless, the dynamic function is presumed to be unknown, hence the polynomial approximation still cannot be used for designing this control. In order to obtain the available function approximation, adaptive strategy is considered to estimate these coefficients. Finally, by learning from the classical adaptive algorithm, the undetermined coefficient problem is addressed, so that the valid tracking control is found for the unknown nonlinear dynamic system. According to Lyapunov stability analysis and simulation experiment, it is concluded that the new adaptive scheme can realize the control objective.

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