Robust method to provide exponential convergence of model parameters solving linear time-invariant plant identification problem |
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Authors: | Anton Glushchenko Vladislav Petrov Konstantin Lastochkin |
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Affiliation: | Automated and Information Control Systems Chair, Stary Oskol Technological Institute n.a. A.A. Ugarov (branch) NUST “MISIS”, Stary Oskol, Russia |
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Abstract: | The scope of this research is a problem of parameters identification of a linear time-invariant plant, which (1) input signal is not frequency-rich, (2) is subjected to initial conditions and external disturbances. The memory regressor extension (MRE) scheme, in which a specially derived differential equation is used as a filter, is applied to solve the above-stated problem. Such a filter allows us to obtain a bounded regressor value, for which a condition of the initial excitation (IE) is met. Using the MRE scheme, the recursive least-squares method with the forgetting factor is used to derive an adaptation law. The following properties have been proved for the proposed approach. If the IE condition is met, then: (1) the parameter error of identification is bounded and converges to zero exponentially (if there are no external disturbances) or to a set (in the case of them) with an adjustable rate, (2) the parameters adaptation rate is a finite value. The above-mentioned properties are mathematically proved and demonstrated via simulation experiments. |
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Keywords: | exponential convergence initial conditions initial excitation parameters identification persistent excitation regression |
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