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Identiication of Hysteretic Control Innuence Operators Representing Smart Actuators: Convergent Approximations

In a previous paper, the authors investigated the lowersemicontinu-ity properties of two generalizations of the classical Preisach operator; the smoothed Preisach operator and the Krasnoselskii / Pokrovskii (KP) integral hysteresis operators. In particular, it was demonstrated that the output least squares identiication problem for the KP operator is well-posed over compact subsets of the Preisach plane. The identiication of the hysteretic control innuence operator was shown to be equivalent to the identiication of a measure in the space of probability measures taken with the weak-topology. In this paper, a consistent and convergent approximation scheme is introduced for this class of integral hysteresis operator. The Galerkin approximation scheme is shown to be function space parameter convergent. A numerical example is presented that illustrates aspects of the theory derived in this paper.