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Identification of hysteric control influence operators representing smart actuators. I: Formulation. (English) Zbl 0934.93036

The authors investigate a second order evolution equation in Hilbert space \[ \ddot{w}(t) + A_1(q)\dot{w}(t) + A_0(q)w(t) = [B_\mu(u,f)](t) \] where \(B_\mu(u,f)(t) = P_\mu(u,f)g\), \(g\) is a fixed element and \(P_\mu(u,f)\) is a scalar hysteresis operator. They consider variants of the Preisach model and prove that, for a two-parameter integral of generalized plays, the corresponding identification problem has a solution.

MSC:

93C25 Control/observation systems in abstract spaces
93B30 System identification
93B28 Operator-theoretic methods
35L20 Initial-boundary value problems for second-order hyperbolic equations
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
74D10 Nonlinear constitutive equations for materials with memory
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