Pavel Krejčí

Hysteresis and periodic solutions of semilinear and quasilinear wave equations

On demontre lexistence de solutions ω-periodiques pour les problemes u tt -u xx ±F(u)=g(t,x), u(t,o)=u(t,Π)=0, u tt -F(u x ) x =g(t,x), u x (t,o)=u x (t,Π)=0 pour chaque g ω-periodique, ou F est loperateur dIshlinskii et ω>0 arbitraire

Vector hysteresis models

Following Krasnosel’skii & Pokrovskii 1983 we express the constitutive law for the PrandtlReuss elastoplastic model in terms of a hysteresis operator and we introduce the vector Ishlinskii model. We investigate some properties (continuity, energy inequalities, dependence on spatial variables) of these operators.

Error estimates for the discrete inversion of hysteresis and creep operators

The accuracy of a numerical scheme for real-time inverse control of piezoelectric actuators taking into account both hysteresis and creep effects is analyzed with respect to the time step and the memory discretization parameter. It is shown that the error is of the first-order for Lipschitz continuous inputs.

Periodic solutions to a parabolic equation with hysteresis

On considere le probleme parabolique correspondant a lequation des telegraphistes quasi-stationnaire dans un milieu ferromagnetique. On donne un schema de discretisation despace

An Adaptive Gradient Law with Projection for Non-smooth Convex Boundaries

The parameter projection method, which has been designed for solving on-line parameter identification problems under smooth convex restrictions, is extended here to arbitrary convex parameter domains. Such problems arise naturally in cases where an admissible solution set results from the intersection of several (possibly smooth) convex constraints. The corresponding adaptive gradient law has the form of a special evolution projected dynamical system with a discontinuous right-hand side. The paper develops an alternative formulation of this projected dynamical system based on the multidimensional stop operator. The advantage of this approach is that the new right-hand side is continuous and the problem is thus accessible to conventional analysis methods, which easily give results on existence, uniqueness, and convergence properties of the corresponding solution trajectories. The method is tested on the parameter identification problem for complex hysteresis nonlinearities.

Existence, Uniqueness and L∞-stability of the Prandtl-Ishlinskii Hysteresis and Creep Compensator

The article presents a rigorous existence, uniqueness and stability proof for a hysteresis and creep compensator of Prandtl-Ishlinskii type which is used in practical applications to compensate the complex hysteretic and creep actuator characteristic of active materials (especially of piezoceramics) in large signal operation. The hysteresis and creep compensator consists of an inverse Prandtl- Ishlinskii hysteresis operator in the feedforward path and a Prandtl-Ishlinskii creep operator in the feedback path. The simple proof of existence, uniqueness and stability with the well-known small-gain theorem is based on the Lipschitzcontinuity of both operators and leads to an additional contraction condition which restricts the application range of the compensator from the theoretical point of view. The proof discussed in this contribution avoids this restrictive contraction condition and thus extends considerably the application range of the compensator.