Automatic feedback control for one class of contact piezoelectric problems


  • М. Z. Zgurovsky
  • P. О. Kasyanov
  • L. S. Paliichuk


In this paper we investigate the dynamics of solutions of the second order evolution inclusion with discontinuous interaction function which can be represented as the difference of subdifferentials. This case is actual for feedback automatic control problems. In particular, we consider mathematical model of contact piezoelectric process between a piezoelectric body and a foundation and for this problem investigate the long-term behavior of state function. We deduce a priory estimates for weak solutions of studied problem in the phase space. The theorem on the existence of a global attractor for multi-valued semiflow generated by weak solutions of the problem and the structural properties of the limit sets is proved. The main results of the paper were applied to the investigated piezoelectric problem.


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Mathematical methods, models, problems and technologies for complex systems research