Journal of Mathematical Sciences

, Volume 196, Issue 3, pp 405–433 | Cite as

Properties of Solutions of a Control System with Hysteresis


We consider a control system described by two nonlinear related equations. The first equation expresses connection between the input and output of the hysteresis operator, whereas the second one is the diffusion equation. The control constraint is expressed by a multivalued mapping of a phase variable with closed nonconvex values in a finitedimensional space. We also consider a system with a convexified control constraint. We study the existence of a solution, topological properties of the set of admissible “trajectory–control” pairs with different control constraints and clarify relations between the sets of solutions. Bibliography: 28 titles.


Multivalued Mapping Density Point Maximal Monotone Operator Control Constraint Lower Semicontinuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute for System Dynamics and Control TheorySiberian Branch of the Russian Academy of SciencesIrkutskRussia

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