Existence and properties of solutions of a control system with hysteresis effect

S. A. Timoshin, A. A. Tolstonogov

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We consider a control system described by two ordinary nonlinear differential equations subject to a control constraint given by a multivalued mapping with closed nonconvex values, which depends on the phase variables. One of the equations contains the subdifferential of the indicator function of a closed convex set depending on the unknown phase variable. The equation containing the subdifferential describes an inputoutput relation of hysteresis type. Along with the original control constraint, we also consider the convexified control constraint and the constraint consisting of the extremal points of the convexified control constraint. We prove the existence of solutions of our control system with various control constraints and establish certain relationships between corresponding solution sets.

Original languageEnglish
Pages (from-to)4433-4447
Number of pages15
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number13
Publication statusPublished - Sept 2011
Externally publishedYes


  • Evolution control systems
  • Extreme points
  • Hysteresis
  • Mosco convergence
  • Nonconvex constraints
  • Subdifferential


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