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Systems with Hysteresis / by Mark A. Krasnosel'skii, Aleksei V. Pokrovskii

Edition 1st ed. 1989.
Publisher (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year 1989
Language English
Size XVIII, 410 p : online resource
Authors *Krasnosel'skii, Mark A author
Pokrovskii, Aleksei V author
SpringerLink (Online service)
Subjects LCSH:Mathematical analysis
LCSH:System theory
LCSH:Control theory
LCSH:Mathematical optimization
LCSH:Calculus of variations
LCSH:Mathematical physics
LCSH:Econometrics
LCSH:Biomathematics
FREE:Analysis
FREE:Systems Theory, Control
FREE:Calculus of Variations and Optimization
FREE:Theoretical, Mathematical and Computational Physics
FREE:Quantitative Economics
FREE:Mathematical and Computational Biology
Notes 1 Static Hysteron -- 1. Short-memory transducer -- 2. Generalized play -- 3. Hysteron -- 4. Canonical representation of hysteron and proof of Theorem 3.2 -- 5. Distances -- 6. Various input spaces -- 2 Identification Theorem -- 7. Identification problem -- 8. Proof of Theorem 7.1 -- 9. ? - identiflability -- 10. Approximate construction of hysteron -- 3 Vibro-Correct Differential Equations and Variable Hysterons -- 11. Necessary condition of vibro-correctness -- 12. Sufficient condition of vibro-correctness -- 13. Vibro-solutions -- 14. Equations with constraints -- 15. Variable hysteron -- 4 Multidimensional Hysterons -- 16. Multidimensional play and stop defined on smooth inputs -- 17. Strictly convex characteristics -- 18. Polyhedral characteristics -- 19. Arbitrary convex characteristics -- 20. Inputs with summable derivatives -- 21. Vibro-correct equations with vector input -- 22. Equations with vector inputs and smooth constraints -- 5 Discontinuous Nonlinearities -- 23. Static elements -- 24. Elements with monotone characteristics -- 25. Elements with multi-valued characteristics -- 26. Closures of static element -- 27. Weak closures and convexification procedure -- 28. Relay -- 6 Self-Magnetization Phenomenon -- 29. Madelung’s hysterons -- 30. Proofs of Theorems 29.1 and 29.2 -- 31. Response to small perturbations of the input -- 32. Closure modulo sets of Wiener measure zero -- 7 Complex Hysteresis Nonlinearities -- 33. Parallel connections and bundles of hysterons -- 34. Sequential connections of hysterons -- 35. Ishlinskii’s material -- 36. Properties of Ishlinskii’s transducer -- 37. Finite systems of relays -- 38. Continual systems of relays -- 39. Rheological models -- Bibliographic comments -- References
Hysteresis phenomena are common in numerous physical, mechanical, ecological and biological systems. They reflect memory effects and process irreversibility. The use of hysteresis operators (hysterons) offers an approach to macroscopic modelling of the dynamics of phase transitions and rheological systems. The applications cover processes in electromagnetism, elastoplasticity and population dynamics in particular. Hysterons are also typical elements of control systems where they represent thermostats and other discontinuous controllers with memory. The book offers the first systematic mathematical treatment of hysteresis nonlinearities. Construction procedures are set up for hysterons in various function spaces, in continuous and discontinuous cases. A general theory of variable hysterons is developed, including identification and stability questions. Both deterministic and non-deterministic hysterons are considered, with applications to the study of feedback systems. Many of the results presented - mostly obtained by the authors and their scientific group - have not been published before. The book is essentially self contained and is addressed both to researchers and advanced students
HTTP:URL=https://doi.org/10.1007/978-3-642-61302-9
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Material Type E-Book
Classification LCC:QA299.6-433
DC23:515
ID 4000110096
ISBN 9783642613029

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