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  • Produktbild: Systems with Hysteresis
  • Produktbild: Systems with Hysteresis

Systems with Hysteresis

51,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.11.2011

Verlag

Springer Berlin

Seitenzahl

410

Maße (L/B/H)

24,4/17/2,4 cm

Gewicht

747 g

Auflage

Softcover reprint of the original 1st ed. 1989

Übersetzt von

Marek Niezgodka

Sprache

Englisch

ISBN

978-3-642-64782-6

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.11.2011

Verlag

Springer Berlin

Seitenzahl

410

Maße (L/B/H)

24,4/17/2,4 cm

Gewicht

747 g

Auflage

Softcover reprint of the original 1st ed. 1989

Übersetzt von

Marek Niezgodka

Sprache

Englisch

ISBN

978-3-642-64782-6

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: ProductSafety@springernature.com

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  • Produktbild: Systems with Hysteresis
  • Produktbild: Systems with Hysteresis
  • 1 Static Hysteron.- 1. Short-memory transducer.- 1.1 Transducer.- 1.2 States of transducer.- 1.3 Some properties of transducers.- 1.4 Admissible inputs.- 1.5 Vibro-correctness.- 2. Generalized play.- 2.1 Ordinary play.- 2.2 Generalized play with piecewise monotone inputs.- 2.3 Estimates.- 2.4 Generalized play with continuous inputs.- 2.5 Dependence of outputs upon initial states.- 2.6 Correctness of the definition of the play.- 2.7 Monotonicity.- 2.8 Periodic inputs.- 2.9 Inputs defined on the whole real axis.- 3. Hysteron.- 3.1 Stop.- 3.2 Determining systems of curves.- 3.3 Piecewise monotone inputs.- 3.4 Passage to arbitrary continuous inputs.- 4. Canonical representation of hysteron and proof of Theorem 3.2.- 4.1 Canonical hysteron.- 4.2 Canonical representation theorem.- 4.3 Proof of Theorem 3.2.- 4.4 Properties of hysteron.- 4.5 Rectification of hysteron.- 5. Distances.- 5.1 Definition of distance.- 5.2 Estimates on differences of output signals.- 6. Various input spaces.- 6.1 Statement of the problem.- 6.2 Spaces of continuously differentiable functions.- 6.3 Play in the space S of absolutely continuous functions.- 6.4 Hysteron in the space S.- 6.5 Hysterons in spaces H?.- 6.6 Discontinuous inputs.- 6.7 Hysteron in the space of functions with bounded variation.- 6.8 Hysteron in Wiener spaces.- 2 Identification Theorem.- 7. Identification problem.- 7.1 General identification problem.- 7.2 Prehysteron.- 7.3 Basic identification theorem.- 7.4 Concluding remarks.- 8. Proof of Theorem 7.1.- 8.1 Singular points of the domain ? (V).- 8.2 Construction of curves ?(M).- 8.3 Construction of curves ?l, ?r.- 8.4 Completion of the proof of Theorem 7.1.- 9. ? - identiflability.- 9.1 Statement of the problem.- 9.2 Normal hysteron.- 9.3 Theorem on ?- identification.- 9.4 A remark.- 10. Approximate construction of hysteron.- 10.1 Distance between hysterons.- 10.2 Bounded inputs.- 10.3 Frames of hysterons.- 10.4 Approximation by operators different from hysterons.- 3 Vibro-Correct Differential Equations and Variable Hysterons.- 11. Necessary condition of vibro-correctness.- 11.1 Integrator.- 11.2 Simple examples.- 11.3 Necessary condition of vibro-correctness.- 11.4 Vibro-correctness in a point.- 12. Sufficient condition of vibro-correctness.- 12.1 Main result.- 12.2 An auxiliary equation.- 12.3 A substitution.- 12.4 Proof of Theorem 12.1.- 12.5 Lemma on differential inequalities.- 12.6 Vibro-correctness on smooth inputs.- 13. Vibro-solutions.- 13.1 Definition.- 13.2 Global vibro-correctness.- 13.3 Inputs on finite time interval.- 13.4 Inputs on infinite time interval.- 14. Equations with constraints.- 14.1 Equations with discontinuous right-hand sides.- 14.2 Arbitrary continuous constraints.- 14.3 Vibro-correct equations with constraints.- 14.4 Properties of vibro-solutions to equations with constraints.- 14.5 Vibro-solutions of parametrized equations.- 15. Variable hysteron.- 15.1 Description of hysteron by differential equations.- 15.2 Variable hysteron.- 15.3 Variable hysteron governed by differential equations.- 15.4 Infinitesimal hysteron.- 15.5 A special class of transducers.- 4 Multidimensional Hysterons.- 16. Multidimensional play and stop defined on smooth inputs.- 16.1 A simple example.- 16.2 A general notion.- 16.3 Correctness of the definitions of play and stop.- 16.4 Properties of play and stop.- 16.5 On the classical solutions of equations with discontinuous right-hand sides.- 17. Strictly convex characteristics.- 17.1 Vibro-correctness modulus.- 17.2 Holder condition.- 17.3 Passage to continuous inputs.- 17.4 Strong convergence.- 17.5 Perturbation of characteristics.- 17.6 Vibro-correctness modulus and differential inclusions.- 17.7 Lower bound for vibro-correctness moduli.- 18. Polyhedral characteristics.- 18.1 Basic theorems.- 18.2 Estimates of the Lipschitz constant.- 18.3 Proofs of Lemma 18.1 and Theorem 18.4.- 18.4 Proof of Theorem 18.3.- 18.5 Remarks.- 19. Arbitrary convex characteristics.- 19.1 Vibro-correctness of play and stop.- 19.2 Estimate for the variation of output.- 19.3 Proof of Theorem 19.1.- 20. Inputs with summable derivatives.- 20.1 Statement of the problem.- 20.2 Lipschitz condition.- 20.3 Remarks.- 21. Vibro-correct equations with vector input.- 21.1 Statement of the problem.- 21.2 Frobenius condition.- 21.3 Necessary condition of vibro-correctness.- 21.4 Sufficient condition of vibro-correctness.- 21.5 Remarks.- 22. Equations with vector inputs and smooth constraints.- 22.1 Constraints.- 22.2 Planar motion.- 22.3 Other descriptions.- 5 Discontinuous Nonlinearities.- 23. Static elements.- 23.1 Continuous characteristics.- 23.2 Elements with discontinuous characteristics.- 23.3 Estimates of outputs.- 23.4 Proper characteristics.- 23.5 Continuity on a fixed input.- 23.6 Additional remarks.- 24. Elements with monotone characteristics.- 24.1 Cones.- 24.2 Special classes of cones.- 24.3 Monotone characteristics.- 24.4 Proof of Theorem 24.1.- 24.5 Proof of Theorem 24.2.- 24.6 Remarks.- 25. Elements with multi-valued characteristics.- 25.1 Selection problem.- 25.2 General theorems on selectors.- 25.3 Monotone selectors.- 25.4 Measurable selectors.- 25.5 Input-output relations.- 26. Closures of static element.- 26.1 Closure of transducer.- 26.2 Characteristic of the closure.- 26.3 Closure modulo a negligence class.- 26.4 Comments.- 27. Weak closures and convexification procedure.- 27.1 Weak closures.- 27.2 Convexification.- 27.3 Weak closures and convexification of static element.- 27.4 Proof of Theorem 27.1.- 27.5 Proof of Theorem 27.2.- 27.6 Convexification of static element modulo negligence class.- 27.7 Examples of open nonlinear systems composed of static elements.- 28. Relay.- 28.1 Ideal relay.- 28.2 Non-ideal relay.- 28.3 Periodic inputs.- 28.4 Closure of relay.- 28.5 Convexification of relay.- 28.6 Relay and “slow” controls.- 28.7 Discontinuous inputs.- 6 Self-Magnetization Phenomenon.- 29. Madelung’s hysterons.- 29.1 Non-correct prehysteron.- 29.2 Periodic inputs.- 29.3 Madelung’s prehysteron.- 29.4 Properties of Madelung’s prehysteron.- 29.5 Madelung’s hysteron.- 29.6 Discontinuous inputs with bounded variation.- 30. Proofs of Theorems 29.1 and 29.2.- 30.1 Passage to classical solutions.- 30.2 Lemma on differential inequalities.- 30.3 Proof of Theorem 29.1.- 30.4 Proof of Theorem 29.2.- 31. Response to small perturbations of the input.- 31.1 General scheme.- 31.2 Intensities.- 31.3 Construction of ?-outputs to Madelung’s hysteron.- 31.4 Construction of ?-vibrosolutions to differential equations.- 31.5 Construction of ?-outputs for hysterons.- 32. Closure modulo sets of Wiener measure zero.- 32.1 A general scheme.- 32.2 Main theorem.- 32.3 Passage to integral equations.- 32.4 Equations with constraints.- 32.5 Implications for stochastic equations.- 7 Complex Hysteresis Nonlinearities.- 33. Parallel connections and bundles of hysterons.- 33.1 Complex nonlinearities.- 33.2 Parallel connections.- 33.3 Completely controllable restrictions.- 33.4 Periodic inputs.- 33.5 An important example.- 33.6 Remarks.- 34. Sequential connections of hysterons.- 34.1 Sequential connections and cascades.- 34.2 Sequential connections of plays and stops.- 34.3 Compensators.- 34.4 Complex connections.- 35. Ishlinskii’s material.- 35.1 Continual systems of hysterons.- 35.2 Ishlinskii’s transducer.- 35.3 Loading and unloading functions.- 35.4 Normal states of Ishlinskii’s transducer.- 35.5 Periodic inputs.- 35.6 Davidenkov’s model.- 35.7 Controllable restrictions of Ishlinskii’s bundles.- 36. Properties of Ishlinskii’s transducer.- 36.1 Continuity of Ishlinskii’s operator.- 36.2 Correctness with respect to weight functions.- 36.3 Unilateral estimates.- 37. Finite systems of relays.- 37.1 Block-diagrams with relays.- 37.2 Parallel connections and bundles of relays.- 37.3 Independent perturbations of inputs.- 37.4 General perturbation of input.- 38. Continual systems of relays.- 38.1 Bundles of relays and CRS-transducers.- 38.2 Monotonicity of CEtS-transducers.- 38.3 Demagnetization function.- 38.4 Periodic inputs.- 38.5 Evaluation of outputs.- 38.6 Vibro-correctness.- 38.7 Controllable restrictions.- 39. Rheological models.- 39.1 Construction of the model.- 39.2 Graphs.- 39.3 Transducer M.- 39.4 Properties of the transducer M.- 39.5 Transducer W.- 39.6 Remarks.- Bibliographic comments.- References.