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Slow and heavy viable trajectories of controlled problems. Smooth viability domains

Part of the Lecture Notes in Mathematics book series (LNM,volume 1091)

Abstract

We define slow and heavy viable trajectories of differential inclusions and controlled problems. Slow trajectories minimize at each time the norm of the velocity of the state (or the control) and heavy trajectories the norm of the acceleration of the state (or the velocity of the control). Macrosystems arising in social and economic sciences or biological sciences seem to exhibit heavy trajectories.

We make explicit the differential equations providing slow and heavy trajectories when the viability domain is smooth.

Keywords

  • Differential Inclusion
  • Economic Science
  • Contingent Cone
  • Contingent Derivative
  • Linear Equality Constraint

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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References

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© 1984 Springer-Verlag

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Aubin, JP. (1984). Slow and heavy viable trajectories of controlled problems. Smooth viability domains. In: Salinetti, G. (eds) Multifunctions and Integrands. Lecture Notes in Mathematics, vol 1091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098804

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  • DOI: https://doi.org/10.1007/BFb0098804

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13882-2

  • Online ISBN: 978-3-540-39083-1

  • eBook Packages: Springer Book Archive