Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations

  • Received: 01 July 2012 Accepted: 29 June 2018 Published: 01 August 2013
  • MSC : 34K29, 34K60, 49K40.

  • In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.

    Citation: H.Thomas Banks, Danielle Robbins, Karyn L. Sutton. Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1301-1333. doi: 10.3934/mbe.2013.10.1301

    Related Papers:

  • In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.


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