Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations.
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.
Center for Research in Scientiﬁc Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212, United States. htbanks@ncsu.edu.
H Thomas
HT
Banks
Danielle
D
Robbins
Karyn L
KL
Sutton
D000465:Algorithms; D000818:Animals; D001695:Biology / Q000379:methods; D003198:Computer Simulation; D003621:Daphnia; D004463:Ecology; D006790:Host-Parasite Interactions; D016018:Least-Squares Analysis; D008433:Mathematics; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D010271:Parasites; D013997:Time Factors