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Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential
H Thomas Banks1, Danielle Robbins, Karyn L Sutton
1Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212, United States. htbanks@ncsu.edu.
Mathematical Biosciences and Engineering : MBE
|November 20, 2013
Summary
This study introduces new methods for analyzing the differentiability of delay systems, crucial for understanding biological models and improving control systems. The findings enhance sensitivity analysis for complex dynamic systems.
Area of Science:
- Dynamical Systems Theory
- Mathematical Biology
- Control Theory
Background:
- Delay systems are prevalent in biological applications, yet their differentiability properties require further investigation.
- Sensitivity functions are vital for control and estimation in systems with delays.
Purpose of the Study:
- To present novel results on the differentiability of delay systems concerning initial conditions and delays.
- To highlight the importance of sensitivity analysis in these systems.
Main Methods:
- Development of new mathematical techniques for analyzing differentiability.
- Summarization of general existence and uniqueness theorems for delay systems.
- Derivation of differentiation results with respect to delays.
Main Results:
- New findings on the differentiability of delay systems with respect to initial conditions.
- Established methods for calculating derivatives with respect to time delays.
- Demonstrated applicability of generalized sensitivity functions.
Conclusions:
- The presented results offer a deeper understanding of delay system dynamics.
- The work provides essential tools for advanced control and estimation strategies in biological and engineering fields.
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