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- Franz Kappel, Alexei V. Kuntsevich
- Comp. Opt. and Appl.
- 2000

The purpose of this paper is to introduce a new spline approximation scheme for retarded functional differential equations. The special feature of this approximation scheme is that it preserves the product space structure of retarded systems and approximates the adjoint semigroup in a strong sense. These facts guarantee the convergence of the solution… (More)

Based on the four compartment model by Grodins we develop a model for the response of the cardiovascular system to a short term submaximal workload. Basic mechanisms included in the model are Starling's law of the heart, the Bowditch effect and autoregulation in the peripheral regions. A fundamental assumption is that the action of the feedback control is… (More)

- Kazufumi Ito, Franz Kappel
- Series on Advances in Mathematics for Applied…
- 2002

- H T Banks, Kathleen Holm, Franz Kappel
- Inverse problems
- 2011

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according… (More)

For an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems. As an application, strong convergence of the approximating Riccati… (More)

This research was supported in part by the National Science Foundation (USA) under NSF grants DMS-8818530 and UINT-8521208 and in part by the FWF (Austria) under grants S3206 and P6005.

We consider the problem of estimating a modeling parameter μ using a weighted least squares criterion Jd(y, μ) = ∑n i=1 1 3⁄4(ti) ( y(ti) − f(ti, μ) )2 for given data y by introducing an abstract framework involving generalized measurement procedures characterized by probability measures. We take an optimal design perspective, the general premise… (More)

- Franz Kappel, Martin Fink, Jerry J Batzel
- Mathematical biosciences
- 2007

This paper considers a model developed to study the cardiovascular control system response to orthostatic stress as induced by two variations of lower body negative pressure (LBNP) experiments. This modeling approach has been previously applied to study control responses to transition from rest to aerobic exercise, to transition to non-REM sleep and to… (More)

- Jerry J Batzel, Franz Kappel
- Mathematical biosciences
- 2011

This article examines the functional and clinical impact of time delays that arise in human physiological systems, especially control systems. An overview of the mathematical and physiological contexts for considering time delays will be illustrated, from the system level to cell level, by examining models that incorporate time delays. This examination will… (More)