Parameter identification for an abstract Cauchy problem by quasilinearization
Abstract : A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasilinearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations. (JHD)
An Unsolicited Proposal for Modeling, Identification, and Active Control of Fluid Dynamics
Abstract : The work accomplished in this research effort has concentrated on developing models, Theoretical tools and computational algorithms for identification and control of fluid-structure interaction problems. Eleven research publications were written under the sponsorship of this grant. Titles include: Optimal Control of Lift/Drag Ratios on a Rotating Cylinder: 'Optimal Control of Viscous Flow past a Cylinder, and Analysis of Regularized Navier Stokes Equations.
A Liouville’s Formula for Systems with Reflection
In this work, we derived an Abel–Jacobi–Liouville identity for the case of two-dimensional linear systems of ODEs (ordinary differential equations) with reflection. We also present a conjecture for the general case and an application to coupled harmonic oscillators.