Uniformly Differentiable Approximation Scheme for Delay Systems Using Splines

摘要

A new spline-based scheme is developed for linear retarded functional differential equations within the framework for semigroups on a certain Hilbert space formula. The approximating semigroups inherit in uniform way the characterization for differentiable semigroups from the solution semigroup of the delay system (e.g., among other things the logarithmic sectorial property for the spectrum). The authors prove convergence of the scheme in state spaces. The uniform differentiability of the approximating semigroups enables us to establish error estimates including quadratic convergence for certain classes of initial data. They also apply the scheme for computing the feedback solutions to linear quadratic optimal control problems. (kr)