A semidiscrete approximation scheme for linear neutral delay-differential equations which preserves adjoint semigroup convergence

摘要

We construct a semidiscrete approximation scheme for a class of linear neutral delay-differential equations. The scheme is shown to yield Trotter-Kato type convergence for both the solution semigroup and the adjoint semigroup. This extends to neutral equations the ideas found in earlier studies which considered only retarded delay-differential equations. Convergence of adjoint semigroup approximations is known to be an important sufficient condition for applications to optimal control problems - for example, to guarantee convergence of the approximating feedback gain operators in LQR problems. We describe the scheme and provide several numerical examples to illustrate its applicability.