Optimality Criterion for Singular Controllers: Linear Boundary Conditions

Boundary Conditions for Singular Perturbations

Let A : D(A) H ! H be an injective self-adjoint operator and let : D(A) ! X, X a Banach space, be a surjective linear map such that k k X c kAAk H. Supposing that Range (0) \ H 0 = f0g, we deene a family A of self-adjoint operators which are extensions of the symmetric operator A jf =0g. Any in the operator domain D(A) is characterized by a sort of boundary conditions on its univocally deened r...

Distance optimality design criterion in linear models

Properties of the most familiar optimality criteria, for example A-, Dand E-optimality, are well known, but the distance optimality criterion has not drawn much attention to date. In this paper properties of the distance optimality criterion for the parameter vector of the classical linear model under normally distributed errors are investigated. DS-optimal designs are derived for ®rst-order po...

Boundary Value Problems with Singular Boundary Conditions

Singular boundary conditions are formulated for non-selfadjoint Sturm-Liouville operators with singularities and turning points. For boundary value problems with singular boundary conditions properties of the spectrum are studied and the completeness of the system of root functions is proved.

Necessary and Sucient Optimality Conditions for a Control Fuzzy Linear Problem

Boundary value problems with regular singularities and singular boundary conditions

where skm are real numbers, pk0(t) ∈ C2[a,b], p00(t)p20(t) = 0, p00(t)/p20(t) > 0 for t ∈ [a,b]. Let s2m < s0m + 2, s2m ≤ s1m + 2, m = 0,1, that is, we consider the case of so-called regular singularities. Operators with irregular singularities possess different qualitative properties and require different investigations. Since the solutions of (1.1) may have singularities at the endpoints of t...