SOME PROBLEMS IN THE THEORY OF APPROXIMATING SOLUTIONS OF DIFFERENTIAL-OPERATOR EQUATIONS IN HILBERT SPACE.
Abstract
In the present paper the author studies certain aspects of the theory of approximating nonlinear differential-operator equations of the form dx/dt = f (x, t) + phi (c sub 1,..., c sub m, u sub 1 (t),..., u sub n (t),t), where f(x,t) and phi (c sub 1, . . . ., c sub m, u sub 1 (t), . . . ,u sub n (t)t) are nonlinear operators satisfying certain conditions; x,u sub 1, . . . , u sub n for given t are elements of a Hilbert space; and c sub 1, c sub 2, ...., c sub m are numbers. An effective method is presented for choosing the functions u sub 1 (t), u sub 2 (t), . . . , u sub n (t), called control functions, and the parameters c sub 1, . . . , c sub m, in order for the given function y(t) to have the least mean square deviation from the solution x(t) of equation. A relationship is pointed out between certain aspects of the stability of solutions of the equation and problems in the theory of approximating solutions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 28, 1966
- Accession Number
- AD0645720
Entities
People
- L. Kh. Liberman
Organizations
- Johns Hopkins University Applied Physics Laboratory