On applications of approximation theory to identification, control and classification.

摘要

Applications of approximation theory to some problems in identification of dynamic systems, their control, and to problems in signal classification are studied. First, an algorithm is given for constructing approximations in a wide variety of settings, and a corresponding error bound is derived. Then weak sufficient conditions for perfect classification of signals are studied. Next the problem of approximating linear functionals with certain sums of integrals is studied, along with its relation to the approximation of nonlinear functionals. Then an approximation theoretic characterization of continuity of nonlinear maps is given. As another application of function approximation, the problem of universally approximating controllers for discrete-time continuous plants is studied. Finally, error bounds for approximation of functions defined on finite dimensional Hilbert spaces are given.