Parameter Estimation and Identification for Systems with Delays

Estimation of Variable Coefficients in Parabolic Distributed Systems.

“…In reality however, we have yet to determine whether any sequence of solutions [ N} of the approximating problems is in fact convergent; even then we have no guarantee that the limiting function a is indeed a solution to the original parameter estimation problem. Our next result, (similar in spirit to that found in [4], [9], [13]), addresses this question and indicates when an approximate identification problem may be used 4 to compute numerical solutions for the original problem.…”

“…We shall -N approximate solutions q of this problem by a sequence {qN} of solutions to q estimation problems that are computationally more tractable than our original problem. The approach taken here is similar in spirit to that of a number of other related efforts (see [1], [4], [5], [6], [7], [9], [13] and [16]) in that the original estimation problem is reformulated in a Hilbert space setting where Ritz-Galerkin type ideas may be applied to construct the approximate problems. To this end, we rewrite (2.1)-(2.3) as an abstract evolution equation (AEE) in an infinite-dimensional state space; although the use of spaces and operators here is quite standard and well-established in the literature, the dependence of our problem on unknown parameters requires that we make an effort to carefully define the operators involved.…”

“…To this end, we observe that T 2T ,1 2 We remark that the important aspect cf the above result is the continuous dependence of z on q which is needed to establish existence of solutions to the approximate estimation problems formulated in the next section (see Theorem 3.2). [4], [9] and [16], where the spaces Z and Z N as well depend on the choice of q.…”

Nonlinear neutral functional differential equations in product spaces

“…This approach is similar in spirit to that used by many authors for retarded equations (see [2][3][4][5][6][7][8][9][10][11]). Other approach is discussed in (23] and [24], In general, numerical methods for neutral equations are difficult to analyze (see [ 15], [ 30]).…”

“…The problem of developing approximation techniques for the identification and optimal control of systems governed by retarded functional differential equations (RFDE) has received considerable attention during the past few years (see [2][3][4][5][6][7][8][9][10][11]16,[26][27][28]). …”