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Abstract

A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasilinearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations. 1. Introduction. During the past fifteen years considerable effort has been devoted to the problem of estimating unknown parameters in distributed parameter systems. The recent book by Banks and Kunisch [9] provides an excellent account of the progress made in the field. Many parameter estimation problems are best formulated as optimization problems (sometimes over infinite-dimensional "parameter spaces"), and algorithms are developed to minimize an appropriate cost function. Although there are several approaches to these problems, their infinite-dimensional nature requires that numerical approximations be introduced at some point in the analysis. Consequently, there are two basic classes of algorithms for optimization-based parameter estimation. The first type of algorithm, and the most frequently used for dynamic problems, is indirect and proceeds by initially approximating the dynamic equations (e.g., finite elements, finite differences, etc.) and then using optimization algorithms on the finite-dimensional problem. This approach is typified by the papers [1-6, 8, 10, 18].