An Approximation Theory for the Identification of Nonlinear Distributed Parameter Systems
Abstract
An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators(satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified)are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original infinite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed. Keywords: Nonlinear distributed systems; Numerical analysis; Inverse problems; Approximation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1988
- Accession Number
- ADA196306
Entities
People
- H. Thomas Banks
- I. G. Rosen
- Simeon Reich