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Numerical studies of identification in nonlinear distributed parameter systems. (English) Zbl 0692.93019
Control and estimation of distributed parameter systems, 4th Int. Conf., Vorau/Austria 1988, ISNM 91, 1-20 (1989).
Summary: [For the entire collection see Zbl 0682.00026.]
An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by H. T. Banks, S. Reich and I. G. Rosen [“An approximation theory for the identification of nonlinear distributed parameter systems”, ICASE Report No.88-26, Inst. Comput. Appl. Sci. Eng., NASA Langley Research Center, Hampton/VA 1988; and “Estimation of nonlinear damping in second order distributed parameter systems” (to appear)] are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution systems.
The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e. damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular with regard to supercomputing, are addressed.

MSC:
93B30 System identification
65J15 Numerical solutions to equations with nonlinear operators
49M15 Newton-type methods
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
93C20 Control/observation systems governed by partial differential equations
93C10 Nonlinear systems in control theory
93B40 Computational methods in systems theory (MSC2010)
58D25 Equations in function spaces; evolution equations