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Least-squares estimation of input/output models for distributed linear systems in the presence of noise. (English) Zbl 0967.93091
The paper characterizes the asymptotic values of recursive least-squares estimates of parameters in digital input/output models of infinite-dimensional linear plants. The plants under consideration have stable time-invariant discrete-time realizations in Hilbert spaces. The plants are driven by unknown white process-noise sequences , and the measured outputs are contaminated by white sensor noise. The main results characterize the asymptotic values to which parameter estimates converge with increasing amounts of data. The most important result is an equivalence between least-squares parameter estimation on an infinite interval (i.e., with infinitely long data sequences) and linear-quadratic optimal control on a finite interval. Numerical results are presented for a sampled data version of a forced, damped one-dimensional wave equation.

MSC:
93E12 Identification in stochastic control theory
93E24 Least squares and related methods for stochastic control systems
93C20 Control/observation systems governed by partial differential equations
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