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Optimal finite-dimensional recursive identification in a polynomial output mapping class. (English) Zbl 0539.93019

The search for optimal finite-dimensional recursive filters in nonlinear differential systems was successful in some restricted system classes [e.g. refer to S. Marcus and A. Willsky, SIAM J. Math. Anal. 9, 312-327 (1978; Zbl 0377.93056)]. This paper considers a new system class admitting an optimal finite dimensional recursive estimator. An explicit filter structure is constructed and two examples are discussed to show the application.
A time-varying polynomial output equation expressing an implicit dependence of the observed signal on the parameter vector admits a finite-dimensional recursive representation for the optimal on-line estimator. Both continuous and discrete observations result in differential systems which give the estimate. An exponentially weighted least-squares formulation is used. Exponential stability of the identifier and convergence to the true parameter value are proved.
A time-continuous algorithm for real time identification of two dissociation constants of a pH-control process is presented. The discrete identification is applied in a dynamic ARMA-type difference model which is quadratic in the parameter to be estimated.
Reviewer: R.K.Bose

MSC:

93B30 System identification
93C10 Nonlinear systems in control theory
93C99 Model systems in control theory
60G35 Signal detection and filtering (aspects of stochastic processes)
93B40 Computational methods in systems theory (MSC2010)
93E10 Estimation and detection in stochastic control theory
93E11 Filtering in stochastic control theory

Citations:

Zbl 0377.93056
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References:

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[2] Marcus, S. I.; Willsky, A. S., Algebraic structure and finite dimensional nonlinear estimation, SIAM J. Math. Anal., 9, 312-327 (1978) · Zbl 0377.93056
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