Common formalism for adaptive identification in signal processing and control

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Abstract
The transversal and recursive approaches to adaptive identification are compared. ARMA modelling in signal processing, and identification in the indirect approach to control are developed in parallel. Adaptivity succeeds because the estimate is a linear function of the variable parameters for transversal identification. Control and signal processing can be imbedded in a unified well-established formalism that guarantees convergence of the adaptive parameters. For recursive identification, the estimate is a nonlinear function of the parameters, possibly resulting in non-uniqueness of the solution, in wandering and even instability of adaptive algorithms. The requirement for recursivity originates in the structure of the signal (MA-part) in signal processing. It is caused by the output measurement noise in control.

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