Date of Award
Electrical and Computer Engineering
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The application of modern control theory to solve dynamic optimization problem requires that the equation and parameters characterizing the system dynamics be known. This work is devoted to the on-line identification of linear discrete-time systems from noise corrupted input and output data, by the method of stochastic approximation.
Criteria have been established on the gain matrix for the convergence of system identification algorithm by stochastic approximation. By minimizing the estimated error at each stage, expressions for the gain sequence namely (a) scalar gain (b) diagonal matrix gain and (c) square matrix gain are developed. A condition has been established under which these gain matrices satisfy the convergence criteria.
The basic algorithm suggested in the past was restricted to 'white' measurement error and further required that the noise variances be known. This thesis extends the algorithms to overcome these limitations.
The extensions are based on the following three techniques a) use of Instrumental Variables (Wong and Polak, 1967), b) use of a noise whitening filter (Hasting-James and Sage, 1969), c) subtraction of correlated part of residuals (Talman and Van den Boom, 1973).
Finally, the algorithms are extended to multiple input-output systems and time varying systems.
The proposed algorithms have been applied to the identification of simulated systems. The convergence,storage and computational requirement have been compared.
Ahmed, Md Shahgir, "Parameter estimation in linear discrete system : new algorithms for stochastic approximation scheme" (1978). Electronic Theses and Dissertations. 8288.