On the stochastic Rayleigh quotient estimation theory

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Abstract
A proposed stochastic Rayleigh quotient estimation theory for the adaptive feedback parameter evaluation of a class of non-linear time-variant closed-loop control systems, with observations that are contaminated by additive statistically-known white Gaussian noise, is developed. A new technique, based upon partitioning the model structure into subsequent sub-structures, that yields computationally more pragmatical solutions is described. An optimal predictor-corrector maximum-likelihood state estimator is presented. In addition, this paper introduces o stochastic Kayleigh quotient algorithm, SRQA, for the identification of the unknown feedback parameters. An adaptive implement is added with the SRQA to ensure its pointwise convergence in the second mean sense. A non-linear programming formulation is suggested for the SRQA initialization. Finally, a numerical example is given for illustration.

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