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robust self-tuning regulator of a class of linear systems, which can be described by the input-output Auto-Regressive Moving Average with exogenous (ARMAX) mathematical model with unknown and time-varying parameters, at bounded external disturbances is developed. A scheme of polynomial approximation has been applied to approximate the unknown and time-varying parameters of systems. The modified recursive extended least squares RELS estimation algorithm with a relative dead zone is proposed and applied to estimate the unknown and time-varying parameters intervening in the ARMAX mathematical model. The formulation of the explicit schemes of self-tuning regulation problem is resolved by using the minimum variance output or the generalized minimum variance output. The obtained control law, which is an optimal solution of minimizing a correspondent criterion, permit to reduce the effect of noise upon the output of system. An example of numerical simulation illustrates the effectiveness of the explicit schemes of self-tuning regulator and presents the performances by using the modified recursive extended least squares estimation algorithm with a relative dead zone in a step of the parametric estimation of a linear time-varying systems.

Robust Self-Tuning Regulator of Time-Varying Linear Systems with Bounded External Disturbances