By making use of extended stochastic Lyapunov functions and martingale limit theorems, established herein are certain basic properties of adaptive d-step ahead predictors associated with the stochasticgradient (witho...
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By making use of extended stochastic Lyapunov functions and martingale limit theorems, established herein are certain basic properties of adaptive d-step ahead predictors associated with the stochasticgradient (without interlacing), and monitored recursive maximum likelihood algorithms for recursive identification of an ARMAX system. Both the direct (or implicit) and indirect (or explicit) approaches to adaptive prediction are considered within a unified framework involving stochastic regression models. Applications to adaptive control of ARMAX systems are also discussed.
For the multidimensional ARMAX model the unknown matrix coefficientsare estimated by both the least squares (LSA) and the stochastic gradient algorithms (SGA) and adaptive controls are designed either for minimizing t...
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For the multidimensional ARMAX model the unknown matrix coefficientsare estimated by both the least squares (LSA) and the stochastic gradient algorithms (SGA) and adaptive controls are designed either for minimizing the quadratic cost or for tracking a reference signal. By using the attenuating excitation and the randomly varying truncation techniques the consistency of estimates and the minimality of the loss function are achieved simultaneously.
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