Stochastic adaptive system theory: Recent advances and a reappraisal
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Progress has been made in the past year towards the solution of several long standing open problems in stochastic adaptive systems for identification, signal processing and control. We provide an account of these recent advances and a fresh reapprasial of the field. This paper divides itself naturally into two parts. Part I considers identification, adaptive prediction and control based on the ARMAX model. Recent results on the self-optimality of adaptive minimum variance prediction and model reference adaptive control for general delay systems are presented. Both direct and indirect approaches based on non-interlaced extended least squares as well as stochastic gradients algorithms are considered. We emphasize the use of a generalized certaity equivalence approach where the estimates of disturbance as well as parameters are utilized. We also show that self-optimality in the mean square sense in general implies self-tuning, by exhibiting the convergence of the parameter estimates to the null space of a certain convariance matrix. Part II considers stochastic parallel model adaptation problems, which include output error identification, adaptive IIR filtering, adaptive noise and echo cancelling, and adaptive feedforward control with or without input contamination. Recent results on the convergence of these parallel model adaptation schemes in the presence of nonstationary colored noise are presented.
