Dither signals, on-line spectral factorization and adaptive prewhitening in adaptive control

Existing "globally" convergent adaptive schemes can fail to converge in stochastic environments if a certain strict passivity condition related to the noise colour is not satisfied. This paper presents an algorithm which applies white noise "dither" signals to guarantee global convergence when the passivity condition fails. A more sophisiticated derivative scheme exploits an on-line spectral factorization technique to recover the asymptotic optimality lost by the noise introduction. In a third scheme, building on the previous two schemes, convergence rates are enhanced and asymptotic efficiency is achieved employing adaptive prewhitening filters. When applied to adaptive control of unknown linear stochastic plants with unknown deterministic signals or disturbances, such as piecewise constant or sinusoidal ones, the simplest algorithm of the paper suffices and appears to be the first that is guaranteed to be globally convergent. The algorithm employing adaptive pre-whitening filters appears to be the first globally convergent adaptive control algorithm that exploits adaptive prewhitening.