Indirect stochastic adaptive control: The general delay-white noise case

Abstract

Recent papers on adaptive stochastic control have established global convergence for the general delay-colored noise case. However, for delays <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> greater than unity they require the implementation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> interlaced adaptation algorithms. Using an indirect adaptive control approach, we show that in the white noise case a single adaptation algorithm suffices to establish that, with probability one, the systems input, output and the output tracking error are sample mean-square bounded. Moreover, the conditional variance of the output tracking error is shown to converge to its global minimum value with probability one.