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

Recent papers on adaptive stochastic control have established global convergence for the general delay-colored noise case. However, for delays greater than unity they require the implementation of 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.