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

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