We present a model for asynchronous distributed computation and then proceed to analyze the convergence of natural asynchronous distributed versions of a large class of deterministic and stochastic gradient-like algorithms. We show that such algorithms retain the desirable convergence properties of their centralized counterparts, provided that the time between consecutive communications between processors and communication delays are not too large.

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This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances.It is demonstrated that there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implication of the existence of such infinite-gain operators is that (a) sinusoidal reference inputs at specific frequencies and/or (b) sinusoidal output disturbances at any frequency (including d.c.), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms cannot be used with confidence in practical designs, because instability can result with high probability.