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.

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We overview recent progress in the field of robust adaptive control with special emphasis on methodologies that use multiple-model architectures. We argue that the selection of the number of models, estimators and compensators in such architectures must be based on a precise definition of the robust performance requirements. We illustrate some of the concepts and outstanding issues by presenting a new methodology that blends robust non-adaptive mixed m-synthesis designs and stochastic hypothesis-testing concepts leading to the so-called robust multiple model adaptive control (RMMAC) architecture. A numerical example is used to illustrate the RMMAC design methodology, as well as its strengths and potential shortcomings. The later motivated us to develop a variant architecture, denoted as RMMAC/XI, that can be effectively used in highly uncertain exogenous plant disturbance environments.

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