Research Initiation Award: Techniques for Design and Analysis of Short Memory Stochastic Adaptive Control Algorithms

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Because the environment in which a system will operate is often time varying and cannot be predicted exactly by the designer, the development of adaptive controllers has been an extremely active research area in the past ten years. A large number of algorithms have been proposed; however, with the exception of the example analysed in ıMeyn and Caines, 1987!, there have been no concrete stability results for adaptive systems with non-trivial parameter variation operating in a stochastic environment. The proposed research considers the application of Markov chain techniques for the stability and performance analysis of short memory adaptive algorithms. Some of the basic issues to be address, and techniques to be applied are: *the analysis of practical algorithms: The adaptive control algorithms which are currently used in practice are not fully understood, and a new set of tools is needed to analyse their stability and performance characteristics. Recent results of the proposer are expected to make an important step towards fulfilling this goal; *the adaptive control of time varying plants in a stochastic setting is poorly understood. A specific goal of the proposed research is to achieve a better understanding of the performance of short memory algorithms using a test function approach initiated in ıMeyn, 1989a!, and currently under investigation by the proposer; *the proposed methods use an equivalent of the state space approach currently used in the local analysis of determistic adaptive control systems; *these methods provide a means to study a combination of nonlinear and stochastic phenomena; *it will be shown that these techniques have several important advantages over current methods used to study stochastic adaptive control algorithms particularly in regards to stability.