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

因为系统运行的环境通常是时间， 变化，不能被设计师准确预测， 自适应控制器的发展一直是一个非常活跃的领域， 在过去的十年里，研究领域。 大量的算法 已经提出;然而，除了例子 Meyn和Caines，1987！没有具体的 具有非平凡参数自适应系统稳定性结果 在随机环境中运行的变化。 建议的研究考虑马尔可夫链的应用 短存储器的稳定性和性能分析技术 自适应算法 需要解决的一些基本问题， 拟采用的技术有： * 实用算法分析：自适应控制 目前在实践中使用的算法并不完全 需要一套新的工具来分析它们的 稳定性和性能特点。 最近的结果 预计提案人将朝着实现目标迈出重要一步 这个目标; * 随机时变对象的自适应控制 设置知之甚少。 拟议的具体目标 研究的目的是更好地了解 使用测试函数方法的短记忆算法， Meyn，1989 a！，目前正在接受申请人的调查; * 所提出的方法使用状态空间的等价物 目前用于局部分析的方法是自适应的 控制系统; * 这些方法提供了一种研究以下组合的手段： 非线性和随机现象; * 它将表明，这些技术有几个重要的 优于目前用于研究随机自适应的方法 控制算法，特别是在稳定性方面。

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.