Adaptive Systems for Identification, Signal Processing and Control: Solvability, Performance, Robustness and Applications

这项研究的目的是发展一个全面的理论来设计和分析用于未知线性随机系统的辨识、滤波和控制的自适应系统。这一建议的重点是研究随机自适应系统理论的几个基本方面，包括自适应可解性、收敛、性能和鲁棒性。具体问题包括递归辨识、自适应反馈和前馈控制、自适应滤波和状态估计、自适应信道均衡、自适应回声抵消、自适应有源噪声抵消和振动控制。在自适应可解性的主题下，我们研究了是否存在一个基本问题，即是否存在一种自校正算法，该算法基于在线数据，在给定滤波或控制目标和一定的先验信息的情况下，自动调整到正确的控制器或滤波器。在性能的主题下，我们考虑了各种自适应算法和配置的信号的渐近行为和参数估计的问题。在稳健性的主题下，我们提出了几种增强稳健性的方法，包括自适应算法的滤波，一种新的H00识别过程，基于辅助变量辨识方法和自适应内模控制的自适应控制。除理论研究外，该项目还将与几个应用研究项目保持密切联系，这些项目包括有源噪声抵消和振动控制的应用，智能和自适应结构的应用研究，数字高清电视中鬼影消除的研究，自动车辆控制的研究。

The goal of this research is to develop a comprehensive theory for designing and analyzing adaptive systems for identification, filtering and control of unknown linear stochastic systems. The focus of this proposal is to investigate several fundamental aspects of stochastic adaptive system theory, including adaptive solvability, convergence, performance, and robustness. The specific problems addressed include recursive identification, adaptive feedback an feedforward control, adaptive filtering and state estimation, adaptive channel equalization, adaptive echo cancelling, adaptive active noise cancelling and vibration control. Under the topic of adaptive solvability, we examine the fundamental issue of whether there exists a self- tuning algorithm which automatically tunes itself to the correct controller or filter based on on-line data, given a filtering or control objective and certain a priori information. Under the topic of performance, we consider the issue of asymptotic behaviors of signals and parameter estimates for a variety of adaptive algorithms and configurations. Under the topic of robustness, we propose to investigate several robustness enhancement methodologies, including the filtering of adaptive algorithms, a new H00 identification procedure, adaptive control based on instrumental variable identification methods and adaptive internal model control. In addition to theoretical research, this project will maintain close ties with several applied research projects which include the applications of active noise cancelling and vibration control, applied research in smart and adaptive structures, research in ghost cancellation in digital high definition TV, and research in automatic vehicle control.