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

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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.